Iterative Bounded Synthesis for Efficient Cycle Detection in Parametric Timed Automata

Abstract

We study semi-algorithms to synthesise the constraints under which a Parametric Timed Automaton satisfies some liveness requirement. The algorithms traverse a possibly infinite parametric zone graph, searching for accepting cycles. We provide new search and pruning algorithms, leading to successful termination for many examples. We demonstrate the success and efficiency of these algorithms on a benchmark. We also illustrate parameter synthesis for the classical Bounded Retransmission Protocol. Finally, we introduce a new notion of completeness in the limit, to investigate if an algorithm enumerates all solutions.

IMITATOR 3: Synthesis of Timing Parameters Beyond Decidability

“…-using aggressive optimizations and abstractions (e.g., [11,19,45]), leading to termination for most case studies in practice; -outputting over-or under-approximated results, i.e., the set of synthesized parameter valuations may be larger or smaller than the exact result.…”

“…A new feature of IMITATOR 3 is cycle synthesis, i.e., parameter valuations for which there exists an infinite run, possibly passing infinitely often by a given discrete state (Büchi condition). IMITATOR uses by default an original algorithm by Laure Petrucci and Jaco van de Pol based on NDFS extended with parametric subsumption and pruning [45] (other algorithms, such as BFS, are also available [11]). In our running example , one can ask for the valuations for which the researcher infinitely often writes papers after drinking (at least) 3 coffees for each of them.…”

“…-the parametric verification of an asynchronous memory circuit by ST-Microelectronics (from a model described in [37]), -verification of parametric scheduling problems by Astrium Space Transportation [40] and ArianeGroup SAS [13], -analysis of music scores [38], -verifying the multi-processor image processing system of an unmanned aerial aircraft with uncertain periods, as a benchmark made public by Thales [46], -parametric pattern matching and monitoring of logs from the automative industry [20], -synthesis of timing/cost parameters in attack-fault trees [23,31], -testing product lines using parametric constraints [44], -verification of an industrial asynchronous leader election algorithm by Thales using IMITATOR combined with abstractions [18], -performing parametric opacity analyses for timed automata [30], and -synthesis of parameter valuations guaranteeing liveness properties for the Bounded Retransmission Protocol [11].…”

“…Acknowledgement. While the author has been the main developer of IMITATOR since 2008, several colleagues brought very valuable enhancements, notably Camille Coti and Sami Evangelista [14] (on distributed algorithms), Nguy Hoàng Gia [27] (on non-Zeno algorithms), Vincent Bloemen [12] (on minimal-time synthesis), Laure Petrucci and Jaco van de Pol [11] (on NDFS-based cycle synthesis), and Jaime Arias for multiple practical enhancements. Many thanks to Dylan Marinho for a careful rereading of this paper, and to Stephan Merz for useful suggestions.…”

Tweaking the Odds in Probabilistic Timed Automata

“…For this model, even basic problems like the existence of a parameter valuation under which a goal state is reachable are undecidable [3,4], except in restricted cases such as bounded integer values [37] or L/U TA [35]. Research on cpTA remains active to this day; recent work, for example, proposes a semi-algorithm for liveness [5]. The inverse method for cpTA [6] extends one parameter valuation v 0 to a set of valuations V ⊇ { v 0 } such that all v ∈ V satisfy the same given reachability properties.…”