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... successfully solved by encoding them into SAT. SAT solvers are now a fundamental tool in most formal verification design flows for hardware systems, both for equivalence, property checking, and ATPG =-=[30, 126, 168]-=-; other application areas include, e.g., the verification of safety-critical systems [167, 34], and AI planning in its classical formulation [106], and in its extensions to non-deterministic do1. E.g....

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...o eventually combine bottom-up and top-down approaches. CNF currently is the most efficient data structure for representing formulas in top-down approaches for SAT. Another general bottom-up approach =-=[16,14,15,6]-=- is also based on quantifier elimination. A SAT solver is used to eliminate multiple innermost variables in parallel. In practice these approaches have only been applied to SAT or model checking. In p...

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...ION RECENT years have seen an increased use of Boolean satisfiability (SAT)-based tools in the design cycle for verylarge-scale-integration (VLSI) circuits. Design verification and model checking [1]–=-=[6]-=-, test generation [7], logic optimization [8], and physical design [9], among other problems, have been successfully tackled with SAT-based solutions. This trend is due to recent advances in SAT solve...

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...t is worth pointing out that, while our prototype uses BDD-based state-space exploration, the approach can easily be adopted to permit other model checking strategies such as SAT-based model checking =-=[8, 18]-=- and counterexample guided abstraction refinement [15, 11]. Related Work. Compositional reasoning using assume-guarantee rules has a long history in the formal verification literature [22, 13, 1, 4, 1...

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...lowup in the initial transformation to DNF and C-qe might even return further disjunctions (as is the case for Presburger arithmetic); this problem has been addressed for the Boolean case by McMillan =-=[14]-=-. The quantifier elimination problem for invariant strengthening, as discussed in Section 5 allows for a purely syntactic quantifier elimination as long as we are restricting ourselves to guarded comm...

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... problems. The advantage of our approach is three-fold: First, we can leverage ecient Boolean quantication algorithms [14] based on BDDs and recent advances in SAT-based techniques for quantication [9=-=, 18]-=-. Second, the single call to the symbolic decision procedure eliminates the overhead of multiple (potentially exponential) calls to decision procedures (e.g., initializing data structures, libraries, ...

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...r example, in the case of propositional logic, the strongest postcondition is given by sp T (φ) ′ = ∃S.(φ ∧ T ) Thus, we can compute it using well-developed methods for Boolean quantifier elimination =-=[3, 11]-=-. This means that we can compute the strongest inductive invariant (also known as the reachable state set) by simply iterating this operator to a semantic fixed point, a procedure known as symbolic re...

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...llow SAT-based BMC to be combined effectively with other techniques to provide complete verification mtehods. There has also been growing interest in the use of SAT for unbounded model checking [33], =-=[34]-=-, [35]. However, these techniques are not as robust as SAT-based BMC techniques. III. SOFTWARE MODELING FOR C PROGRAMS Symbolic model checkers (both SAT- and BDD-based) work on a symbolic transition r...

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...h only for transitions. Recently, a BDD-based BMC algorithm has been proposed in [14]. In opposition to BMC, the model checking that is not limited by a bound is called unbounded model checking (UMC) =-=[15]-=-. In this paper, we propose a SAT-based UMC algorithm in which the sets of states and the transition relation are expressed in conjunctive normal form (CNF). The proposed algorithm performs quantifica...