Interval Temporal Logic Model Checking: The Border Between Good and Bad HS Fragments

Bozzelli, Laura; Molinari, Alberto; Montanari, Angelo; Peron, Adriano; Sala, Pietro

doi:10.1007/978-3-319-40229-1_27

Cited by 9 publications

(26 citation statements)

References 28 publications

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“…We prove that, as expected, HS lin is not comparable with either of the branching versions, HS ct and HS st . The interesting result is that, on the other hand, HS ct is strictly included in HS st : this supports HS st , adopted in [30,31,32,33,7,9], as a reasonable and adequate semantic choice.…”

Section: Introductionsupporting

confidence: 60%

“…To this end, we restrict our attention to the fragment BE lin . Since modalities 〈B〉 and 〈E〉 only allow one to 'move' from an interval to its subintervals, BE lin actually coincides with BE st , whose MC is known to be hard for EXPSPACE [7]. Thus, in particular, it is possible to encode by means of a BE lin formula ψ cpt the (unique) computation of a deterministic Turing machine using b(n) ∈ O(2 n ) bits that, when executed on input 0 n , for some natural number n ≥ 1, counts in binary from 0 to 2 2 n − 1, by repeatedly summing 1, and finally accepts.…”

Section: Corollary 34 Hs Lin and Ltl Have The Same Expressive Powermentioning

confidence: 99%

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Interval vs. Point Temporal Logic Model Checking

Bozzelli

Molinari

Montanari

et al. 2018

ACM Trans. Comput. Logic

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In the last years, model checking with interval temporal logics is emerging as a viable alternative to model checking with standard point-based temporal logics, such as LTL, CTL, CTL * , and the like. The behavior of the system is modelled by means of (finite) Kripke structures, as usual. However, while temporal logics which are interpreted "point-wise" describe how the system evolves state-by-state, and predicate properties of system states, those which are interpreted "interval-wise" express properties of computation stretches, spanning a sequence of states. A proposition letter is assumed to hold over a computation stretch (interval) if and only if it holds over each component state (homogeneity assumption). A natural question arises: is there any advantage in replacing points by intervals as the primary temporal entities, or is it just a matter of taste?In this paper, we study the expressiveness of Halpern and Shoham's interval temporal logic (HS) in model checking, in comparison with those of LTL, CTL, and CTL * . To this end, we consider three semantic variants of HS: the state-based one, introduced by Montanari et al. in [34,30], that allows time to branch both in the past and in the future, the computationtree-based one, that allows time to branch in the future only, and the trace-based variant, that disallows time to branch. These variants are compared among themselves and to the aforementioned standard logics, getting a complete picture. In particular, we show that HS with trace-based semantics is equivalent to LTL (but at least exponentially more succinct), HS with computation-tree-based semantics is equivalent to finitary CTL * , and HS with state-based semantics is incomparable with all of them (LTL, CTL, and CTL * ). The work has been supported by the GNCS project Formal Methods for Verification and Synthesis of Discrete and Hybrid Systems. The work by A. Molinari and A. Montanari has also been supported by the project (PRID) ENCASE -Efforts in the uNderstanding of Complex interActing SystEms. * This work is an extended and revised version of [8].Structure of the paper. In Section 2, we introduce basic notation and preliminary notions. In Subsection 2.1 we define Kripke structures and interval structures, in Subsection 2.2 we recall the well-known PTLs LTL, CTL, and CTL * , and in Subsection 2.3 we present the interval temporal logic HS. Then, in Subsection 2.4 we define the three semantic variants of HS (HS st , HS ct , and HS lin ). Finally, in Subsection 2.5 we provide a detailed example which gives an intuitive account of the three semantic variants and highlights their differences. In the next three sections, we analyze and compare their expressiveness. In Section 3 we show the expressive equivalence of LTL and HS lin . Then, in Section 4 we prove the expressive equivalence of HS ct and finitary CTL * . Finally, in Section 5 we compare the expressiveness of HS st , HS ct , and HS lin . Conclusions summarize the work done and outline some directions for future research.0 ), where the set of node...

