The complexity of propositional linear temporal logics

Sistla, A. Prasad; Clarke, Edmund M.

doi:10.1145/800070.802189

Cited by 178 publications

(246 citation statements)

References 11 publications

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“…We recall that M, s |= φ where M is a Kripke structure and φ is an LTL formula whenever there is an infinite path σ starting from s such that σ |= φ. Hence, for linear-time logics (LTL and its fragments) we follow [51] and assume, for the sake of uniformity, that the question "M, s |= φ?" asks for the existence of a path from s that verifies φ, which is dual to the universal "all paths from s" formulation commonly used in applications.…”

Section: Linear Timementioning

confidence: 99%

“…LTL model checking for non-flat systems is PSPACE-complete (consequence of [51]). In our parameterized setting we have: PROOF.…”

Section: Linear Timementioning

confidence: 99%

“…Investigating the computational complexity of model checking started with [51], and today the complexity of the main model-checking problems is known 2 , see [50] for a survey. This led to the understanding that, in practice, the source of intractability is the size of the model and not the size of the property to be checked.…”

Section: Introductionmentioning

confidence: 99%

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A Parametric Analysis of the State Explosion Problem in Model Checking

2002

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In model checking, the state-explosion problem occurs when one checks a non-flat system, i.e., a system implicitly described as a synchronized product of elementary subsystems. In this paper, we investigate the complexity of a wide variety of modelchecking problems for non-flat systems under the light of parameterized complexity, taking the number of synchronized components as a parameter. We provide precise complexity measures (in the parameterized sense) for most of the problems we investigate, and evidence that the results are robust.

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Section: Linear Timementioning

confidence: 99%

“…LTL model checking for non-flat systems is PSPACE-complete (consequence of [51]). In our parameterized setting we have: PROOF.…”

Section: Linear Timementioning

confidence: 99%

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A Parametric Analysis of the State Explosion Problem in Model Checking

2002

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“…All in all, given an ETL can be solved in polynomial space. Matching lower bounds are easy to show, hence the problems are PSPACE-complete, as are the ones for ETLc or LTL [SC85]. It follows that the in spite of the succinctness of two-way and alternating automata, the advantages of ETL £ ¡ are obtained without a major increase in space complexity.…”

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confidence: 91%

Extended Temporal Logic Revisited

Kupferman

Piterman

Vardi

2001

Lecture Notes in Computer Science

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Abstract.A key issue in the design of a model-checking tool is the choice of the formal language with which properties are specified. It is now recognized that a good language should extend linear temporal logic with the ability to specify all -regular properties. Also, designers, who are familiar with finite-state machines, prefer extensions based on automata than these based on fixed points or propositional quantification. Early extensions of linear temporal logic with automata use nondeterministic Büchi automata. Their drawback has been inability to refer to the past and the asymmetrical structure of nondeterministic automata. In this work we study an extension of linear temporal logic, called ETL © , that uses two-way alternating automata as temporal connectives. Two-way automata can traverse the input word back and forth and they are exponentially more succinct than one-way automata. Alternating automata combine existential and universal branching and they are exponentially more succinct than nondeterministic automata. The rich structure of two-way alternating automata makes ETL © a very powerful and convenient logic. We show that ETL © formulas can be translated to nondeterministic Büchi automata with an exponential blow up. It follows that the satisfiability and model-checking problems for ETL © are PSPACEcomplete, as are the ones for LTL and its earlier extensions with automata. So, in spite of the succinctness of two-way and alternating automata, the advantages of ETL © are obtained without a major increase in space complexity. The recent acceptance of alternating automata by the industry and the development of symbolic procedures for handling them make us optimistic about the practicality of ETL © .

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“…While LTL and CTL * have exponential verification procedures, CTL can be checked in linear time w.r.t. the length of the specification and the size of the system [7,8]. On the other hand, some properties can be specified in a more succinct and more readable manner in LTL.…”

Section: Introductionmentioning

confidence: 99%

Model Checking on Product Structures

Schneider

1998

Formal Methods in Computer-Aided Design

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We present an algorithm for checking CTL formulas in Kripke structures with side conditions, where the side conditions define new variables in terms of path formulas. Given any CTL formula where the defined variables may occur, the presented algorithm will determine the set of states where the CTL * formula holds that is obtained by replacing each new variable defined by a side condition by its definition. The basic idea of our algorithm is to translate each side condition to a Kripke structure that encodes precisely the definition of the new variable. After that, we compute the products of these structures with the given structure and use a generalization of the well-known CTL model checking procedure. The presented model checking procedure can still be implemented as a symbolic model checking procedure (e.g. with BDDs). We moreover show how each CTL * model checking problem can be translated efficiently to a CTL model checking problem with side conditions, and hence show that the method can be used to construct efficient CTL * and LTL model checking procedures. Moreover, it is shown that for LTL model checking, we can still use standard CTL model checking procedures instead of our generalized version.

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The complexity of propositional linear temporal logics

Cited by 178 publications

References 11 publications

A Parametric Analysis of the State Explosion Problem in Model Checking

A Parametric Analysis of the State Explosion Problem in Model Checking

Extended Temporal Logic Revisited

Model Checking on Product Structures

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