{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,23]],"date-time":"2024-06-23T04:30:28Z","timestamp":1719117028004},"reference-count":262,"publisher":"Springer Science and Business Media LLC","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Synthesis Lectures on Digital Circuits and Systems"],"published-print":{"date-parts":[[2012,6,23]]},"DOI":"10.2200\/s00420ed1v01y201205dcs037","type":"journal-article","created":{"date-parts":[[2012,6,25]],"date-time":"2012-06-25T10:58:51Z","timestamp":1340621931000},"page":"1-168","source":"Crossref","is-referenced-by-count":14,"title":["Representation of Multiple-Valued Logic Functions"],"prefix":"10.1007","volume":"7","author":[{"given":"Radomir S.","family":"Stankovi\u0107","sequence":"first","affiliation":[]},{"given":"Jaakko T.","family":"Astola","sequence":"additional","affiliation":[]},{"given":"Claudio","family":"Moraga","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"p_4","doi-asserted-by":"crossref","unstructured":"Adams, K.J., McGregor, J. \"Comparison of different features of quaternary Reed-Muller canonical forms and some new statistical results,\" Proc. 32nd Int. Symp. on Multiple-Valued Logic, Boston, Massachusetts, USA, May 2002, 83-88. DOI: 10.1109\/ISMVL.2002.1011074 Cited on page(s) 4010.1109\/ISMVL.2002.1011074","DOI":"10.1109\/ISMVL.2002.1011074"},{"key":"p_5","doi-asserted-by":"crossref","unstructured":"Adams, K.J., McGregor, J. \"New information on the effectiveness of different Reed-Muller algebras on the representation of quaternary functions,\" Proc. 33rd Int. Symp. on Multiple-Valued Logic, Tokyo, Japan, May16-19,2003, 33-39. DOI: 10.1109\/ISMVL.2003.1201381 Cited on page(s) 4010.1109\/ISMVL.2003.1201381","DOI":"10.1109\/ISMVL.2003.1201381"},{"key":"p_6","doi-asserted-by":"crossref","unstructured":"Adams, K.J., McGregor, J. \"On the optimisation of Reed-Muller expressions,\" Proc. 34th International Symposium on Multiple-Valued Logic, Toronto, Canada, May19-22,2004, 168-176. DOI: 10.1109\/ISMVL.2004.1319937 Cited on page(s) 4010.1109\/ISMVL.2004.1319937","DOI":"10.1109\/ISMVL.2004.1319937"},{"key":"p_7","first-page":"8","volume-title":"Learning, Applications","author":"Aizenberg I.N.","year":"2000"},{"key":"p_8","first-page":"8","volume-title":"IX Vsesoyuznoe sovetschanie po problemam upravleniya, Tezisy doklada","author":"Aizenberg N.N.","year":"1983"},{"key":"p_9","first-page":"8","volume-title":"Kibernetika, No. 2","author":"Aizenberg N.N.","year":"1965"},{"key":"p_10","first-page":"8","volume-title":"Kibernetika, No. 5","author":"Aizenberg N.N.","year":"1981"},{"key":"p_11","doi-asserted-by":"publisher","DOI":"10.1109\/TC.1968.227407"},{"key":"p_12","unstructured":"Antonenko, V., Guvakov, I., Shmerko, V., Kaczmarek, A., Yanushkevich, S. \"Linear arithmetical forms of k-valued functions,\" Proc. European Conf. on Circuit Theory and Design, Turkey, 1995, 323-328. Cited on page(s)48"},{"key":"p_13","unstructured":"Astola, J.T., Stankovi\u0107, R.S., Fundamentals of Switching Theory and Logic Design, Springer, 2006. Cited on page(s)11, 16"},{"key":"p_14","doi-asserted-by":"crossref","unstructured":"Astola, J., Stankovi\u0107, R.S. \"Signal processing algorithms and multiple-valued logic design methods,\" Proc. 36th Int. Symp. on Multiple-Valued Logic, May17-20,2006, Singapore, 16\/1 - 16\/8. DOI: 10.1109\/ISMVL.2006.38 Cited on page(s)11 10.1109\/ISMVL.2006.38","DOI":"10.1109\/ISMVL.2006.38"},{"key":"p_15","unstructured":"Astola, J.T., Stankovi\u0107, R.S. \"Application of Covering Codes in Determination of Sparse Representations of Switching Functions,\" Proc. 39th Int. Symp. on Multiple-Valued Logic, Naha, Okinawa, Japan, May 21-23, 1009, 304-311. Cited on page(s)54"},{"issue":"1","key":"p_16","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1109\/TC.1976.5009207","volume":"25","author":"Benjauthrit B.","year":"1976","journal-title":"IEEE Trans. Computers"},{"key":"p_17","doi-asserted-by":"publisher","DOI":"10.1109\/TEC.1958.5222096"},{"key":"p_18","unstructured":"Bernstein, B.A. \"Modular representations of finite algebras,\" Proc. 7th Int. Congress Mathematicians, Univ. Toronto Press, 1928, Vol.1, 1924,207-216. Cited on page(s)11"},{"key":"p_19","first-page":"6","volume":"131","author":"Besslich Ph.W.","year":"1983","journal-title":"IEE Proc."},{"key":"p_20","unstructured":"Boole, G., The Matehamtical Analysis of Logic - Being an Essay Towards a Calculus of Deductive Reasoning, Publisher MacMilland,Barclay, & MacMillan, Cambridge, George Bell, London,1847. Cited on page(s)1"},{"key":"p_21","doi-asserted-by":"crossref","unstructured":"Boole, G., An Investigation of the Laws of Thought on which are Founded the Mathematical Theories of Logic and Probabilities, Publisher Walton and Maberly, London, MacMillan and Co., Cambridge, 1854. Cited on page(s)1","DOI":"10.5962\/bhl.title.29413"},{"issue":"8","key":"p_22","first-page":"667","volume":"35","author":"Bryant R.E.","year":"1986","journal-title":"IEEE Trans. Computers"},{"key":"p_23","unstructured":"Bryant, R.E., Chen, Y.A. \"Verification of arithmetic functions with binary moment decision diagrams,\" unpublished paper,May31,1994, CMU-CS-94-160.Citedon page(s)100, 106, 107, 108"},{"key":"p_24","first-page":"8","volume-title":"Hassoun, S., Sasao,T., (eds.), Logic Synthesis and Verification","author":"Brayton R.K.","year":"2002"},{"key":"p_25","doi-asserted-by":"crossref","unstructured":"Butler, J.T., Sasao, T. \"On the properties of multiple-valued functions that are symmetric in both variable values and labels,\" Proc. 28th Int. Symp. on Multiple-Valued Logic, Fukuoka, Japan, May27-29,1998, 83-88. DOI: 10.1109\/ISMVL.1998.679299 Cited on page(s) 1210.1109\/ISMVL.1998.679299","DOI":"10.1109\/ISMVL.1998.679299"},{"key":"p_26","doi-asserted-by":"crossref","unstructured":"Butler, J.T., Schueller, K.A. \"Worst case number of terms in symmetric multiple-valued functions,\" Proc. 21st Inx. Symp. on Multiple-Valued Logic, Victoria, BC, Canada, May26-29,1991, 94-101. DOI: 10.1109\/ISMVL.1991.130712 Cited on page(s) 1210.1109\/ISMVL.1991.130712","DOI":"10.1109\/ISMVL.1991.130712"},{"key":"p_27","doi-asserted-by":"crossref","unstructured":"Chen, X., Moraga, C. \"An algebra for current-mode CMOS multivalued circuits,\" Proc. 23rd Int. Symp. on Multi-Valued Logic, 1993, 239-244. DOI: 10.1109\/ISMVL.1993.289553 Cited on page(s) 11 10.1109\/ISMVL.1993.289553","DOI":"10.1109\/ISMVL.1993.289553"},{"key":"p_28","doi-asserted-by":"publisher","DOI":"10.1007\/BF02943514"},{"key":"p_29","unstructured":"Lee, C.U., Han, L. S.I., Kim, J.O., Kim, H.S.\"The generation sequential method to generalized Reed-Muller coefficients over GF(3),\" Proc. of the IEEE Region 10 Conference, (TENCON 99), Vol.1, 1999, 387-390. Cited on page(s) 49"},{"key":"p_30","doi-asserted-by":"publisher","DOI":"10.1155\/1999"},{"key":"p_31","first-page":"9","volume-title":"S. Aguzzoli et al.