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275
Reasoning about Infinite Computations
 Information and Computation
, 1994
"... We investigate extensions of temporal logic by connectives defined by finite automata on infinite words. We consider three different logics, corresponding to three different types of acceptance conditions (finite, looping and repeating) for the automata. It turns out, however, that these logics all ..."
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Cited by 252 (55 self)
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We investigate extensions of temporal logic by connectives defined by finite automata on infinite words. We consider three different logics, corresponding to three different types of acceptance conditions (finite, looping and repeating) for the automata. It turns out, however, that these logics all have the same expressive power and that their decision problems are all PSPACEcomplete. We also investigate connectives defined by alternating automata and show that they do not increase the expressive power of the logic or the complexity of the decision problem. 1 Introduction For many years, logics of programs have been tools for reasoning about the input/output behavior of programs. When dealing with concurrent or nonterminating processes (like operating systems) there is, however, a need to reason about infinite computations. Thus, instead of considering the first and last states of finite computations, we need to consider the infinite sequences of states that the program goes through...
An automatatheoretic approach to linear temporal logic
 Logics for Concurrency: Structure versus Automata, volume 1043 of Lecture Notes in Computer Science
, 1996
"... Abstract. The automatatheoretic approach to linear temporal logic uses the theory of automata as a unifying paradigm for program specification, verification, and synthesis. Both programs and specifications are in essence descriptions of computations. These computations can be viewed as words over s ..."
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Cited by 221 (22 self)
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Abstract. The automatatheoretic approach to linear temporal logic uses the theory of automata as a unifying paradigm for program specification, verification, and synthesis. Both programs and specifications are in essence descriptions of computations. These computations can be viewed as words over some alphabet. Thus,programs and specificationscan be viewed as descriptions of languagesover some alphabet. The automatatheoretic perspective considers the relationships between programs and their specifications as relationships between languages.By translating programs and specifications to automata, questions about programs and their specifications can be reduced to questions about automata. More specifically, questions such as satisfiability of specifications and correctness of programs with respect to their specifications can be reduced to questions such as nonemptiness and containment of automata. Unlike classical automata theory, which focused on automata on finite words, the applications to program specification, verification, and synthesis, use automata on infinite words, since the computations in which we are interested are typically infinite. This paper provides an introduction to the theory of automata on infinite words and demonstrates its applications to program specification, verification, and synthesis. 1
Combining Partial Order Reductions with Onthefly Modelchecking
, 1994
"... Abstract Partial order modelchecking is an approach to reduce time and memory in modelchecking concurrent programs. Onthefly modelchecking is a technique to eliminate part of the search by intersecting an automaton representing the (negation of the) checked property with the state space during i ..."
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Cited by 190 (14 self)
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Abstract Partial order modelchecking is an approach to reduce time and memory in modelchecking concurrent programs. Onthefly modelchecking is a technique to eliminate part of the search by intersecting an automaton representing the (negation of the) checked property with the state space during its generation. We prove conditions under which these two methods can be combined in order to gain reduction from both methods. An extension of the modelchecker SPIN, which implements this combination, is studied, showing substantial reduction over traditional search, not only in the number of reachable states, but directly in the amount of memory and time used. We also describe how to apply partialorder modelchecking under given fairness assumptions.
Property preserving abstractions for the verification of concurrent systems
 FORMAL METHODS IN SYSTEM DESIGN, VOL 6, ISS
, 1995
"... We study property preserving transformations for reactive systems. The main idea is the use of simulations parameterized by Galois connections ( �), relating the lattices of properties of two systems. We propose and study a notion of preservation of properties expressed by formulas of a logic, by a ..."
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Cited by 137 (5 self)
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We study property preserving transformations for reactive systems. The main idea is the use of simulations parameterized by Galois connections ( �), relating the lattices of properties of two systems. We propose and study a notion of preservation of properties expressed by formulas of a logic, by a function mapping sets of states of a system S into sets of states of a system S'. We give results on the preservation of properties expressed in sublanguages of the branching timecalculus when two systems S and S' are related via h � isimulations. They can be used to verify a property for a system by verifying the same property on a simpler system which is an abstraction of it. We show also under which conditions abstraction of concurrent systems can be computed from the abstraction of their components. This allows a compositional application of the proposed verification method. This is a revised version of the papers [2] and [16] � the results are fully developed in [27].
A Partial Approach to Model Checking
 INFORMATION AND COMPUTATION
, 1994
"... This paper presents a modelchecking method for lineartime temporal logic that can avoid most of the state explosion due to the modelling of concurrency by interleaving. The method relies on the concept of Mazurkiewicz's trace as a semantic basis and uses automatatheoretic techniques, including aut ..."
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Cited by 113 (5 self)
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This paper presents a modelchecking method for lineartime temporal logic that can avoid most of the state explosion due to the modelling of concurrency by interleaving. The method relies on the concept of Mazurkiewicz's trace as a semantic basis and uses automatatheoretic techniques, including automata that operate on words of ordinality higher than \omega.
