Special section on advances in reachability analysis and decision procedures: contributions to abstraction-based system verification

Abstract

Reachability analysis asks whether a system can evolve from legitimate initial states to unsafe states. It is thus a fundamental tool in the validation of computational systems—be they software, hardware, or a combination thereof. We recall a standard approach for reachability analysis, which captures the system in a transition system, forms another transition system as an over-approximation, and performs an incremental fixed-point computation on that over-approximation to determine whether unsafe states can be reached. We show this method to be sound for proving the absence of errors, and discuss its limitations for proving the presence of errors, as well as some means of addressing this limitation. We then sketch how program annotations for data integrity constraints and interface specifications—as in Bertrand Meyer’s paradigm of Design by Contract—can facilitate the validation of modular programs, e.g., by obtaining more precise verification conditions for software verification supported by automated theorem proving. Then we recap how the decision problem of satisfiability for formulae of logics with theories—e.g., bit-vector arithmetic—can be used to construct an over-approximating transition system for a program. Programs with data types comprised of bit-vectors of finite width require bespoke decision procedures for satisfiability. Finite-width data types challenge the reduction of that decision problem to one that off-the-shelf tools can solve effectively, e.g., SAT solvers for propositional logic. In that context, we recall the Tseitin encoding which converts formulae from that logic into conjunctive normal form—the standard format for most SAT solvers—with only linear blow-up in the size of the formula, but linear increase in the number of variables. Finally, we discuss the contributions that the three papers in this special section make in the areas that we sketched above.