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89
Symbolic Model Checking: 10^20 States and Beyond
, 1992
"... Many different methods have been devised for automatically verifying finite state systems by examining stategraph models of system behavior. These methods all depend on decision procedures that explicitly represent the state space using a list or a table that grows in proportion to the number of st ..."
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Cited by 574 (30 self)
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Many different methods have been devised for automatically verifying finite state systems by examining stategraph models of system behavior. These methods all depend on decision procedures that explicitly represent the state space using a list or a table that grows in proportion to the number of states. We describe a general method that represents the state space symbolical/y instead of explicitly. The generality of our method comes from using a dialect of the MuCalculus as the primary specification language. We describe a model checking algorithm for MuCalculus formulas that uses Bryant’s Binary Decision Diagrams (Bryant, R. E., 1986, IEEE Trans. Comput. C35) to represent relations and formulas. We then show how our new MuCalculus model checking algorithm can be used to derive efficient decision procedures for CTL model checking, satistiability of lineartime temporal logic formulas, strong and weak observational equivalence of finite transition systems, and language containment for finite wautomata. The fixed point computations for each decision procedure are sometimes complex. but can be concisely expressed in the MuCalculus. We illustrate the practicality of our approach to symbolic model checking by discussing how it can be used to verify a simple synchronous pipeline circuit.
An AutomataTheoretic Approach to BranchingTime Model Checking
 JOURNAL OF THE ACM
, 1998
"... Translating linear temporal logic formulas to automata has proven to be an effective approach for implementing lineartime modelchecking, and for obtaining many extensions and improvements to this verification method. On the other hand, for branching temporal logic, automatatheoretic techniques ..."
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Cited by 300 (65 self)
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Translating linear temporal logic formulas to automata has proven to be an effective approach for implementing lineartime modelchecking, and for obtaining many extensions and improvements to this verification method. On the other hand, for branching temporal logic, automatatheoretic techniques have long been thought to introduce an exponential penalty, making them essentially useless for modelchecking. Recently, Bernholtz and Grumberg have shown that this exponential penalty can be avoided, though they did not match the linear complexity of nonautomatatheoretic algorithms. In this paper we show that alternating tree automata are the key to a comprehensive automatatheoretic framework for branching temporal logics. Not only, as was shown by Muller et al., can they be used to obtain optimal decision procedures, but, as we show here, they also make it possible to derive optimal modelchecking algorithms. Moreover, the simple combinatorial structure that emerges from the a...
Model Checking and Modular Verification
 ACM Transactions on Programming Languages and Systems
, 1991
"... We describe a framework for compositional verification of finite state processes. The framework is based on two ideas: a subset of the logic CTL for which satisfaction is preserved under composition; and a preorder on structures which captures the relation between a component and a system containing ..."
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Cited by 272 (11 self)
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We describe a framework for compositional verification of finite state processes. The framework is based on two ideas: a subset of the logic CTL for which satisfaction is preserved under composition; and a preorder on structures which captures the relation between a component and a system containing the component. Satisfaction of a formula in the logic corresponds to being below a particular structure (a tableau for the formula) in the preorder. We show how to do assumeguarantee style reasoning within this framework. In addition, we demonstrate efficient methods for model checking in the logic and for checking the preorder in several special cases. We have implemented a system based on these methods, and we use it to give a compositional verification of a CPU controller. 1 Introduction Temporal logic model checking procedures are useful tools for the verification of finite state systems [3, 12, 20]. However, these procedures have traditionally suffered from the state explosion proble...
TableauBased Model Checking in the Propositional MuCalculus
 Acta Informatica
, 1990
"... This paper describes a procedure, based around the construction of tableau proofs, for determining whether finitestate systems enjoy properties formulated in the propositional mucalculus. It presents a tableaubased proof system for the logic and proves it sound and complete, and it discusses tech ..."
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Cited by 91 (7 self)
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This paper describes a procedure, based around the construction of tableau proofs, for determining whether finitestate systems enjoy properties formulated in the propositional mucalculus. It presents a tableaubased proof system for the logic and proves it sound and complete, and it discusses techniques for the efficient construction of proofs that states enjoy properties expressed in the logic. The approach is the basis of an ongoing implementation of a model checker in the Concurrency Workbench, an automated tool for the analysis of concurrent systems. 1 Introduction One area of program verification that has proven amenable to automation involves the analysis of finitestate processes. While computer systems in general are not finitestate, many interesting ones, including a variety of communication protocols and hardware systems, are, and their finitary nature enables the development and implementation of decision procedures that test for various properties. Model checking has p...
Model Checking for ContextFree Processes
, 1992
"... We develop a modelchecking algorithm that decides for a given contextfree process whether it satisfies a property written in the alternationfree modal mucalculus. The central idea behind this algorithm is to raise the standard iterative modelchecking techniques to higher order: in contrast to t ..."
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Cited by 78 (8 self)
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We develop a modelchecking algorithm that decides for a given contextfree process whether it satisfies a property written in the alternationfree modal mucalculus. The central idea behind this algorithm is to raise the standard iterative modelchecking techniques to higher order: in contrast to the usual approaches, in which the set of formulas that are satisfied by a certain state are iteratively computed, our algorithm iteratively computes a property transformer for each state class of the finite process representation. These property transformers can then simply be applied to solve the modelchecking problem. The complexity of our algorithm is linear in the size of the system's representation and exponential in the size of the property being investigated.
