Behavioral Cartography of Timed Automata

Abstract

Abstract. We aim at finding a set of timing parameters for which a given timed automaton has a "good" behavior. We present here a novel approach based on the decomposition of the parametric space into behavioral tiles, i.e., sets of parameter valuations for which the behavior of the system is uniform. This gives us a behavioral cartography according to the values of the parameters. It is then straightforward to partition the space into a "good" and a "bad" subspace, according to the behavior of the tiles. We extend this method to probabilistic systems, allowing to decompose the parametric space into tiles for which the minimal (resp. maximal) probability of reaching a given location is uniform. An implementation has been made, and experiments successfully conducted.

Distributed Behavioral Cartography of Timed Automata

“…In [AF10], we proposed the behavioral cartography algorithm (BC ), that covers a bounded parameter domain with tiles, i.e., parametric zones of uniform discrete behavior. BC relies on iterative calls to another algorithm (the "inverse method" IM ), that builds a tile from a reference valuation (or point).…”

“…IM was extended in [AF10] into the behavioral cartography algorithm (BC ): given a PTA A and a bounded parameter domain D (usually a rectangle in M dimensions), by repeatedly calling IM on (some of the) integer points of D (of which there is a finite number), one is able to cover D with tiles. Hence, the result is a cartography of the tiles in which the discrete behavior is uniform in A.…”

“…We recall the original cartography algorithm from [AF10] in Algorithm 1. We extend the |= notation as follows:-given a set S of constraints, we write π |= S if there exists some K in S such that π |= K.…”

Synthesising optimal timing delays for timed I/O automata

“…They consider the special case of L/U automata for which they show that the emptiness problem is decidable. [4,5] describe an approach to derive the constraints on parameters such that the behaviours of the timed automata are time-abstract equivalent, starting from a reference valuation rather than a logic formula. In [10], undecidability for parametric reachability problem is proved.…”

“…We consider properties expressed in counting metric temporal logic, which can count the number of actions in a given interval of time. For instance, the formula ϕ = # 7 5 VP 1 states that the number of VP actions in the interval of time [5,7] is greater than 1. There may be more than one set, possibly many sets, of parameter values that satisfy the set of linear inequalities.…”