Reducing Clocks in Timed Automata while Preserving Bisimulation

Abstract

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

An automated system repair framework with signal temporal logic

“…Both repair procedures add two new clocks and up to four unique simple clock constraints (c 1 < c 2 , c 1 > c 2 , c 1 = c 2 , c 1 < v(b)) to the model; therefore, the number of clocks and the number of unique simple constraints in the repaired TA increase linearly with the number of sub-formulae synthesized by Algorithm 1. The increase in the number of clocks can be reduced by applying a clock reduction algorithm [22,38]. In the case studies, we run the algorithm from [38] on the repaired models and report the results.…”

“…Our framework repairs the model in 1.11s (0.94s for Algorithm 1), increases the number of clocks to six (three for each instance of the model), and running [38] on the repaired model reduces this number to four (two for each instance of the model). Notice that, integrating expression simplification methods [22] into [38] can further reduce the number of clocks to two (one for each instance of the model) by automating the presented detailed clock analysis.…”

Quasi-Equal Clock Reduction On-the-Fly

“…The general case (whether there exists a language equivalent timed automaton with fewer clocks than a given one) is undecidable [9]. Guha et al [10] have shown that a minimal timed bisimilar automaton is effectively constructable, the procedure is expensive in the number of locations and time. Saeedloei et al [17] minimise under further constraints (same graph, same pattern of clock resets and uses).…”