Reachability Preservation Based Parameter Synthesis for Timed Automata

Abstract

The synthesis of timing parameters consists in deriving conditions on the timing constants of a concurrent system such that it meets its specification. Parametric timed automata are a powerful formalism for parameter synthesis, although most problems are undecidable. We first address here the following reachability preservation problem: given a reference parameter valuation and a (bad) control state, do there exist other parameter valuations that reach this control state iff the reference parameter valuation does? We show that this problem is undecidable, and introduce a procedure that outputs a possibly underapproximated answer. We then show that our procedure can efficiently replace the behavioral cartography to partition a bounded parameter subspace into good and bad subparts; furthermore, our procedure can even outperform the classical bad-state driven parameter synthesis semi-algorithm, especially when distributed on a cluster.

Timed Automata Relaxation for Reachability

“…, e n , l n be a finite path of A, and D Ă Ψ pΔq, I Ă Ψ pIq be guard and invariant constraint sets. If the MILP constructed from A, π, D and I as defined in (12) is feasible, then l n is reachable on A ăD,I,rą with r as defined in (13).…”

Learning-Based Compositional Parameter Synthesis for Event-Recording Automata

“…Let us briefly recall the parametric reachability preservation algorithm PRP [7]. Given a set of locations L , PRP(A, v, L ) synthesizes a dense (convex) constraint K containing at least v and such that, for all v ∈ K, v (A) preserves the reachability of L in v(A).…”

“…Lemma 1 (Soundness of PRP [7]). Let A be a PTA, v a parameter valuation, and L a subset of locations.…”

“…In [12], approximated parametric reachability synthesis is performed using counter-example guided abstraction refinement (CEGAR) techniques for parametric linear hybrid automata, a class of models more expressive than PTAs. In [7], we proposed a point-based technique: instead of attacking the reachability synthesis in a brute-force manner, we iterate on (some) integer parameter valuations, and derive for each of them a constraint around this valuation that preserves the (non-)reachability of the bad locations. Although numerous iterations may be needed, each of them explores a much smaller part of the state space than the brute-force exploration of EFsynth, often resulting in a faster execution than EFsynth.…”

“…Outline Section 2 introduces the necessary preliminaries. Section 3 recalls the parametric reachability preservation [7]. Section 4 introduces parametric eventrecording automata, and proves the undecidability of the reachability emptiness problem.…”