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Section: Introductionsupporting

confidence: 60%

Section: Corollary 34 Hs Lin and Ltl Have The Same Expressive Powermentioning

confidence: 99%

Interval vs. Point Temporal Logic Model Checking

Bozzelli

Molinari

Montanari

et al. 2018

ACM Trans. Comput. Logic

Self Cite

View full text Add to dashboard Cite

show abstract

“…In that paper, the authors showed that finite Kripke structures can be suitably mapped into interval-based structures, called abstract interval models, over which HS formulas can be interpreted. Then, they proved a small model theorem showing (with a non-elementary procedure) the decidability of MC for full HS, which was later proved to be EXPSPACE-hard by Bozzelli et al in [8]. 1 The MC problem for some large fragments of HS was studied in [8,37,38].…”

Section: Related Workmentioning

confidence: 99%

“…Then, they proved a small model theorem showing (with a non-elementary procedure) the decidability of MC for full HS, which was later proved to be EXPSPACE-hard by Bozzelli et al in [8]. 1 The MC problem for some large fragments of HS was studied in [8,37,38]. In [38], Molinari et al devised an EXPSPACE MC algorithm for the HS fragment AABBE (resp., AAEBE) of Allen's relations meets, met-by, starts, finishes, and started-by (resp., finished-by), which exploits the possibility of finding, for each trace (of unbounded length), an equivalent bounded-length trace representative in such a way that, while checking a property, the algorithm only needs to consider traces whose length does not exceed the given bound.…”

Section: Related Workmentioning

confidence: 99%

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Model checking for fragments of the interval temporal logic HS at the low levels of the polynomial time hierarchy

Bozzelli¹,

Molinari²,

Montanari³

et al. 2018

Information and Computation

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Some temporal properties of reactive systems, such as actions with duration, accomplishments, and temporal aggregations, which are inherently interval-based, can not be properly dealt with by the standard, point-based temporal logics LTL, CTL and CTL*, as they give a state-by-state account of system evolution. Conversely, interval temporal logics-which feature intervals, instead of points, as their primitive entities-are highly expressive formalisms for temporal representation and reasoning that naturally allow one to deal with them. In this paper, we study the model checking (MC) problem for Halpern and Shoham's modal logic of time intervals (HS), interpreted on Kripke structures, under the homogeneity assumption, according to which a proposition letter holds over a finite computation path (interval) if and only if it holds at all of its states. HS is the best known interval-based temporal logic, which has one modality for each of the 13 possible ordering relations between pairs of intervals (the so-called Allen's relations), apart from equality. We focus on the MC problem for some HS fragments featuring modalities for (a subset of) Allen's relations meet, met-by, started-by, and finished-by, showing that it is in P NP , a class to which other pointbased logics (e.g., CTL+ and FCTL) are known to belong. Additionally, we provide some complexity lower bounds to the problem. All the algorithms we propose can be efficiently implemented by means of a polynomial-time procedure which iteratively invokes a SATsolver, enabling us to directly exploit the great speed of SAT-solvers.

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An In-Depth Investigation of Interval Temporal Logic Model Checking with Regular Expressions

Bozzelli

Molinari

Montanari

et al. 2017

Software Engineering and Formal Methods

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In the last years, the model checking (MC) problem for interval temporal logic (ITL) has received an increasing attention as a viable alternative to the traditional (point-based) temporal logic MC, which can be recovered as a special case. Most results have been obtained by imposing suitable restrictions on interval labeling. In this paper, we overcome such limitations by using regular expressions to define the behavior of proposition letters over intervals in terms of the component states. We first prove that MC for Halpern and Shoham’s ITL (HS), extended with regular expressions, is decidable. Then, we show that formulas of a large class of HS fragments, namely, all fragments featuring (a subset of) HS modalities for Allen’s relations meets, met-by, starts, and started-by, can be model checked in polynomial working space (MC for all these fragments turns out to be PSPACE-complete)

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Interval Temporal Logic Model Checking: The Border Between Good and Bad HS Fragments

Cited by 9 publications

References 28 publications

Interval vs. Point Temporal Logic Model Checking

Interval vs. Point Temporal Logic Model Checking

Model checking for fragments of the interval temporal logic HS at the low levels of the polynomial time hierarchy

An In-Depth Investigation of Interval Temporal Logic Model Checking with Regular Expressions

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