(Eds.), Algebraic and Proof-theoretic Aspects, LNAI 4460","author":"Cignoli R.","year":"2007"},{"key":"p_32","unstructured":"Clarke, E.M., McMillan, Zhao, X. Fujita, M. \"Spectral transforms for extremely large Boolean functions,\" in: Kebschull, U., Schubert, E., Rosentiel, W., Eds. Proc. IFIP WG 10.5 Workshop on Applications of the Reed-Muller Expansion in Circuit Design, 16-17.9.1993, Hamburg, Germany, 86-90. Cited on page(s)16"},{"key":"p_34","doi-asserted-by":"publisher","DOI":"10.2307\/2300689"},{"key":"p_35","doi-asserted-by":"publisher","DOI":"10.1109\/12.165392"},{"key":"p_36","first-page":"336","author":"De Morgan A.","year":"1874","journal-title":"London"},{"key":"p_37","doi-asserted-by":"publisher","DOI":"10.1109\/54.587742"},{"key":"p_38","doi-asserted-by":"crossref","unstructured":"Drechsler, R., Jankovi\u0107, D., Stankovi\u0107, R.S. \"Generic implementation of DD packages in MVL,\" Proc. 25th EUROMICRO Conference, Vol.1, 1999, 352-359. DOI: 10.1109\/EURMIC.1999.794491 Cited on page(s) 106 10.1109\/EURMIC.1999.794491","DOI":"10.1109\/EURMIC.1999.794491"},{"issue":"1","key":"p_39","first-page":"106","volume":"11","author":"Drechsler R.","year":"2005","journal-title":"Multiple-Valued Logic and Soft Computing"},{"key":"p_40","doi-asserted-by":"crossref","unstructured":"Dubrova, E. \"Evaluation of m-valued fixed polarity generalizations of Reed-Muller canonical form,\" Proc. 29th Int. Symp. on Multiple-Valued Logic, May20-22,1999, 92-98. Cited on page(s) 27","DOI":"10.1109\/ISMVL.1999.779701"},{"key":"p_41","doi-asserted-by":"crossref","unstructured":"Dubrova, E.V., Muzio, J.C.\"Testability of generalized multiple-valued Reed-Muller circuits,\" Proc. 26th Int. Symp. on Multiple-Valued Logic, 1996, 56-61. DOI: 10.1109\/ISMVL.1996.508336 Cited on page(s) 49 10.1109\/ISMVL.1996.508336","DOI":"10.1109\/ISMVL.1996.508336"},{"key":"p_42","first-page":"65","volume":"1","author":"Dubrova E.V.","year":"1996","journal-title":"Multi-Valued Logic Jr."},{"key":"p_43","doi-asserted-by":"publisher","DOI":"10.1109\/TEC.1958.5222097"},{"key":"p_44","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1960-0112855-8"},{"key":"p_45","unstructured":"Epstein, G. \"General synthesis of electronic circuits for symmetric functions,\" Computer Science Conference Abstracts, Columbus Ohio, 35,Feb. 1973. Cited on page(s)11"},{"key":"p_46","doi-asserted-by":"publisher","DOI":"10.1109\/T-C.1973.223731"},{"key":"p_47","unstructured":"Epstein, G., Multiple-Valued Logic Design: An Introduction, IOP Publishing Ltd, 1993. Cited on page(s)11"},{"key":"p_48","unstructured":"Epstein, G., D.M. Miller and J.C. Muzio, \"Some preliminary views on the general synthesis of electronic circuits for symmetric and partially symmetric functions,\" Proc. 7th Int. Symp. on Multiple-Valued Logic, May 1977, 29-34. Cited on page(s) 12"},{"key":"p_49","unstructured":"Epstein, G., D.M. Miller and J.C. Muzio,\"Selecting don't-care sets for many-valued functions: a pictorial approach using matrices,\" Proc. 10th Int. Symp. on Multiple-Valued Logic, June 1980, 219-225. Cited on page(s) 12"},{"key":"p_50","unstructured":"Farm, P. Dubrova, E., Stankovi\u0107, R.S., Astola, J. \"Conjunctive decomposition for multiplevalued input binary-valued output functions,\" Proc. TISCP Workshop on Spectral Methods and Multirate Signal Processing, SMMSP'02, Toulouse, France, September7-8,2002, 227-234. Cited on page(s)49"},{"key":"p_51","doi-asserted-by":"publisher","DOI":"10.1109\/12.795128"},{"key":"p_52","unstructured":"Falkowski, B.J. \"Haar transform, calculation, generalization and applications in logic design,\" Proc. 2nd Int. Workshop on Transforms and Filter Banks, Brandenburg, Germany, March 1999, Edited by R. Creutzburg and J. Astola, TICSP Series # 4, March 2000, 101-120. Cited on page(s) 49"},{"key":"p_53","doi-asserted-by":"crossref","unstructured":"Falkowski, B.J., Chang, C.H. \"Efficient algorithm for the calculation of arithmetic spectrum from OBDD and synthesis of OBDD from arithmetic spectrum for incompletely specified Boolean functions,\" Proc. IEEE Int. Symp. on Circuits and Systems ISCAS94, USA,1994. DOI: 10.1109\/ISCAS.1994.408789 Cited on page(s) 49 10.1109\/ISCAS.1994.408789","DOI":"10.1109\/ISCAS.1994.408789"},{"key":"p_54","doi-asserted-by":"publisher","DOI":"10.1109\/12.644301"},{"key":"p_55","doi-asserted-by":"publisher","DOI":"10.1049\/ip-cds:20000588"},{"key":"p_56","doi-asserted-by":"publisher","DOI":"10.1049\/ip-cdt:20045162"},{"key":"p_57","unstructured":"Falkowski, B.J., Holowinski, G., Malecki, K. \"Effective minimization of logic functions in Reed-Muller domain,\" Proc. Int. Conf. on Applications of Computer Systems, Poland, 1997, 248-255. Cited on page(s)49"},{"key":"p_58","doi-asserted-by":"publisher","DOI":"10.1016\/j.compeleceng.2005.01.002"},{"key":"p_59","doi-asserted-by":"crossref","unstructured":"Falkowski, B.J., Lozano, C.C., Rahardja, S. \"Spectra generation for fixed-polarity Reed-Muller transform over GF (5),\"Proc. 34th Int. Symp. on Multiple-Valued Logic, Toronto, Canada, May19-22,2004, 177-183. DOI: 10.1109\/ISMVL.2004.1319938 Cited on page(s) 4910.1109\/ISMVL.2004.1319938","DOI":"10.1109\/ISMVL.2004.1319938"},{"key":"p_60","doi-asserted-by":"crossref","unstructured":"Falkowski, B.J., Rahardja, S. \"Fast construction of polarity coefficient matrices for fixed polarity quaternary Reed-Muller expansions,\" Proc. 5th Int. Workshop on Spectral Techniques, 15.17.3.1994, Beijing, China, 220-225. DOI: 10.1016\/j.compeleceng.2005.01.002 Cited on page(s) 4910.1016\/j.compeleceng.2005.01.002","DOI":"10.1016\/j.compeleceng.2005.01.002"},{"key":"p_61","doi-asserted-by":"crossref","unstructured":"Falkowski, B.J., Rahardja, S. \"Efficient algorithm for the generation of fixed polarity quaternary Reed-Muller expansions,\" Proc. 25th International Symposium on Multiple-Valued Logic, 1995, 158-163. DOI: 10.1109\/ISMVL.1995.513525 Cited on page(s) 18, 49, 54 10.1109\/ISMVL.1995.513525","DOI":"10.1109\/ISMVL.1995.513525"},{"key":"p_62","doi-asserted-by":"publisher","DOI":"10.1049\/ip-cdt:19952126"},{"key":"p_63","doi-asserted-by":"crossref","unstructured":"Falkowski, B.J., Rahardja, S. \"Novel quantized transform for ternary systems,\" Proc. 25th Int. Symp. on Multiple-Valued Logic, 23.25.5.1995, Bloomington, Indiana, USA, 117-122. DOI: 10.1109\/ISMVL.1995.513519 Cited on page(s) 4910.1109\/ISMVL.1995.513519","DOI":"10.1109\/ISMVL.1995.513519"},{"key":"p_64","doi-asserted-by":"publisher","DOI":"10.1049\/ip-cdt:19952126"},{"key":"p_65","doi-asserted-by":"publisher","DOI":"10.1049\/ip-cds:19970874"},{"key":"p_66","unstructured":"Falkowski B., Shmerko V., Yanushkevich, S. \"Arithmetic logic - its status and achievement,\" Proc. Int. Conf on Applications of Computer Systems, Szczecin, Poland, 1997, 208-223. Cited on page(s)49"},{"key":"p_67","doi-asserted-by":"publisher","DOI":"10.1049\/ip-vis:20045248"},{"key":"p_68","first-page":"8","volume-title":"Izv. Akad. Nauk Aizerb. SSR, Ser. Fiz.