The complexity of propositional linear temporal logics

Sistla, A. Prasad; Clarke, Edmund M.

doi:10.1145/3828.3837

Cited by 860 publications

(389 citation statements)

References 7 publications

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“…In particular they define business process patterns corresponding to compliance requirements. The problem of determining whether a business process is compliant reduces to a model checking problem in the underlaying logic, LTL, which is known to be PSPACE-complete [16]. Accordingly, such systems adopt a more complex (and more expressive) formalism.…”

Section: Resultsmentioning

confidence: 99%

Business Process Regulatory Compliance is Hard

Tosatto

Governatori

Kelsen

2015

IEEE Trans. Serv. Comput.

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Abstract-Verifying whether a business process is compliant with a regulatory framework is a difficult task. In the present paper we prove the hardness of the business process regulatory compliance problem by taking into account a sub-problem of the general problem. This limited problem allows to verify only the compliance of structured processes with respect to a regulatory framework composed of a set of conditional obligations including a deadline. Experimental evidence from existing studies shows that compliance is a difficult task. In this paper, despite considering a sub-problem of the general problem, we provide some theoretical evidence of the difficulty of the task. In particular we show that the source of the complexity lies in the core language of verifying conditional obligations with a deadline. We prove that for this simplified case verifying partial compliance belongs to the class of NP-complete problems, and verifying full compliance belongs to the class of coNP-complete problems. Thus by proving the difficulty of a simplified compliance problem we prove that the general problem of verifying business process regulatory compliance is hard.

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Section: Resultsmentioning

confidence: 99%

Business Process Regulatory Compliance is Hard

Tosatto

Governatori

Kelsen

2015

IEEE Trans. Serv. Comput.

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“…The main advantage of temporal logic is that several computational problems can be solved more efficiently than in the case of using first-order formulae [64,65], see also [22,24]. A huge variety of fragments defined in terms of temporal logic has been researched.…”

Section: More Logicsmentioning

confidence: 99%

A Survey on Small Fragments of First-Order Logic Over Finite Words

Diekert

Gastin

Kufleitner

2008

Int. J. Found. Comput. Sci.

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We consider fragments of first-order logic over finite words. In particular, we deal with first-order logic with a restricted number of variables and with the lower levels of the alternation hierarchy. We use the algebraic approach to show decidability of expressibility within these fragments. As a byproduct, we survey several characterizations of the respective fragments. We give complete proofs for all characterizations and we provide all necessary background. Some of the proofs seem to be new and simpler than those which can be found elsewhere. We also give a proof of Simon's theorem on factorization forests restricted to aperiodic monoids because this is simpler and sufficient for our purpose. PreambleThere are many brilliant surveys on formal language theory [36,41,48,85,86]. Quite many surveys cover first-order and monadic second-order definability. But there are also nuggets below. There are deep theorems on proper fragments of firstorder definability. The most prominent fragment is FO 2 ; it is the class of languages which are defined by first-order sentences which do not use more than two names for variables. Although various characterizations are known for this class, there seems to be little knowledge in a broad community. A reason for this is that the proofs are spread over the literature and even in the survey [76] many proofs are referred to the original literature which in turn is sometimes quite difficult to read. This is our starting point. We restrict our attention to fragments strictly below first-order definability. We concentrate on algebraic and formal language theoretic characterizations for those fragments where decidability results are known, although we do not discuss complexity issues here. We give a clear preference to full proofs rather than to state all results. In our proofs we tried to be minimalistic. All technical concepts which are introduced are also used in the proofs for the main results.

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“…While the former has restrictions in terms of the size of models considered, the latter has problems in terms of worst-case complexity. For propositional (discrete, linear) temporal logics, the decision procedure is already PSPACE [37]. In spite of this, a range of useful tools have been developed, with our clausal resolution approach [12] having been shown to be particularly effective [26].…”

Section: Temporal Toolsmentioning

confidence: 99%

Monodic ASMs and Temporal Verification

Fisher

Lisitsa

2004

Lecture Notes in Computer Science

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Abstract. In this paper, we pursue the goal of automatic deductive verification for certain classes of ASM. In particular, we base our work on a translation of general ASMs to full first-order temporal logic. While such a logic is, in general, not finitely axiomatisable, recent work has identified a fragment, termed the monodic fragment, that is finitely axiomatisable and many of its subfragments are decidable. Thus, in this paper, we define a class of monodic ASMs whose semantics in terms of temporal logic fits within the monodic fragment. This, together with recent work on clausal resolution methods for monodic fragments, allows us to carry out temporal verification of monodic ASMs. The approach is illustrated by the deductive verification of FloodSet algorithm for Consensus problem, and Synapse N+1 cache coherence protocol; both are specified by monodic ASMs.

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The complexity of propositional linear temporal logics

Cited by 860 publications

References 7 publications

Business Process Regulatory Compliance is Hard

Business Process Regulatory Compliance is Hard

A Survey on Small Fragments of First-Order Logic Over Finite Words

Monodic ASMs and Temporal Verification

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