A Unifying Approach to Decide Relations for Timed Automata and their Game Characterization

Guha, Shibashis; Krishna, Shankara Narayanan; Narayan, Chinmay; Arunkumar, S.

doi:10.4204/eptcs.120.5

Cited by 4 publications

(4 citation statements)

References 21 publications

(52 reference statements)

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“…In this paper, from now on, unless stated otherwise, zone graph will refer to this form of the pre-stable zone graph that is described above. An algorithmic procedure for the construction of the zone graph is given in [15].…”

Section: A Hyperplanementioning

confidence: 99%

“…We also describe the construction of the zone graph in Section 3 used in reducing the number of clocks. This construction of the zone graph has also been used in [15] for deciding several timed and time abstracted relations. In Section 4, we discuss our approach in detail along with a few examples.…”

Section: Introductonmentioning

confidence: 99%

“…A zone graph captures the behaviour of the timed automaton and hence timed bisimilarity between two TAs can be checked using their zone graphs [23,15]. This is why we create the pre-stable zone graph as described in Section 2 as it enables one to directly check timed bisimilarity on this zone graph created through Algorithm 1 following the procedure described in [15]. Lemma 5.…”

mentioning

confidence: 99%

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Reducing Clocks in Timed Automata while Preserving Bisimulation

Guha

Narayan

Arunkumar

2014

CONCUR 2014 – Concurrency Theory

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Abstract. Model checking timed automata becomes increasingly complex with the increase in the number of clocks. Hence it is desirable that one constructs an automaton with the minimum number of clocks possible. The problem of checking whether there exists a timed automaton with a smaller number of clocks such that the timed language accepted by the original automaton is preserved is known to be undecidable. In this paper, we give a construction, which for any given timed automaton produces a timed bisimilar automaton with the least number of clocks. Further, we show that such an automaton with the minimum possible number of clocks can be constructed in time that is doubly exponential in the number of clocks of the original automaton. IntroductonTimed automata [4] is a formalism for modelling and analyzing real time systems. The complexity of model checking is dependent on the number of clocks of the timed automaton (TA) [4,3]. Model checkers use the region graph or a zone graph construction for analysing reachability and other properties in timed automata. These graphs have sizes exponential in the number of clocks of the timed automaton. The algorithms for model checking in turn depend on the sizes of these graphs. Hence it is desirable to construct a timed automaton with the minimum number of clocks that preserves some property of interest (such as timed language equivalence or timed bisimilarity). Here we show that checking the existence of a timed automaton with fewer clocks that is timed bisimilar to the original timed automaton is decidable. Our method is constructive and we provide a 2-EXPTIME algorithm to construct the timed bisimilar automaton with the least possible number of clocks. We also note that if the constructed TA has a smaller number of clocks, then it implies that there exists an automaton with a smaller number of clocks accepting the same timed language.Related work: In [11], an algorithm has been provided to reduce the number of clocks of a given timed automaton. It produces a new timed automaton that is timed bisimilar to the original one. The algorithm detects a set of active clocks at every location and partitions these active clocks into classes such that

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Section: A Hyperplanementioning

confidence: 99%

Section: Introductonmentioning

confidence: 99%

mentioning

confidence: 99%

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Reducing Clocks in Timed Automata while Preserving Bisimulation

Guha

Narayan

Arunkumar

2014

CONCUR 2014 – Concurrency Theory

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“…The improved (i.e., less space-consuming) approach of Weise and Lenzkes [27] employs a variation of zone graphs, called FBS graphs, which also builds the basis for our zone-history graphs. Guha et al [13,11] also follow a zone-based approach for bisimilarity-checking on TA as well as the weaker notion of timed prebisimilarity, by employing so-called zone-valuation graphs and the notion of spans as also used in our approach. Finally, Tanimoto et al [25] employ timed bisimulation to check if a given behavioral abstraction preserves time-critical system behaviors.…”

Section: Introductionmentioning

confidence: 99%

Checking Timed Bisimulation with Bounded Zone-History Graphs -- Technical Report

Luthmann,

Göttmann,

Bacher

et al. 2019

Preprint

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Timed automata (TA) are a well-established formalism for discrete-state/continuous-time behaviors of time-critical reactive systems. Concerning the fundamental analysis problem of comparing a candidate implementation against a specification, both given as TA, it has been shown that timed trace equivalence is undecidable, whereas timed bisimulation equivalence is decidable. The corresponding proof utilizes region graphs, a finite, but very space-consuming characterization of TA semantics. In practice, most TA tools use zone graphs instead, a symbolic and generally more efficient representation of TA semantics, to automate analysis tasks. However, zone graphs only produce sound results for analysis tasks being reducible to plain reachability problems thus being too imprecise for checking timed bisimilarity. To the best of our knowledge, no practical tool is currently available for automated timed bisimilarity-checking. In this paper, we propose bounded zone-history graphs, a novel characterization of TA semantics facilitating an adjustable trade-off between precision and scalability of timed-bisimilarity checking. Our approach supports non-deterministic timed automata with silent moves. We further present experimental results gained from applying our tool TIMBRCHECK to a collection of community benchmarks, providing insights into trade-offs between precision and efficiency.

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