-Techn, i Mat. Nauk, No. 6","author":"Garaev M.U.","year":"1968"},{"key":"p_70","doi-asserted-by":"publisher","DOI":"10.1049\/el:19770086"},{"key":"p_71","first-page":"16","volume":"1","author":"Gibbs J.E.","year":"1990","journal-title":"Beograd"},{"key":"p_72","doi-asserted-by":"publisher","DOI":"10.1049\/ip-e.1990.0047"},{"key":"p_73","doi-asserted-by":"publisher","DOI":"10.1049\/piee.1974.0105"},{"key":"p_74","unstructured":"Gongli, Z., Moraga, C. \"Polynomial Fourier transforms,\" Proc. 18th Int. Symp. on Multiple-Valued Logic, May24-26,1988, 412-419. Cited on page(s) 110"},{"key":"p_75","doi-asserted-by":"publisher","DOI":"10.2307\/2012970"},{"key":"p_76","doi-asserted-by":"publisher","DOI":"10.1007\/BF01456326"},{"key":"p_77","doi-asserted-by":"crossref","unstructured":"Hansen, J.P., Sekine, M. \"Synthesis by spectral translation using Boolean decision diagrams,\" Proc. Design. Automation Conf., June 1996, 248-253. DOI: 10.1145\/240518.240564 Cited on page(s) 93 10.1145\/240518.240564","DOI":"10.1145\/240518.240564"},{"key":"p_78","doi-asserted-by":"crossref","unstructured":"Hansen, J.P., Sekine, M. \"Decision diagrams based techniques for the Haar wavelet transform,\" Proc. IEEE Int. Conf. on Information, Communications and Signal Processing (1st ICICS), Singapore, Vol.1,September 1997, 59-63. DOI: 10.1109\/ICICS.1997.647057 Cited on page(s) 9310.1109\/ICICS.1997.647057","DOI":"10.1109\/ICICS.1997.647057"},{"key":"p_79","doi-asserted-by":"crossref","unstructured":"Harking, B., Moraga, C. \"Efficient derivation of Reed-Muller expansions in multiple-valued logic systems,\" Proc. 22nd Int. Symp. on Multiple-Valued Logic, Sendai, Japan, May27-29,1992, 436-441. DOI: 10.1109\/ISMVL.1992.186828 Cited on page(s) 8, 18, 25, 3510.1109\/ISMVL.1992.186828","DOI":"10.1109\/ISMVL.1992.186828"},{"key":"p_80","doi-asserted-by":"publisher","DOI":"10.1109\/12.76409"},{"key":"p_81","unstructured":"Holowinski, G. \"Parallel version of generalized Zakrevskij's algorithm for minimization of weakly specified multi-valued functions,\" Proc. Int. Conf. on Pattern Recognition and Information Processing, Minsk, Belarus, Vol.1, 1997, 332-339. Cited on page(s) 48"},{"key":"p_82","unstructured":"Holowinski, G., Yanushkevich, S. \"Fast heuristic minimization of MVL functions in generalized Reed-Muller domain,\" Proc. Int. Conf. on Applications of Computer Systems, Szczecin, Poland, 1996, 57-64. Cited on page(s)48"},{"key":"p_83","doi-asserted-by":"crossref","unstructured":"Hong, Q., Fei, B., Wu, H., Perkowski, M.A., Zhuang, N. \"Fast synthesis for ternary Reed-Muller expansion,\" Proc. of The Twenty-Third International Symposium on Multiple-Valued Logic, 1993, 14-16. DOI: 10.1109\/ISMVL.1993.289588 Cited on page(s) 49 10.1109\/ISMVL.1993.289588","DOI":"10.1109\/ISMVL.1993.289588"},{"key":"p_84","first-page":"11","author":"Hurst S.L.","year":"1978","journal-title":"London and Basel"},{"key":"p_85","doi-asserted-by":"publisher","DOI":"10.1093\/comjnl"},{"key":"p_86","unstructured":"Hurst, S.L. \"The Haar transform in digital network synthesis,\" Proc. 11th Int. Symp. on Multiple-valued Logic, Oklahoma City, Oklahoma, USA, May 1981, 10-18. Cited on page(s)93"},{"key":"p_87","doi-asserted-by":"crossref","unstructured":"Hurst, S.L., Miller, D.M., Muzio, J.C., Spectral Techniques in Digital Logic, Academic Press, 1985. Cited on page(s)8, 17","DOI":"10.1016\/0165-1684(85)90052-0"},{"key":"p_88","doi-asserted-by":"publisher","DOI":"10.1109\/TCAD.2008.917586"},{"key":"p_89","first-page":"27","volume-title":"Soldek, J., Pejas, J., (eds.), Advanced Computer Systems","author":"Jankovi\u0107 D.","year":"2002"},{"key":"p_90","doi-asserted-by":"crossref","unstructured":"Jankovi\u0107, D., Stankovi\u0107, R.S., Drechsler, R.\"Efficient calculation of fixed-polarity polynomial expressions for multiple-valued logic functions,\" Proc. 32nd Int. Symp. on Multiple-Valued Logic, Boston, Massachusetts, USA, May15-18,2002, 76-82. DOI: 10.1109\/ISMVL.2002.1011073 Cited on page(s) 2710.1109\/ISMVL.2002.1011073","DOI":"10.1109\/ISMVL.2002.1011073"},{"key":"p_91","doi-asserted-by":"crossref","unstructured":"Jankovi\u0107, D., Stankovi\u0107, R.S., Drechsler, R. \"Decision diagrams optimization using copy properties,\" EUROMICRO 2002, Dortmund, Germany, September 2002. DOI: 10.1109\/DSD.2002.1115374 Cited on page(s) 8110.1109\/DSD.2002.1115374","DOI":"10.1109\/DSD.2002.1115374"},{"key":"p_92","doi-asserted-by":"crossref","unstructured":"Jankovi\u0107, D., Stankovi\u0107, R.S., Drechsler, R. \"Reduction of sizes of multi-valued decision diagrams by copy properties,\" Proc. 34th Int. Symp. on Multiple-Valued Logic,Toronto, Canada, May19-22,2004, 229-234. DOI: 10.1109\/ISMVL.2004.1319945 Cited on page(s) 8110.1109\/ISMVL.2004.1319945","DOI":"10.1109\/ISMVL.2004.1319945"},{"key":"p_93","unstructured":"Jankovi\u0107, D., Stankovi\u0107, R.S., Moraga, C. \"Optimization of Kronecker expressions using the extended dual polarity property,\" ICIEST 2002, October4-6,2002, 749-752. Cited on page(s) 27"},{"key":"p_94","doi-asserted-by":"crossref","unstructured":"Jankovi\u0107, D., Stankovi\u0107, R.S., Moraga, C. \"Optimization of GF (4) expressions using the extended dual polarity property,\" Proc. 33rd Int. Symp. on Multiple-valued Logic, May16-19,2003, 50-55. DOI: 10.1109\/ISMVL.2003.1201384 Cited on page(s) 27 10.1109\/ISMVL.2003.1201384","DOI":"10.1109\/ISMVL.2003.1201384"},{"key":"p_95","doi-asserted-by":"publisher","DOI":"10.2298\/SJEE0301071J"},{"key":"p_96","doi-asserted-by":"crossref","unstructured":"Jankovi\u0107, D., Stankovi\u0107, R.S., Moraga, C. \"Exploiting homogeneous dual polarity routes in implementation of algorithms for optimization of Galois field expressions for ternary functions,\" Proc. 37th Int. Symp. on Multiple-Valued Logic, May 2007, 28-28 (CD-publication). DOI: 10.1109\/ISMVL.2007.22 Cited on page(s) 27 10.1109\/ISMVL.2007.22","DOI":"10.1109\/ISMVL.2007.22"},{"key":"p_97","doi-asserted-by":"publisher","DOI":"10.1109\/TC.2009.113"},{"key":"p_98","unstructured":"Jaroszewicz, S., Shmerko, V., Yanushkevich, S. \"Exact irredundant searching for a minimal Reed-Muller expansion for an incompletely specified MVL function,\" Proc. Int. Conf. on Applications of Computer Systems, Szczecin, Poland, 1996, 65-74. Cited on page(s)48"},{"key":"p_99","unstructured":"Kalganova, T., Kochergov, E., Zaitseva, E., Yanushkevich, S. \"A genetic approach to optimise polynomial forms of incompletely specified MVL functions,\" Proc. Workshop on Evolutionary Computing, Brighton, UK, 1996, 89-102. Cited on page(s)48"},{"key":"p_100","unstructured":"Karpovsky, M.G., Finite Orthogonal Series in the Design of Digital Devices, John Wiley, 1976. Cited on page(s)8, 16, 18, 109, 110, 111"},{"key":"p_101","doi-asserted-by":"publisher","DOI":"10.1002\/9780470289228"},{"key":"p_102","doi-asserted-by":"publisher","DOI":"10.1109\/ISMVL.2001.924553"},{"key":"p_103","doi-asserted-by":"crossref","unstructured":"Kebschull, U., Schubert, E., Rosenstiel, W. \"Multilevel