Model Checking Mobile Processes
, 1993
"... We introduce a temporal logic for the polyadic ßcalculus based on fixed point extensions of HennessyMilner logic. Features are added to account for parametrisation, generation, and passing of names, including the use, following Milner, of dependent sum and product to account for (unlocalised) inpu ..."
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Cited by 63 (11 self)
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We introduce a temporal logic for the polyadic ßcalculus based on fixed point extensions of HennessyMilner logic. Features are added to account for parametrisation, generation, and passing of names, including the use, following Milner, of dependent sum and product to account for (unlocalised) input and output, and explicit parametrisation on names using lambdaabstraction and application. The latter provides a single name binding mechanism supporting all parametrisation needed. A proof system and decision procedure is developed based on Stirling and Walker's approach to model checking the modal ¯calculus using constants. One difficulty, for both conceptual and efficiencybased reasons, is to avoid the explicit use of the !rule for parametrised processes. A key idea, following Hennessy and Lin's approach to deciding bisimulation for certain types of valuepassing processes, is the relativisation of correctness assertions to conditions on names. Based on this idea a proof system and ...
Combining Deduction and Model Checking into Tableaux and Algorithms for ConversePDL
 Information and Computation
, 1998
"... . This paper presents a prefixed tableaux calculus for Propositional Dynamic Logic with Converse based on a combination of different techniques such as prefixed tableaux for modal logics and model checkers for ¯calculus. We prove the correctness and completeness of the calculus and illustrate its f ..."
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Cited by 57 (7 self)
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. This paper presents a prefixed tableaux calculus for Propositional Dynamic Logic with Converse based on a combination of different techniques such as prefixed tableaux for modal logics and model checkers for ¯calculus. We prove the correctness and completeness of the calculus and illustrate its features. We also discuss the transformation of the tableaux method (naively NEXPTIME) into an EXPTIME algorithm. 1 Introduction Propositional Dynamic Logics (PDLs) are modal logics introduced in [10] to model the evolution of the computation process by describing the properties of states reached by programs during their execution [15, 24, 27]. Over the years, PDLs have been proved to be a valuable formal tool in Computer Science, Logic, Computational Linguistics, and Artificial Intelligence far beyond their original use for program verification (e.g. [4, 12, 14, 15, 24, 23]). In this paper we focus on ConversePDL (CPDL) [10], obtained from the basic logic PDL by adding the converse operat...
Games for the µCalculus
"... Given a formula of the propositional µcalculus, we construct a tableau of the formula and define an infinite game of two players of which one wants to show that the formula is satisfiable, and the other seeks the opposite. The strategy for the first player can be further transformed into a model of ..."
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Cited by 51 (5 self)
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Given a formula of the propositional µcalculus, we construct a tableau of the formula and define an infinite game of two players of which one wants to show that the formula is satisfiable, and the other seeks the opposite. The strategy for the first player can be further transformed into a model of the formula while the strategy for the second forms what we call a refutation of the formula. Using Martin's Determinacy Theorem, we prove that any formula has either a model or a refutation. This completeness result is a starting point for the completeness theorem for the µcalculus to be presented elsewhere. However, we argue that refutations have some advantages of their own. They are generated by a natural system of sound logical rules and can be presented as regular trees of the size exponential in the size of a refuted formula. This last aspect completes the small model theorem for the µcalculus established by Emerson and Jutla [3]. Thus, on a more practical side, refutations can be...
Actions Speak Louder than Words: Proving Bisimilarity for ContextFree Processes
, 1991
"... Baeten, Bergstra, and Klop (and later Caucal) have proved the remarkable result that bisimulation equivalence is decidable for irredundant contextfree grammars. In this paper we provide a much simpler and much more direct proof of this result using a tableau decision method involving goaldirec ..."
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Cited by 45 (9 self)
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Baeten, Bergstra, and Klop (and later Caucal) have proved the remarkable result that bisimulation equivalence is decidable for irredundant contextfree grammars. In this paper we provide a much simpler and much more direct proof of this result using a tableau decision method involving goaldirected rules. The decision procedure also provides the essential part of the bisimulation relation between two processes which underlies their equivalence. We also show how to obtain a sound and complete sequentbased equational theory for such processes from the tableau system and how one can extract what Caucal calls a fundamental relation from a successful tableau.
Modal Logics and muCalculi: An Introduction
, 2001
"... We briefly survey the background and history of modal and temporal logics. We then concentrate on the modal mucalculus, a modal logic which subsumes most other commonly used logics. We provide an informal introduction, followed by a summary of the main theoretical issues. We then look at modelchec ..."
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Cited by 44 (3 self)
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We briefly survey the background and history of modal and temporal logics. We then concentrate on the modal mucalculus, a modal logic which subsumes most other commonly used logics. We provide an informal introduction, followed by a summary of the main theoretical issues. We then look at modelchecking, and finally at the relationship of modal logics to other formalisms.