Quasi-Equal Clock Reduction: More Networks, More Queries

Abstract

Abstract. Quasi-equal clock reduction for networks of timed automata replaces equivalence classes of clocks which are equal except for unstable phases, i.e., points in time where these clocks differ on their valuation, by a single representative clock. An existing approach yields significant reductions of the overall verification time but is limited to so-called wellformed networks and local queries, i.e., queries which refer to a single timed automaton only. In this work we present two new transformations. The first, for networks of timed automata, summarises unstable phases without losing information under weaker well-formedness assumptions than needed by the existing approach. The second, for queries, now supports the full query language of Uppaal. We demonstrate that the cost of verifying non-local properties is much lower in transformed networks than in their original counterparts with quasi-equal clocks.

Quasi-Equal Clock Reduction On-the-Fly

“…Future work includes an extension of our algorithm on DBM T with a correspondence of the offline partial-order reduction as included in [11][12][13][14] in order to also realise the savings in number of configurations that have been observed for models with so-called simple edges (cf. [12]).…”

“…In this section, we introduce a new data-structure called DBM T that realises the idea from [11][12][13][14] to only store representative clocks for sets of quasi-equal clocks together with boolean tokens that encode whether a clock is equal to the representative or has value 0. While the syntactical transformation of [11][12][13][14] has a set of equivalence-classes wrt. quasi-equality as an input, our approach aims at detecting quasi-equality on-the-fly and exploiting phase-wise quasi-equality.…”

“…Thereby, clocks become unequal but may be quasi-equal. In previous work [11][12][13][14] we have developed a source-to-source transformation of descriptions of networks of timed automata. The transformed network reflects all properties of the Supported by the German Research Council (DFG) under grant WE 6198/1-1.…”

Quasi-dependent variables in hybrid automata

“…We have attacked this problem in our previous work [4][5][6] by proposing the notion of quasi-equal clocks for timed automata to efficiently reduce the system complexity. Intuitively, two clocks are quasi-equal if they always agree on their values except possibly when those clocks are reset.…”

Verification of Fault-Tolerant Clock Synchronization Algorithms

“…Quasi-dependency of variables is a generalization of quasi-equality of clocks [8,9,10]. Intuitively, between two variables x and y of a hybrid automaton H, there exists a quasi-dependency, namely, x quasi-depends on y via function f , if and only if at all runs of H and at all points in time, the value of x is the value of f applied to the value of y, except when the values of x and y are updated by discrete actions.…”