logic synthesis based on functional decision diagrams,\" Proc. 3rd European Conf. on Design Automation, 1992, 43-47. DOI: 10.1109\/EDAC.1992.205890 Cited on page(s) 78 10.1109\/EDAC.1992.205890","DOI":"10.1109\/EDAC.1992.205890"},{"key":"p_104","unstructured":"Kodandapani, K.L., Setur, R.V. \"Multi-valued algebraic generalization of Reed-Muller canonical forms,\" Proc. Int. Symp. on Multiple-Valued Logic, 1974, 505-544. Cited on page(s) 8, 49"},{"key":"p_105","doi-asserted-by":"publisher","DOI":"10.1109\/43.298033"},{"key":"p_106","first-page":"278","volume":"75","author":"Lee C.Y.","year":"1956","journal-title":"Trans. AIEE"},{"key":"p_107","unstructured":"Lee, S.C., Modern Switching Theory and Digital Design, Prentice-Hall, 1978. Cited on page(s)8"},{"key":"p_108","doi-asserted-by":"publisher","DOI":"10.1109\/TC.1972.5008957"},{"key":"p_109","doi-asserted-by":"crossref","unstructured":"Luis, M., Moraga, C. \"On functions with flat Chrestenson spectra,\" Proc. 19th Int. Symp. on Multiple-Valued Logic, May29-31,1989, 406-413. DOI: 10.1109\/ISMVL.1989.37814 Cited on page(s) 74 10.1109\/ISMVL.1989.37814","DOI":"10.1109\/ISMVL.1989.37814"},{"key":"p_110","first-page":"170","volume":"5","author":"Lukasiewicz J.","year":"1920","journal-title":"Ruch filozoficzny"},{"key":"p_111","first-page":"1939","volume":"1920","author":"Lukasiewicz J.","year":"1967","journal-title":"Polish Logic"},{"key":"p_112","first-page":"54","author":"MacWilliams S.","year":"1977","journal-title":"Amsterdam"},{"key":"p_113","unstructured":"Malyugin, V.D., Paralleled Calculation by Means of Arithmetic Polynomials, Physical and Mathematical Publishing Company, Russian Academyof Science, Moscow,1997. Cited on page(s)8, 41, 42"},{"key":"p_114","first-page":"17","volume":"4","author":"Malyugin V.D.","year":"1993","journal-title":"Automatika and Telemekhanika"},{"key":"p_115","doi-asserted-by":"publisher","DOI":"10.2307\/2267650"},{"key":"p_116","doi-asserted-by":"publisher","DOI":"10.1109\/T-C.1969.222637"},{"key":"p_117","unstructured":"Miller, D.M. \"A canonical representation for many-valued symmetric functions,\" Proc. 6th Manitoba Conf. Numerical Mathematics and Computing, Oct. 1976, 303-313. Cited on page(s) 12"},{"key":"p_118","doi-asserted-by":"crossref","unstructured":"Miller, D.M. \"Spectral transformation of multiple-valued decision diagrams,\" Proc. 24th Int. Symp. on Multiple-Valued Logic, Boston, Massachusetts, USA, May25-27,1994, 89-96. DOI: 10.1109\/ISMVL.1994.302209 Cited on page(s) 10010.1109\/ISMVL.1994.302209","DOI":"10.1109\/ISMVL.1994.302209"},{"key":"p_119","doi-asserted-by":"crossref","unstructured":"Miller, D.M., Drechsler, R. \"On the construction of multiple-valued decision diagrams,\" Proc. 32nd Int. Symp. on Multiple-Valued Logic, Boston, Massachusetts, USA, May15-18,2002, 245-253. DOI: 10.1109\/ISMVL.2002.1011095 Cited on page(s) 10610.1109\/ISMVL.2002.1011095","DOI":"10.1109\/ISMVL.2002.1011095"},{"key":"p_120","doi-asserted-by":"crossref","unstructured":"Miller, D.M., Muranaka, N. \"Multiple-valued decision diagrams with symmetric variable nodes,\" Proc. 26th Int. Symp. on Multiple-Valued Logic, Santiago de Compostela, Spain, May29-31,1996, 242-247. DOI: 10.1109\/ISMVL.1996.508375 Cited on page(s) 81, 100, 10110.1109\/ISMVL.1996.508375","DOI":"10.1109\/ISMVL.1996.508375"},{"key":"p_121","doi-asserted-by":"publisher","DOI":"10.2200\/S00065ED1V01Y200709DCS012"},{"key":"p_122","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-1385-4"},{"key":"p_123","doi-asserted-by":"crossref","unstructured":"Minasyan, S., Astola, J., Egiazarian, K., Stankovi\u0107, R.S. \"Hybrid Reed-Muller-Haar transform and its applications in reduction the spectral representations of logic functions,\" Proc. 38th Int. Symp. on Multiple-Valued Logic, Dallas, Texas, USA, May22-24,2008, 232-237. DOI: 10.1109\/ISMVL.2008.8 Cited on page(s) 4910.1109\/ISMVL.2008.8","DOI":"10.1109\/ISMVL.2008.8"},{"key":"p_124","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-04772-5_67"},{"key":"p_125","doi-asserted-by":"publisher","DOI":"10.1109\/ISMVL.2008.8"},{"key":"p_126","first-page":"1","volume":"22","author":"Moisil G.","year":"1935","journal-title":"Ann. Sci. Univ. Jassy"},{"key":"p_127","first-page":"9","volume-title":"Annalles Scientifiques de l' Udversit\u00e9 de Jassy, premiere section, 26","author":"Moisil G","year":"1940"},{"key":"p_128","first-page":"86","volume":"27","author":"Moisil G.C.","year":"1941","journal-title":"Ann. Sci. Univ. Jassy"},{"key":"p_129","first-page":"9","volume-title":"Acad\u00e9mie de la R'epublique Socialiste de Roumanie","author":"Moisil G.","year":"1972"},{"key":"p_130","unstructured":"Moraga, C. \"Ternary spectral logic,\" Proc. Int. Symp. on Multiple-Valued Logic, 1977, 7-12. Cited on page(s) 74"},{"key":"p_131","unstructured":"Moraga, C. \"Complex spectral logic,\" Proc. 8th Int. Symp. on Multiple-valued Logic, Rosemond, Illinois, U.S.A., 1978, 149-156. Cited on page(s)18, 74"},{"key":"p_132","doi-asserted-by":"publisher","DOI":"10.1049\/el:19780164"},{"key":"p_133","doi-asserted-by":"publisher","DOI":"10.1049\/el:19790573"},{"key":"p_134","doi-asserted-by":"publisher","DOI":"10.1049\/el:19790573"},{"key":"p_135","first-page":"74","volume-title":"Cybernetics and Systems Research","volume":"2","author":"Moraga C.","year":"1984"},{"key":"p_136","doi-asserted-by":"publisher","DOI":"10.1016\/0378-4754(85)90062-X"},{"key":"p_137","doi-asserted-by":"publisher","DOI":"10.1109\/TC.1986.1676739"},{"key":"p_138","doi-asserted-by":"crossref","unstructured":"Moraga, C. \"A decade of spectral techniques,\" Proc. 21st Int. Symp. on Multiple-Valued Logic, May26-29,1991, 182-288. DOI: 10.1109\/ISMVL.1991.130726 Cited on page(s) 74 10.1109\/ISMVL.1991.130726","DOI":"10.1109\/ISMVL.1991.130726"},{"key":"p_139","doi-asserted-by":"crossref","unstructured":"Moraga, C. \"Improving the characterization of p-valued threshold functions,\" Proc. 32nd Int. Symp. on Multiple-Valued Logic, May15-18,2002, 28-34. DOI: 10.1109\/ISMVL.2002.1011066 Cited on page(s) 74 10.1109\/ISMVL.2002.1011066","DOI":"10.1109\/ISMVL.2002.1011066"},{"key":"p_140","first-page":"110","volume-title":"No. 567 of Forschungsberichte des Fachbereichs Informatik der Universit\u00e4t Dortmund, Universit\u00e4t (Dortmund), Germany","author":"Moraga C.","year":"1995"},{"key":"p_141","first-page":"245","volume":"2","author":"Moraga C.","year":"1997","journal-title":"Multi Valued Logic"},{"key":"p_142","doi-asserted-by":"crossref","unstructured":"Moraga, C., Stankovi\u0107, R.S., Astola, J.T.