Maximal Synthesis for Hennessy-Milner Logic

Abstract

Abstract-We present a solution for the synthesis on Kripkestructures with labelled transitions, with respect to HennessyMilner Logic. This encompasses the definition of a theoretical framework that is able to express how such a transition system should be modified in order to satisfy a given HMLformula. The transition system is mapped under bisimulation equivalence onto a recursive structure, thereby unfolding up to the applicable reach of a given HML-formula. Operational rules define the required adaptations to ensure validity upon this structure. Synthesis might result in multiple valid adaptations which are all related to the original transition system via simulation. The set of synthesized products contains an outcome which is maximal with respect to all deterministic simulants which satisfy the HML-formula.

Maximal Synthesis for Hennessy-Milner Logic with the Box Modality

“…Synthesis as presented in Van Hulst et al (2013) possibly results in a set of multiple maximal solutions, in particular for disjunctive formulas. As these solutions are essentially incomparable, a choice was made in Van Hulst et al (2013) to include all of these in the result set.…”

“…Synthesis as presented in Van Hulst et al (2013) possibly results in a set of multiple maximal solutions, in particular for disjunctive formulas. As these solutions are essentially incomparable, a choice was made in Van Hulst et al (2013) to include all of these in the result set. This is a key difference between the research presented in this paper and the unrestricted setting for disjunctive formulas in Van Hulst et al (2013).…”

“…Propositional temporal formulas are also used in Manna and Wolper (1984) in order to synthesize synchronizations in communicating processes using a tableau-like method. This method employs a separate unfolding step, similar to Van Hulst et al (2013). Using ready simulation as a behavioral relation, the work in Lüttgen and Vogler (2011) embeds a temporal specification in a Logic LTS.…”

“…In Van Hulst et al (2013) we proposed a recursive construction for synthesis for Hennessy-Milner Logic, which lacks the ability to express that a property holds for all reachable states. This method incorporates a separate unfolding step up to the applicable reach of the synthesized modal formula.…”

“…As these solutions are essentially incomparable, a choice was made in Van Hulst et al (2013) to include all of these in the result set. This is a key difference between the research presented in this paper and the unrestricted setting for disjunctive formulas in Van Hulst et al (2013).…”