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The Complexity of Membership Problems for Circuits over Sets of Positive Numbers

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Fundamentals of Computation Theory (FCT 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4639))

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Abstract

We investigate the problems of testing membership in the subset of the positive numbers produced at the output of combinational circuits. These problems are a natural modification of those studied by McKenzie and Wagner (2003), where circuits computed sets of natural numbers. It turns out that the missing 0 has strong implications, not only because 0 can be used to test for emptiness. We show that the membership problem for the general case and for is PSPACE-complete, whereas it is NEXPTIME-hard if one allows 0. Furthermore, testing membership for is NL-complete (as opposed to -hard), and several other cases are resolved.

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Authors and Affiliations

  1. Universität Würzburg, Institut für Informatik, Am Hubland, 97074 Würzburg, Germany

    Hans-Georg Breunig

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  1. Hans-Georg Breunig
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Erzsébet Csuhaj-Varjú Zoltán Ésik

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Breunig, HG. (2007). The Complexity of Membership Problems for Circuits over Sets of Positive Numbers. In: Csuhaj-Varjú, E., Ésik, Z. (eds) Fundamentals of Computation Theory. FCT 2007. Lecture Notes in Computer Science, vol 4639. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74240-1_12

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  • DOI: https://doi.org/10.1007/978-3-540-74240-1_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74239-5

  • Online ISBN: 978-3-540-74240-1

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