\"Properties of matrix-valued spectral coefficients obtained with the Fourier Transform on a non-Abelian group,\" Proc. 36th Int. Symp. on Multiple-Valued Logic, May17-20,2006, Singapore, 35\/1-35\/6. DOI: 10.1109\/ISMVL.2006.34 Cited on page(s)78 10.1109\/ISMVL.2006.34","DOI":"10.1109\/ISMVL.2006.34"},{"key":"p_143","doi-asserted-by":"crossref","unstructured":"Moraga, C., Stankovi\u0107, M., Stojkovi\u0107, S. \"Spectral analysis of special properties of ternary functions,\" Proc. 37th Int. Symp. on Multiple-Valued Logic, May 2007, 4-4 (CD-publication). DOI: 10.1109\/ISMVL.2007.52 Cited on page(s) 12 10.1109\/ISMVL.2007.52","DOI":"10.1109\/ISMVL.2007.52"},{"key":"p_144","first-page":"6","volume":"3","author":"Muller D.E.","year":"1954","journal-title":"IRE Trans. Electron. Comp."},{"key":"p_145","doi-asserted-by":"publisher","DOI":"10.1109\/PGEC.1966.264561"},{"key":"p_146","first-page":"17","volume":"36","author":"Muzio J.C.","year":"1989","journal-title":"C. Moraga, Ed., Theory and Applications of Spectral Techniques, Dortmund"},{"key":"p_147","first-page":"8","author":"Muzio J.C.","year":"1986","journal-title":"Bristol"},{"key":"p_148","doi-asserted-by":"crossref","unstructured":"Nagayama, S., Sasao, T., Butler, J.T. \"Numeric function generators using piecewise arithmetic expressions,\" Proc. 41th Int. Symp. on Multiple-Valued Logic,Tuusula, Finlad, May23-25,2011, 16-21. DOI: 10.1109\/ISMVL.2011.32 Cited on page(s) 5410.1109\/ISMVL.2011.32","DOI":"10.1109\/ISMVL.2011.32"},{"key":"p_149","doi-asserted-by":"publisher","DOI":"10.1587\/transinf.E93.D.2059"},{"key":"p_150","doi-asserted-by":"crossref","unstructured":"Oenning, R., Moraga, C.\"Properties of the Zhang-Watari transform,\" Proc. 25th Int. Symp. on Multiple-Valued Logic, May23-25,1995, 44-49. DOI: 10.1109\/ISMVL.1995.513508 Cited on page(s) 110 10.1109\/ISMVL.1995.513508","DOI":"10.1109\/ISMVL.1995.513508"},{"key":"p_151","first-page":"9","volume":"3","author":"Peirce C.S.","year":"1933","journal-title":"USA"},{"key":"p_152","doi-asserted-by":"publisher","DOI":"10.2307\/2370324"},{"key":"p_154","unstructured":"Pradhan, D.K. \"A multi-valued algebra based on finite fields,\" Proc. 1974 Int. Symp. on Multiple-Valued Logic, Morgantown, WV, USA, May 1974, 95-112. Cited on page(s)8, 11"},{"key":"p_155","doi-asserted-by":"publisher","DOI":"10.1109\/TC.1978.1675077"},{"key":"p_156","doi-asserted-by":"crossref","unstructured":"Rahardja, S., Falkowski, B.J. \"Family of fast mixed arithmetic Logic transforms for multiplevalued input binary functions,\" Proc. 26th Int. Symp. on Multiple-Valued Logic, 1996, 24-29. DOI: 10.1109\/ISMVL.1996.508331 Cited on page(s) 54 10.1109\/ISMVL.1996.508331","DOI":"10.1109\/ISMVL.1996.508331"},{"key":"p_157","doi-asserted-by":"publisher","DOI":"10.1109\/12.795227"},{"key":"p_158","doi-asserted-by":"crossref","unstructured":"Rahardja, S., Falkowski, B.J. \"A new algorithm to compute quaternary Reed-Muller expansions,\" Proc. 30th IEEE International Symposium on Multiple-Valued Logic, 2000, 153-158. DOI: 10.1109\/ISMVL.2000.848614 Cited on page(s) 17, 49 10.1109\/ISMVL.2000.848614","DOI":"10.1109\/ISMVL.2000.848614"},{"key":"p_159","doi-asserted-by":"publisher","DOI":"10.1109\/12.795227"},{"key":"p_160","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1954.1057465"},{"key":"p_161","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1109\/MC.1974.6323303","volume":"7","author":"Rine D.C.","year":"1975","journal-title":"IEEE Computer"},{"key":"p_162","first-page":"11","volume-title":"Rine","author":"Rine D.C.","year":"1977"},{"key":"p_163","unstructured":"Rudin, W., Fourier Analysis on Groups, Interscience Publisher, New York, 1960. Cited on page(s)71"},{"key":"p_164","unstructured":"Salomaa, A. \"On many-valued systems of logic,\" Ajatus, No. 22, 1959, 115-159. Cited on page(s) 9"},{"key":"p_165","doi-asserted-by":"crossref","unstructured":"Sarabi, A., Perkowski, M.A. \"Fast exact and quasi-minimal minimization of highly testable fixed polarity AND\/XOR canonical networks,\" Proc. Design Automation Conference, June 1992, 30-35. DOI: 10.1109\/DAC.1992.227867 Cited on page(s) 12 10.1109\/DAC.1992.227867","DOI":"10.1109\/DAC.1992.227867"},{"key":"p_166","doi-asserted-by":"publisher","DOI":"10.1109\/TC.1984.1676349"},{"key":"p_167","doi-asserted-by":"crossref","unstructured":"Sasao, T. \"Optimization of multiple-valued AND-EXOR expressions using multiple-place decision diagrams,\" Proc. 22nd IEEE Int. Symp. on Multiple-Valued Logic, 1992, 451-458. DOI: 10.1109\/ISMVL.1992.186830 Cited on page(s) 49 10.1109\/ISMVL.1992.186830","DOI":"10.1109\/ISMVL.1992.186830"},{"key":"p_168","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-3154-8"},{"key":"p_169","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-5139-3"},{"key":"p_170","unstructured":"Sasao, T. \"Arithmetic ternary decision diagrams and their applications,\" Fourth International Workshop on Applications of the Reed-Muller Expansion in Circuit Design, (Reed-Muller 99), Victoria, Canada, August20-21,1999. Cited on page(s)42"},{"key":"p_171","doi-asserted-by":"crossref","unstructured":"Sasao, T., Butler, J.T. \"A design method for look-up table type FPGA by pseudo-Kronecker expansions,\" Proc. 24th Int. Symp. on Multiple-valued Logic, Boston, Massachusetts, 25.27.5. 1994, 97-104. DOI: 10.1109\/ISMVL.1994.302215 Cited on page(s) 5, 7, 49, 10010.1109\/ISMVL.1994.302215","DOI":"10.1109\/ISMVL.1994.302215"},{"key":"p_172","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-1385-4"},{"key":"p_173","doi-asserted-by":"crossref","unstructured":"Sasao, T., Butler, J.T. \"Comparison of the worst and best sum-of-products expressions for multiple-valued functions,\" Proc. 27th Int. Symp. on Multiple-Valued Logic, Nova Scotia, Canada, May28-30,1997, 55-60. DOI: 10.1109\/ISMVL.1997.601374 Cited on page(s) 1210.1109\/ISMVL.1997.601374","DOI":"10.1109\/ISMVL.1997.601374"},{"key":"p_174","doi-asserted-by":"crossref","unstructured":"Schafer, I., Perkowski, M.A. \"Multiple-valued generalized Reed-Muller forms,\" Proc. of the Twenty-First International Symposium on Multiple-Valued Logic, 1991, 40-48. DOI: 10.1109\/ISMVL.1991.130703 Cited on page(s) 49 10.1109\/ISMVL.1991.130703","DOI":"10.1109\/ISMVL.1991.130703"},{"key":"p_175","doi-asserted-by":"publisher","DOI":"10.1049\/ip-e.1992.0074"},{"key":"p_176","unstructured":"Shmerko, V., Holowinski, G., Song, N., Dill, K., Oanguly, K., Salranek, R., Perkowski, M. \"High-quality minimization of multi-valued input binary-output Exclusive-Or Sum of Product expressions for strongly unspecified multi-output functions,\" Proc. Int. Conf. on Applications of Computer Systems, Poland, 1997, 248-255. Cited on page(s)49"},{"key":"p_177","doi-asserted-by":"crossref","unstructured":"Song, N., Perkowski, M.A. \"EXORCISM-MV-2: Minimisation of Exclusive Sum of Products expressions for multiple-valued input incompletely specified functions,\" Proc. 23rd Int. Symp. on Multiple-Valued Logic, 1993, 132-137. DOI: 10.1109\/ISMVL.1993.289569 Cited on page(s) 49 10.1109\/ISMVL.1993.289569","DOI":"10.1109\/ISMVL.1993.289569"},{"key":"p_178","doi-asserted-by":"publisher","DOI":"10.1109\/ISMVL.1993.289569"},{"key":"p_179","doi-asserted-by":"crossref","unstructured":"Srinivasan, A., Kam, T., Malik, Sh., Brayant, R.K. \"Algorithms