Parametric Interrupt Timed Automata

Abstract

Abstract. Parametric reasoning is particularly relevant for timed models, but very often leads to undecidability of reachability problems. We propose a parametrised version of Interrupt Timed Automata (an expressive model incomparable to Timed Automata), where polynomials of parameters can occur in guards and updates. We prove that different reachability problems, including robust reachability, are decidable for this model, and we give complexity upper bounds for a fixed or variable number of clocks and parameters.

Language Emptiness of Continuous-Time Parametric Timed Automata

“…Parametric reachability problems for interrupt timed automata were investigated by Bérard, Haddad, Jovanović and Lime [7] with a number of positive decidability results although their model is incomparable with the formalism of timed automata studied in this paper. Other approaches include the inverse method of [17] where the authors describe a procedure for deriving constrains on parameters in order to satisfy that timed automata remain time-abstract equivalent, however, the termination of the procedure is in general not guaranteed.…”

Parametric multisingular hybrid Petri nets: Formal definitions and analysis techniques

“…In [48], a parameterized version of interrupt timed automata where polynomials of parameters can occur in guards and updates is given and it is proven that different reachability problems, including robust reachability, are decidable for this model.…”

Polynomial Interrupt Timed Automata

“…Here we show how to add three features consisting in: (1) including parameters in the expressions of guards and updates, (2) associating with each level a subset of auxiliary clocks, and (3) allowing to update clocks of lower levels than the current one. Since in the context of ITA, the first two extensions have already been studied in [9] and the third one in [10], our presentation will not be fully formalized.…”

“…The particular hierarchical structure of ITA makes them particularly well suited for modeling systems with interruptions, like real-time operating systems. ITA were extended with parameters in [9] while preserving decidability by combining the finite abstraction of original ITA with a finite partition of parameter values.…”

“…Finally, we prove that the decidability result still holds with several extensions: adding auxiliary clocks and parameters, and enriching the possible updates. In particular, parametric ITA [9] can be seen as a subclass of PolITA, and the complexity of our reachability algorithm is better than [9] (2EXPSPACE).…”