Strategies for Temporal Resolution
, 1995
"... Verifying that a temporal logic specification satisfies a temporal property requires some form of theorem proving. However, although proof procedures exist for such logics, many are either unsuitable for automatic implementation or only deal with small fragments of the logic. In this thesis the algo ..."
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Cited by 94 (42 self)
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Verifying that a temporal logic specification satisfies a temporal property requires some form of theorem proving. However, although proof procedures exist for such logics, many are either unsuitable for automatic implementation or only deal with small fragments of the logic. In this thesis the algorithms for, and strategies to guide, a fully automated temporal resolution theorem prover are given, proved correct and evaluated. An approach to applying resolution, a proof method for classical logics suited to mechanisation, to temporal logics has been developed by Fisher. The method involves translation to a normal form, classical style resolution within states and temporal resolution over states. It has only one temporal resolution rule and is therefore particularly suitable as the basis of an automated temporal resolution theorem prover. As the application of the temporal resolution rule is the most costly part of the method, involving search amongst graphs, different algorithms on w...
Bisimulation and Model Checking
 In Proc. Compositionality Workshop, LNCS 1536
, 1999
"... State space minimization techniques are crucial for combating state explosion. A variety of verification tools use bisimulation minimization to check equivalence between systems, to minimize components before composition, or to reduce a state space prior to model checking. This paper explores the th ..."
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Cited by 70 (11 self)
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State space minimization techniques are crucial for combating state explosion. A variety of verification tools use bisimulation minimization to check equivalence between systems, to minimize components before composition, or to reduce a state space prior to model checking. This paper explores the third use in the context of verifying invariant properties. We consider three bisimulation minimization algorithms. From each, we produce an onthefly model checker for invariant properties and compare this model checker to a conventional one based on backwards reachability. Our comparisons, both theoretical and experimental, lead us to conclude that bisimulation minimization does not appear to be viable in the context of invariance verification, because performing the minimization requires as many, if not more, computational resources as model checking the unminimized system through backwards reachability. Keywords: Bisimulation minimization, model checking, invariant properties, onthefly...
Verification on Infinite Structures
, 2000
"... In this chapter, we present a hierarchy of infinitestate systems based on the primitive operations of sequential and parallel composition; the hierarchy includes a variety of commonlystudied classes of systems such as contextfree and pushdown automata, and Petri net processes. We then examine the ..."
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Cited by 68 (2 self)
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In this chapter, we present a hierarchy of infinitestate systems based on the primitive operations of sequential and parallel composition; the hierarchy includes a variety of commonlystudied classes of systems such as contextfree and pushdown automata, and Petri net processes. We then examine the equivalence and regularity checking problems for these classes, with special emphasis on bisimulation equivalence, stressing the structural techniques which have been devised for solving these problems. Finally, we explore the model checking problem over these classes with respect to various linear and branchingtime temporal logics.
Temporal Concurrent Constraint Programming: Denotation, Logic and Applications
, 2002
"... The tcc model is a formalism for reactive concurrent constraint programming. We present a model of temporal concurrent constraint programming which adds to tcc the capability of modeling asynchronous and nondeterministic timed behavior. We call this tcc extension the ntcc calculus. We also give a d ..."
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Cited by 65 (22 self)
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The tcc model is a formalism for reactive concurrent constraint programming. We present a model of temporal concurrent constraint programming which adds to tcc the capability of modeling asynchronous and nondeterministic timed behavior. We call this tcc extension the ntcc calculus. We also give a denotational semantics for the strongestpostcondition of ntcc processes and, based on this semantics, we develop a proof system for lineartemporal properties of these processes. The expressiveness of ntcc is illustrated by modeling cells, timed systems such as RCX controllers, multiagent systems such as the Predator /Prey game, and musical applications such as generation of rhythms patterns and controlled improvisation. 1
The Power of QDDs
, 1997
"... . Queuecontent Decision Diagrams (QDDs) are finiteautomaton based data structures for representing (possibly infinite) sets of contents of a finite collection of unbounded FIFO queues. Their intended use is to serve as a symbolic representation of the possible queue contents that can occur in the ..."
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Cited by 56 (1 self)
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. Queuecontent Decision Diagrams (QDDs) are finiteautomaton based data structures for representing (possibly infinite) sets of contents of a finite collection of unbounded FIFO queues. Their intended use is to serve as a symbolic representation of the possible queue contents that can occur in the state space of a protocol modeled by finitestate machines communicating through unbounded queues. This is done with the help of a loopfirst search, a statespace exploration technique that attempts whenever possible to compute symbolically the effect of repeatedly executing a loop any number of times, making it possible to analyze protocols with infinite state spaces though without the guarantee of termination. This paper first solves a key problem concerning the use of QDDs in this context: it precisely characterizes when, and shows how, the operations required by a loopfirst search can be applied to QDDs. Then, it addresses the problem of exploiting QDDs and loopfirst searches to broad...