for discrete function manipulation,\" in:Proc. Inf. Conf. on CAD, 1990, 92-95. DOI: 10.1109\/ICCAD.1990.129849 Cited on page(s) 81, 106, 107 10.1109\/ICCAD.1990.129849","DOI":"10.1109\/ICCAD.1990.129849"},{"key":"p_180","first-page":"125","volume-title":"Scientific Review, No. 21-22","author":"Stankovi\u0107 M.","year":"1996"},{"key":"p_181","unstructured":"Stankovi\u0107, M., Jankovi\u0107, D., Stankovi\u0107, R.S. \"Efficient algorithm for Haar spectrum calculation,\" Proc. IEEE Int. Conf. on Information, Communications and Signal Processing (1st ICICS), Singapore, Vol.4,September 1997, 6-10. Cited on page(s)125"},{"key":"p_182","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7906(01)00022-2"},{"key":"p_183","unstructured":"Stankovi\u0107, M., Stojkovi\u0107, S. \"Calculation of symmetric transform of Boolean functions represented by decision diagrams,\" Proc. XLII Yugoslav Conference for ETRAN, Vrnja\u010dka Banja, June3-5,1998, 63-66, (in Serbian). Cited on page(s) 125"},{"key":"p_184","doi-asserted-by":"crossref","unstructured":"Stankovi\u0107, M., Stojkovi\u0107, S., Moraga, C. \"Linearization of ternary decision diagrams by using the polynomial Chrestenson spectrum,\" Proc. 37th Int. Symp. on Multiple-Valued Logic, May 2007, 41-41 (CD-publication). DOI: 10.1109\/ISMVL.2007.31 Cited on page(s) 74 10.1109\/ISMVL.2007.31","DOI":"10.1109\/ISMVL.2007.31"},{"key":"p_185","first-page":"51","volume":"37","author":"Stankovi\u0107 R.S.","year":"1985","journal-title":"Publ. Inst. Math. Beograd, (N.S.)"},{"key":"p_186","doi-asserted-by":"crossref","unstructured":"Stankovi\u0107, R.S. \"Some remarks on Fourier transforms and differential operators for digital functions,\" Proc. 22nd Int. Symp. on Multiple-Valued Logic, Sendai, Japan, 1992, 365-370. DOI: 10.1109\/ISMVL.1992.186818 Cited on page(s) 8, 11, 18, 28, 2910.1109\/ISMVL.1992.186818","DOI":"10.1109\/ISMVL.1992.186818"},{"key":"p_187","doi-asserted-by":"crossref","unstructured":"Stankovi\u0107, R.S. \"Some remarks about spectral transform interpretation of MTBDDs and EVBDDs', Proc. of the Asian and South Pacific Design Automation Conference, (ASP-DAC'95), 29.8-1.9.1995, Makuhari Messe, Chiba, Japan, 1995,385-390. DOI: 10.1109\/ASPDAC.1995.486348 Cited on page(s) 100, 10310.1109\/ASPDAC.1995.486348","DOI":"10.1145\/224818.224928"},{"key":"p_188","doi-asserted-by":"crossref","unstructured":"Stankovi\u0107, R.S. \"Functional decision diagrams for multiple-valued functions,\" Proc. 25-th Int. Symp. on Multiple-Valued Logic, 23-25.5.1995, Bloomington, Indiana, U. S. A., 284-289. DOI: 10.1109\/ISMVL.1995.513544 Cited on page(s) 84, 86, 10010.1109\/ISMVL.1995.513544","DOI":"10.1109\/ISMVL.1995.513544"},{"key":"p_189","first-page":"13","volume":"9","author":"Stankovi\u0107 R.S.","year":"1995","journal-title":"UK"},{"key":"p_190","doi-asserted-by":"publisher","DOI":"10.1109\/ISMVL.1997.601415"},{"key":"p_191","doi-asserted-by":"publisher","DOI":"10.1109\/ISMVL.1995.513544"},{"key":"p_192","doi-asserted-by":"publisher","DOI":"10.1023\/A:1011265018200"},{"key":"p_193","doi-asserted-by":"publisher","DOI":"10.1080\/10236620215293"},{"issue":"3","key":"p_194","first-page":"287","volume":"10","author":"Stankovi\u0107 R.S.","year":"2004","journal-title":"Multiple-Valued Logic and Soft Computing"},{"key":"p_195","doi-asserted-by":"crossref","unstructured":"Stankovic, R.S., Astola, H., Astola, J.T. \"Determining minimized Galois field expressions for ternary functions,\" Proc. 41st Int. Symp. on Multiple-Valued Logic, Tuusula, Finland, May23-25,2011, 117-124. DOI: 10.1109\/ISMVL.2011.26 Cited on page(s) 4910.1109\/ISMVL.2011.26","DOI":"10.1109\/ISMVL.2011.26"},{"key":"p_196","first-page":"3","volume":"86","author":"Stankovi\u0107 R.S.","year":"2003","journal-title":"IEICE Trans. Fundamentals"},{"key":"p_197","unstructured":"Stankovi\u0107, R.S., Astola, J.T., Spectral Interpretation of Decision Diagrams, Springer, 2003. Cited on page(s)16, 77, 78, 99, 100, 101, 117"},{"key":"p_198","doi-asserted-by":"crossref","unstructured":"Stankovi\u0107, R.S., Astola, J.T. \"Edge-valued decision diagrams for multiple-valued functions,\" Proc. 34th Int. Symp. on Multiple-Valued Logic, Toronto, Canada, May19-22,2004, 229-234. DOI: 10.1109\/ISMVL.2004.1319946 Cited on page(s) 10510.1109\/ISMVL.2004.1319946","DOI":"10.1109\/ISMVL.2004.1319946"},{"key":"p_199","unstructured":"Stankovi\u0107, R.S., Astola, J. \"Remarks on the complexity of arithmetic representations of elementary functions for circuit design,\" Workshop on Applications of the Reed-Muller Expansion"},{"key":"p_202","unstructured":"Stankovi\u0107, R.S., Astola, J.T., Egiazarian, K. \"Remarks on symmetric binary and multiplevalued logic functions,\" Proc. 6th Int. Workshop on Boolean Problems, Freiberg, Germany, September23-24,2004, 83-87. Cited on page(s)12"},{"key":"p_203","first-page":"51","volume-title":"Advances in Signal Transforms, Theory and Applications","volume":"7","author":"Stankovi\u0107 R.S.","year":"2007"},{"key":"p_204","doi-asserted-by":"publisher","DOI":"10.1109\/ISMVL.1997.601413"},{"key":"p_205","doi-asserted-by":"crossref","unstructured":"Stankovi\u0107, R.S., Jankovi\u0107, D., Moraga, C. \"Reed-Muller-Fourier versus Galois field representations of four-valued logic functions,\" Proc. 28th Int. Symp. on Multiple-Valued Logic, May27-29,1998, 186-191. DOI: 10.1109\/ISMVL.1998.679340 Cited on page(s) 35 10.1109\/ISMVL.1998.679340","DOI":"10.1109\/ISMVL.1998.679340"},{"key":"p_206","unstructured":"Stankovi\u0107, R.S., Moraga, C. \"Fast algorithms for detecting some properties of multiplevalued functions, Proc. 14th Int. Symp. on Multiple-valued Logic, Winnipeg, Canada, May29-31,1984. Cited on page(s)12"},{"issue":"5","key":"p_207","first-page":"421","volume":"139","author":"Stankovi\u0107 R.S.","year":"1992","journal-title":"IEE Proc., Part E"},{"key":"p_208","doi-asserted-by":"crossref","unstructured":"Stankovi\u0107, R.S., Jankovi\u0107, D., Moraga, C. \"Reed-Muller-Fourier versus Galois field representations of four-valued logic functions\"`Proc. 28th IEEE International Symposium on Multiple-Valued Logic, 1998, 186-191. DOI: 10.1109\/ISMVL.1998.679340 Cited on page(s) 35, 46 10.1109\/ISMVL.1998.679340","DOI":"10.1109\/ISMVL.1998.679340"},{"key":"p_209","unstructured":"Stankovi\u0107, R.S., Moraga, C. \"Reed-Muller-Fourier representations of multiple-valued functions over Galois fields of prime cardinality,\" Kebschull, U., Schubert, E., Rosentiel, W. (eds.), Proc. IFIP WG10.5Workshop on Applications of the Reed-Muller Expansion in Circuit Design, Hamburg, Germany, September16-17,1993, 115-124. Cited on page(s)8, 11, 18, 28, 88"},{"key":"p_210","unstructured":"Stankovi\u0107, R.S., Stankovi\u0107, M., Moraga, C., Sasao, T. \"Calculation of Vilenkin-Chrestenson transform coefficients of multiple-valued functions through multiple-place decision diagrams,\" Proc. 5th Int. Workshop on Spectral Techniques, 15.17.3.1994, Beijing, China, 