On the Expressive Power of Invariants in Parametric Timed Automata

Abstract

The verification of systems combining hard timing constraints with concurrency is challenging. This challenge becomes even harder when some timing constants are missing or unknown. Parametric timed formalisms, such as parametric timed automata (PTAs), tackle the synthesis of such timing constants (seen as parameters) for which a property holds. Such formalisms are highly expressive, but also undecidable, and few decidable subclasses were proposed. We propose here a syntactic restriction on PTAs consisting in removing guards (constraints on transitions) to keep only invariants (constraints on locations). While this restriction preserves the expressiveness of PTAs (and therefore their undecidability), an additional restriction on the type of constraints allows to not only prove decidability, but also to perform the exact synthesis of parameter valuations satisfying reachability. This formalism, that seems trivial at first sight as it benefits from the decidability of the reachability problem with a better complexity than Timed Automata (TAs), suffers from the undecidability of the whole TCTL logic that TAs, on the contrary enjoy. We believe our formalism allows for an interesting trade-off between decidability and practical expressiveness and is therefore promising. We show its applicability in a small case study.

Configuring Timing Parameters to Ensure Execution-Time Opacity in Timed Automata

“…We finally define weak ET-opacity, not considered in [9], but defined in the specific context of expiring opacity [8]. We therefore reintroduce this definition in the "normal" opacity setting considered in this section, in the following:…”

“…1. defining and studying ET-opacity problems [9] in TAs (Section 3) and PTAs (Section 4); these notions from [9] are presented differently (including the problem names) in this paper for sake of consistency; and 2. defining and studying expiring execution-time opacity (exp-ET-opacity) problems [8] in both TAs and PTAs (Section 5).…”

“…In Tables 1 and 2, we summarize the decidability results recalled in this paper for ET-opacity and exp-ET-opacity. We denote a problem with a green check if it is decidable, with a red cross if it is undecidable, and with a yellow question mark if it is open (or not considered in the aforementioned papers [9,8]). We emphasize using a bold font the original results of this paper.…”

“…Table 3: Summary of the definitions for ET-opacity and expiring ET-opacity [9,8] Secret runs Non-secret runs ET-opacity Runs visiting the private location (= private runs)…”

“…The aforementioned negative result leaves hope only if the definition or the setting is changed, which was done in three main lines of works. The different studied options were to reduce the expressiveness of the formalism [36,37], to constrain the system to evolve in a time-bounded setting [4] or to consider a weaker attacker, who has access only to the execution time [9,8], rather than to all observable actions with their timestamps. We present here a summary of our recent works in this latter setting [9,8].…”