Practical synthesis of reactive systems from LTL specifications via parity games

Abstract

You can teach an old dog new tricks: making a classic approach structured, forward-explorative, and incremental. Abstract The synthesis of reactive systems from linear temporal logic (LTL) specifications is an important aspect in the design of reliable software and hardware. We present our adaption of the classic automata-theoretic approach to LTL synthesis, implemented in the tool Strix which has won the two last synthesis competitions (Syntcomp2018/2019). The presented approach is (1) structured, meaning that the states used in the construction have a semantic structure that is exploited in several ways, it performs a (2) forward exploration such that it often constructs only a small subset of the reachable states, and it is (3) incremental in the sense that it reuses results from previous inconclusive solution attempts. Further, we present and study different guiding heuristics that determine where to expand the on-demand constructed arena. Moreover, we show several techniques for extracting an implementation (Mealy machine or circuit) from the witness of the tree-automaton emptiness check. Lastly, the chosen constructions use a symbolic representation of the transition functions to reduce runtime and memory consumption. We evaluate the proposed techniques on the Syntcomp2019 benchmark set and show in more detail how the proposed techniques compare to the techniques implemented in other leading LTL synthesis tools.

A Unified Translation of Linear Temporal Logic to ω-Automata

“…Further, MoChiBa [73] has extended PRISM to use also LDBAs. Besides, Strix [55] uses the translations to deterministic automata for synthesis of reactive systems from LTL specifications. In particular, to obtain a deterministic parity automaton, it makes use of a compositional construction that uses the simpler LTL fragments translations whenever possible, and only falling back to the more general procedure [21] for small parts of the formula.…”

“…On top of its theoretical advantages, our translation is comparable to or even better in practice than previous translations to NBAs, LDBAs, and DRAs. The LTL synthesis tool Strix [55,57], which won the LTL synthesis track of the 2018, 2019, and 2020 editions of the SyntComp competition [36], picks from a portfolio of the translations presented here (LDBAs, DBAs, DCAs, DRAs) and the LDBA-to-DPA algorithm of Reference [21] to translate formulas into DPAs. Moreover, we show that the special structure of the LDBAs delivered by the translation makes them suitable for the verification of probabilistic models.…”

“…As a result, the tool Strix [55,57], based on the latter construction, has recently won all LTL tracks of the synthesis competition SyntComp [36]. Besides, the preserved semantic labelling of the states of the automata allows for heuristics guiding the exploration of the on-the-fly generated automaton [55] together with efficient deployment of learning-based algorithms and lifelong learning paradigms in LTL synthesis [42]. Such efforts have a great impact on the practical performance of solutions to this 2-EXPTIME-complete problem.…”

“…Such semantics-based reductions cannot be applied in general to Safra-based constructions, because the semantic structure gets lost in translation. Besides, semantic description of states can be further exploited for generic [55] and learning-based heuristics [42] to speed up synthesis.…”

Practical “Paritizing” of Emerson-Lei Automata

“…Our motivation comes from one such problem: reactive synthesis from LTL specifications, i.e., building an I/O transducer whose input and output signals satisfy an LTL specification ϕ [4]. The high-level approach taken by our ltlsynt tool [20], or even by the SyntComp'19 winner Strix [18], is to transform the LTL formula into a deterministic transition-based parity automaton (DTPA), interpret the DTPA as a parity game by splitting the alphabet on inputs and outputs, then solve the game and use any winning strategy to synthesize a transducer. Let us zoom on the first step: transforming an LTL formula into a DTPA.…”