107-116. Cited on page(s)17, 18"},{"key":"p_211","unstructured":"Stankovi\u0107, R.S., Moraga, C. \"An algebraic transform for prime-valued functions,\" Proc. 5th Int. Workshop on Spectral Techniques, 15.17.3.1994, Beijing, China, 205-209. Cited on page(s)46"},{"key":"p_212","unstructured":"Stankovi\u0107, R.S., Moraga, C. \"Edge-valued functional decision diagrams,\" Proc. Int. Conf. on Computer Aided Design of Discrete Devices, 15.17.11.1995, Minsk, Belarus, Vol. 2, 69-73. Cited on page(s)103"},{"key":"p_213","first-page":"7","volume-title":"Stankovi\u0107","author":"Stankovi\u0107 R.S.","year":"1996"},{"key":"p_214","doi-asserted-by":"crossref","unstructured":"Stankov\u0107, R.S., Moraga, C. \"Edge-valued decision diagrams for multiple-valued functions,\" Proc. 3rd Int. Conf. Application of Computer Systems, Szczecin, Poland, November21-22,1996. DOI: 10.1109\/ISMVL.2004.1319946 Cited on page(s) 100, 102, 104, 10510.1109\/ISMVL.2004.1319946","DOI":"10.1109\/ISMVL.2004.1319946"},{"key":"p_215","doi-asserted-by":"publisher","DOI":"10.1007\/s002000100068"},{"issue":"1","key":"p_216","first-page":"5","volume":"10","author":"Stankovi\u0107 R.S.","year":"2004","journal-title":"Multiple-Valued Logic and Soft Computing"},{"key":"p_217","doi-asserted-by":"crossref","unstructured":"Stankovi\u0107, R.S., Moraga, C., Astola, J.T. \"Derivatives for multiple-valued functions induced by Galois field and Reed-Muller-Fourier expressions,\" Proc. 34th Int. Symp. on Multiple-Valued Logic, Toronto, Canada, May19-22,2004, 184-189. DOI: 10.1109\/ISMVL.2004.1319939 Cited on page(s) 1610.1109\/ISMVL.2004.1319939","DOI":"10.1109\/ISMVL.2004.1319939"},{"key":"p_218","doi-asserted-by":"crossref","unstructured":"Stankovi\u0107, R.S., Moraga, C., Astola, J.T. \"Remarks on the structure of matrix-valued spectral transforms on finite non-Abelian groups,\" Proc. 34th Int. Symp. on Multiple-Valued Logic, Calgary, Canada, May18-21,2005, 188-193. DOI: 10.1109\/ISMVL.2005.42 Cited on page(s) 710.1109\/ISMVL.2005.42","DOI":"10.1109\/ISMVL.2005.42"},{"key":"p_219","doi-asserted-by":"publisher","DOI":"10.1002\/047174543X"},{"key":"p_220","doi-asserted-by":"publisher","DOI":"10.1109\/ASPDAC.1998.669518"},{"key":"p_221","unstructured":"Stankovi\u0107, R.S., Sasao,T.\"Komamiya equation for multiple-valued adders,\" Invited talk, Proc. 10th Int. Workshop on Post-Binary ULSI Systems, Warszawa, Poland, May21,2001, 63-68. Cited on page(s)12"},{"key":"p_222","unstructured":"Stankovi\u0107, R.S., Stankovi\u0107, M., Astola, J.T., Egiazarian, K. \"Haar spectral transform decision diagrams with exact algorithm for minimization of the number of paths,\" Proc. 4th Int. Workshop on Boolean Problems, Freiberg, Germany, September21-22,2000. Cited on page(s)93"},{"key":"p_223","first-page":"125","author":"Stankovi\u0107 R.S.","year":"1998","journal-title":"Belgrade"},{"key":"p_224","doi-asserted-by":"crossref","unstructured":"Stankovi\u0107, R.S., Stankovi\u0107, M., Moraga, C. \"Design of Haar wavelet transforms and Haar spectral transform decision diagrams for multiple-valued functions,\" Proc. 31st Int. Symp. on Multiple-Valued Logic, Warzsawa, Poland, May22-24,2001, 311-316. DOI: 10.1109\/ISMVL.2001.924589 Cited on page(s) 49, 94, 10810.1109\/ISMVL.2001.924589","DOI":"10.1109\/ISMVL.2001.924589"},{"key":"p_225","doi-asserted-by":"crossref","unstructured":"Stankovi\u0107, R.S., Stankovi\u0107, M., Moraga, C., Sasao, T. \"Calculation of Reed-Muller-Fourier coefficients of multiple-valued functions through multiple-place decision diagrams,\" Proc. Twenty-Fourth International Symposium on Multiple-Valued Logic, Boston, Massachusetts, USA, May22-25,1994, 82-88. DOI: 10.1109\/ISMVL.1994.302216 Cited on page(s) 12410.1109\/ISMVL.1994.302216","DOI":"10.1109\/ISMVL.1994.302216"},{"key":"p_226","unstructured":"Stankovi\u0107, R.S., Stankovi\u0107, M., Moraga, C., Sasao, T. \"Calculation of Vilenkin-Chrestenson transform coefficients of multiple-valued functions through multiple-place decision diagrams,\" Proc. 5th Int. Workshop on Spectral Techniques, 15.17.3.1994, Beijing, China, 107-116. Cited on page(s)18, 124"},{"key":"p_227","doi-asserted-by":"publisher","DOI":"10.2298\/FUEE0703259S"},{"key":"p_228","doi-asserted-by":"crossref","unstructured":"Stojmenovi\u0107, I., Miyakawa, M., Tosi\u0107, R. \"On spectra of many-valued logic symmetric functions,\" 18th Int. Symp. on Multiple-Valued Logic, 1988, 285-292. DOI: 10.1109\/ISMVL.1988.5185 Cited on page(s) 12 10.1109\/ISMVL.1988.5185","DOI":"10.1109\/ISMVL.1988.5185"},{"key":"p_229","unstructured":"Tamari, D. \"Some mutual applications of logic and mathematics,\" Proc. 2nd Int. Colloq. Math. Logic, August 1952, 89-90. Cited on page(s) 11"},{"key":"p_230","doi-asserted-by":"publisher","DOI":"10.1049\/ip-cdt:19960770"},{"key":"p_231","doi-asserted-by":"publisher","DOI":"10.1007\/BF01271287"},{"key":"p_232","unstructured":"Thayse, A., Boolean Differential Calculus, Springer-Verlag, 1980. Cited on page(s)16"},{"key":"p_233","unstructured":"Thayse, A., Davio, M., Deschamps, J.P. \"Optimization of multiple-valued decision diagrams,\" Proc. 8th Int. Symp.on Multiple-Valued Logic, 1978, 171-177. Cited on page(s) 81, 100"},{"key":"p_234","unstructured":"Aiken, H. (ed.),The Annals of the Computation Laboratory of Harvard University, VolumeXXVII, Synthesis of Electronic Computing and Control Circuits,Cambridge, Massachusetts, USA, 1951. Citedon page(s)54"},{"key":"p_235","doi-asserted-by":"crossref","unstructured":"Thornton, M.A. \"Spectral transforms of mixed-radix MVL functions,\" 33rd Int. Symp. on Multiple-Valued Logic, May16-19,2003, 329-333. DOI: 10.1109\/ISMVL.2003.1201425 Cited on page(s) 27 10.1109\/ISMVL.2003.1201425","DOI":"10.1109\/ISMVL.2003.1201425"},{"key":"p_236","doi-asserted-by":"publisher","DOI":"10.1023\/B:AURC.0000030910.23047.2d"},{"key":"p_237","doi-asserted-by":"crossref","unstructured":"Thornton, M.A., Drechsler, R. \"Computation of spectral information from logic netlists,\" 30th Int. Symp. on Multiple-Valued Logic, May23-25,2000, 53-58. DOI: 10.1109\/ISMVL.2000.848600 Cited on page(s) 118 10.1109\/ISMVL.2000.848600","DOI":"10.1109\/ISMVL.2000.848600"},{"key":"p_238","doi-asserted-by":"publisher","DOI":"10.1109\/ISMVL.2002.1011079"},{"key":"p_239","doi-asserted-by":"crossref","unstructured":"Thornton, M.A., Miller, D.M., Townsend, W.J. \"Chrestenson spectrum computation using Cayley color graphs,\" Proc. 32nd Int. Symp. on Multiple-Valued Logic, Boston, Massachusetts, USA, May15-18,2002, 123-128. DOI: 10.1109\/ISMVL.2002.1011079 Cited on page(s) 11810.1109\/ISMVL.2002.1011079","DOI":"10.1109\/ISMVL.2002.1011079"},{"key":"p_240","doi-asserted-by":"publisher","DOI":"10.1201\/9781420037586.ch5"},{"key":"p_242","unstructured":"Tosi\u0107, R., Stojmenovi\u0107, I., Miyakawa, M.