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...variable dependency graph. Note that the localization reduction either leaves a variable unchanged or replaces it by a nondeterministic assignment. A similar approach has been described by Balarin in =-=[2,15]-=-. In our approach, the abstraction functions exploit logical relationships among variables appearing in atomic formulas that occur in the control structure of the program. Moreover, the way we use abs...

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...s and does not provide a single specification language. The work in [14] is closer in spirit to our method in that languages of finite strings are used although not as part of a logical framework. In =-=[2]-=-, another approach is given based on iterating abstractions. The parameterized Dining Philosopher’s problem is solved in [11] by a finite-state induction principle. A tool for M2L on finite, binary tr...

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...a concrete counterexample, we must find a valuation for the unconstrained variables, such that all the original constraints are satisfied. A number of variations on this basic technique have appeared =-=[1, 5, 9, 21]-=-. Some of the recent methods pose the construction of a concrete counterexample as a Boolean satisfiability (SAT) problem (or equivalently, an ATPG problem)sand apply modern SAT methods [14] to this p...

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...ple in the form of a specific execution path of the program. A key paradigm behind some of the new software verification tools is the principle of counterexample-guided abstraction refinement (CEGAR) =-=[1,3,4,21,49,61,78]-=-. In this paradigm, the model checker attempts to verify the property starting with a coarse abstraction of the program, which 123s506 D. Beyer et al. tracks only a few relations (called predicates) b...

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...rwise, the reason for�Ìbeing a spurious counterexample is identified, and the whole process is iterated with a refined abstraction function�. Counterexample analysis has been introduced previously in =-=[18, 1]-=-. The counterexample-guided abstraction refinement was implemented in the system aSMV based on SMV. Originally, aSMV was only complete for the fragment of ACTL with linear counterexamples. In the rest...

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...ided predicates to produce the abstract system. Counter-example guided renement is a generally useful technique. It has been used in by Kurshan et al. [2] for checking timed automata, Balarin et al. [3] for language containment and Clarke et al [7] in the context of verication using abstraction for dierent variables in a version of the SMV model checker. Counter-example guided renement has even b...

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... Related Work The use of counter-examples to automatically guide refinement in model checking has been described in many papers, including those by Alur et al. [16], Balarin & Sangiovanni-Vincentelli =-=[17]-=- and Clarke et al. [18]. Predicate abstraction combined with counter-example driven refinement has been since widely adopted for the verification of software-like systems. Examples of tools that use t...

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...al cells (flops or latches). To verify real-world designs, the user must obtain from the RTL design an abstract model that is within the capacity of the symbolic model checker. Abstraction refinement =-=[2]-=-[6][7][10][12] is a strategy that automates this process. Starting from a simple abstract model of the design, abstraction refinement incrementally refines the abstract model by including more and mor...