Robust Analysis of Timed Automata Via Channel Machines

Abstract

Abstract. Whereas formal verification of timed systems has become a very active field of research, the idealised mathematical semantics of timed automata cannot be faithfully implemented. Several works have thus focused on a modified semantics of timed automata which ensures implementability, and robust model-checking algorithms for safety, and later LTL properties have been designed. Recently, a new approach has been proposed, which reduces (standard) model-checking of timed automata to other verification problems on channel machines. Thanks to a new encoding of the modified semantics as a network of timed systems, we propose an original combination of both approaches, and prove that robust model-checking for coFlat-MTL, a large fragment of MTL, is EXPSPACE-Complete.

Robust Model-Checking of Timed Automata via Pumping in Channel Machines

“…In fact, the greatest constant in is now multiplied by 1 0 and the regions of 0 can still be encoded in polynomial space. The problem is PSPACE-hard since it is already for timed automata with progress cycles [5].…”

“…A simpler over-approximation, the so-called enlarged semantics was also studied, which models the imprecisions by relaxing all clock constraints of the automaton of the form ∈ [ , ] to ∈ [ − , + ] for some > 0. The problem of robust model-checking, that is determining whether for some > 0, the enlarged semantics satisfies a given property, was first solved for safety properties [14,8], then for linear temporal logic (LTL) [4] (both in PSPACE, which is the complexity of the problem in the exact semantics), and for a timed extension of LTL [5]. These robust model-checking algorithms are all valid for a particular class of timed automata, namely, those in which all cycles are progress cycles.…”

“…In order to establish our results, we develop proof techniques based on the encoding of the states of timed automata with channel machines, introduced in [3], and used in [5] in the context of robustness. In this encoding, a word represents the content of a FIFO channel, which roughly contains all clock symbols ordered by their fractional parts.…”

“…It turns out that the finitary representation by these words capture well the behaviour of timed automata under enlargement. This was used in [5] to design a robust model-checking algorithm for a timed extension of LTL. We further develop these techniques and prove a pumping lemma for those channel machines, which preserves -regular properties.…”

Untimed Language Preservation in Timed Systems

“…An important problem is then to determine whether a given timed automaton is implementable, that is, whether its implementation is correct with respect to a given property, in a fast enough hardware. For this purpose, robust model-checking, which asks for the existence of a parameter ∆ under which the resulting enlarged semantics is correct, was proven decidable for safety properties [15,11] and for richer lineartime properties [8,9]. If robust model-checking succeeds, then the given timed automaton is implementable in a fast enough hardware in the sense of [12].…”