\"On the maximum size of the terms in the realization of symmetric functions,\" Proc. 21st Int. Symp. on Multiple-Valued Logic, Victoria, BC, Canada, May26-29,1991, 110-117. Cited on page(s)12"},{"key":"p_243","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-3154-8"},{"key":"p_244","first-page":"118","volume":"331","author":"Trachtenberg E.A.","year":"1996","journal-title":"Belgrade"},{"key":"p_245","doi-asserted-by":"publisher","DOI":"10.1049\/ip-e.1991.0011"},{"key":"p_246","doi-asserted-by":"crossref","unstructured":"Vasiliev, N.A. \"Imaginary (non-Aristotelian) logic,\"Atti del Congresso Internazionale di Filosofia, (Napoli 5-9 Maggio 1924), 107-109. DOI: 10.1007\/BF02229852 Cited on page(s) 9 10.1007\/BF02229852","DOI":"10.1007\/BF02229852"},{"key":"p_247","doi-asserted-by":"publisher","DOI":"10.1109\/T-C.1970.222803"},{"key":"p_248","unstructured":"Vrudhula, S.B.K., Lai, Y.T., Pedram, M. \"Efficient computation of the probability and Reed-Muller spectra of Boolean functions using edge-valued binary decision diagrams,\" in: Sasao, T., Fujita, M.Eds.,Proc. IFIP WG 10.5 Workshop on Applications of the Reed-Muller Expansion in Circuit Design, Reed-Muller'95, 27-29.8.1995, Makuhari, Chiba, Japan, 62-69. Cited on page(s)100"},{"key":"p_249","doi-asserted-by":"publisher","DOI":"10.2748\/tmj"},{"key":"p_250","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.21.5.252"},{"key":"p_251","doi-asserted-by":"publisher","DOI":"10.1109\/TC.1978.1675076"},{"key":"p_252","unstructured":"Yanushkevich, S. \"Matrix algorithms of synthesis of polynomial forms for MVL functions,\" Proc. Int. Conf. on Parallel Processing and Applied Mathematics, Poland, 1994, 113-122. Cited on page(s)41"},{"key":"p_253","unstructured":"Yanushkevich, S. \"Spectral and differential methods to synthesize polynomial forms of MVL functions on systolic arrays,\" Proc. 5th Int. Workshop on Spectral Techniques, C. Moraga, Q. Zhang, (Eds.), Beijing, China, 1994, 78-93. Cited on page(s)48"},{"key":"p_254","doi-asserted-by":"publisher","DOI":"10.1049\/ip-cdt:19971368"},{"key":"p_255","unstructured":"Yanushkevich, S.N., Logic Differential Calculus in Multi-Valued Logic Design,Techn. University of Szczecin Academic Publisher, Poland, 1998. Cited on page(s)8, 16, 48"},{"key":"p_256","doi-asserted-by":"crossref","unstructured":"Yanushkevich, S.N., Butler, J.T., Dueck, G.W., Shmerko, V.P. \"Experiments on FPRM expressions for partially symmetric logic functions,\" Proc. 30th IEEE Int. Symp. on Multiple-Valued Logic, 2000, 141-146. DOI: 10.1109\/ISMVL.2000.848612 Cited on page(s) 12 10.1109\/ISMVL.2000.848612","DOI":"10.1109\/ISMVL.2000.848612"},{"key":"p_257","unstructured":"Yanushkevich, S., Holowinski, G. \"Fast heuristic minimization of MVL functions in generalized Reed-Muller domain,\" Proc. Int. Conf. on Applications of Computer Systems, Szczecin, Poland, 1996, 57-6.1. Cited on page(s)49"},{"key":"p_258","unstructured":"Yanushkevich, S.N., Miller, D.M., Shmerko, V.P., Stankovi\u0107, R.S., Decision Diagram Technique for Micro - and Nanoelectronic Design, CRC Press, Taylor& Francis, Boca Raton, London, New York,2006. Cited on page(s)8, 16"},{"key":"p_259","doi-asserted-by":"crossref","unstructured":"Yanushkevich, S.N., Shmerko, V.D., Popel, D., Cheushev, V., Stankovi\u0107, R.S. \"Information theoretic approach to minimization of polynomial expressions over GF (4),\" Proc. 30th Int. Symp. on Multiple-Valued Logic, Portland, Oregon, USA, May23-25,2000, 265-270. DOI: 10.1109\/ISMVL.2000.848630 Cited on page(s) 4910.1109\/ISMVL.2000.848630","DOI":"10.1109\/ISMVL.2000.848630"},{"key":"p_260","unstructured":"Zakrevskij, A. \"Search Space Reducing: a super - fast algorithm for minimum AND-EXOR implementation of systems of weakly specified Boolean functions,\" Proc. Int. Conf. on Pattern Recognition and Information Processing, Minsk, Belarus, Vol.1, 1997, 327-331. Cited on page(s) 27"},{"key":"p_261","unstructured":"Zakrevskij, A., Jaroszewicz, S., Yanushkevich, S. \"Minimization of Reed-Muller expansions for systems of incompletely specified MVL functions,\" Proc. Int. Symp. on Methods and Models in Automation and Robotics, Miedzyzdroje, Poland, Vol. 3, 1996, 1085-1090. Cited on page(s)27"},{"key":"p_262","unstructured":"Zakrevskij, A., Toropov, N. \"Optimizing polynomial implementation of incompletely specified Boolean functions,\" Proc. Int. Conf. on Computer Aided Design of Discrete Devices, Minsk, Belarus, Vol.I, 1995, 93-98. Cited on page(s) 48"},{"key":"p_263","doi-asserted-by":"crossref","unstructured":"Zakrevskij, A.D., Zakrevski, L.A. \"Fast algorithm for minimizing Reed-Muller expansions of systems of incompletely specified MVL functions,\" Proc. 27th International Symposium on Multiple-Valued Logic, 1997, 61-65. DOI: 10.1109\/ISMVL.1997.601375 Cited on page(s) 48 10.1109\/ISMVL.1997.601375","DOI":"10.1109\/ISMVL.1997.601375"},{"key":"p_264","first-page":"9","volume":"34","author":"Zhegalkin I.I.","year":"1927","journal-title":"Math. Sb."},{"key":"p_265","first-page":"311","volume":"35","author":"Zhegalkin I.I.","year":"1928","journal-title":"Math. Sb."},{"key":"p_266","first-page":"48","volume-title":"Ph. D. thesis","author":"Zilic Z."},{"key":"p_267","doi-asserted-by":"crossref","unstructured":"Zilic, Z., Vranesic, Z. \"Current-Mode CMOS Galois Field Circuits,\" Proc. 23rd Int. Symp. on Multiple-Valued Logic, 1993, 245-250. DOI: 10.1109\/ISMVL.1993.289552 Cited on page(s) 17, 25 10.1109\/ISMVL.1993.289552","DOI":"10.1109\/ISMVL.1993.289552"},{"key":"p_268","doi-asserted-by":"publisher","DOI":"10.1109\/12.403717"},{"key":"p_269","doi-asserted-by":"crossref","unstructured":"Zilic, Z., Vranesic, Z.G. \"Reed-Muller forms for incompletely specified functions via sparse polynomial interpolation,\" Proc. 25th International Symposium on Multiple-Valued Logic, 1995, 36-43. DOI: 10.1109\/ISMVL.1995.513507 Cited on page(s) 48 10.1109\/ISMVL.1995.513507","DOI":"10.1109\/ISMVL.1995.513507"},{"key":"p_270","doi-asserted-by":"crossref","unstructured":"Zilic, Z., Vranesic, Z.G. \"New interpolation algorithms for multiple-valued Reed-Muller forms,\" Proc. 26th Int. Symp. on Multiple-Valued Logic, 1996, 16-23. Cited on page(s) 48","DOI":"10.1109\/ISMVL.1996.508330"},{"key":"p_271","doi-asserted-by":"publisher","DOI":"10.1109\/TC.2002.1032628"}],"container-title":["Synthesis Lectures on Digital Circuits and Systems"],"original-title":[],"language":"en","deposited":{"date-parts":[[2022,7,22]],"date-time":"2022-07-22T16:03:24Z","timestamp":1658505804000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.morganclaypool.com\/doi\/abs\/10.2200\/S00420ED1V01Y201205DCS037"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,6,23]]},"references-count":262,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2012,6,23]]}},"alternative-id":["10.2200\/S00420ED1V01Y201205DCS037"],"URL":"https:\/\/doi.org\/10.2200\/s00420ed1v01y201205dcs037","relation":{},"ISSN":["1932-3166","1932-3174"],"issn-type":[{"value":"1932-3166","type":"print"},{"value":"1932-3174","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,6,23]]}}}