A multi-paradigm language for reactive synthesis

This paper proposes a language for describing reactive synthesis problems that integrates imperative and declarative elements. The semantics is defined in terms of two-player turn-based infinite games with full information. Currently, synthesis tools accept linear temporal logic (LTL) as input, but this description is less structured and does not facilitate the expression of sequential constraints. This motivates the use of a structured programming language to specify synthesis problems. Transition systems and guarded commands serve as imperative constructs, expressed in a syntax based on that of the modeling language Promela. The syntax allows defining which player controls data and control flow, and separating a program into assumptions and guarantees. These notions are necessary for input to game solvers. The integration of imperative and declarative paradigms allows using the paradigm that is most appropriate for expressing each requirement. The declarative part is expressed in the LTL fragment of generalized reactivity(1), which admits efficient synthesis algorithms, extended with past LTL. The implementation translates Promela to input for the Slugs synthesizer and is written in Python. The AMBA AHB bus case study is revisited and synthesized efficiently, identifying the need to reorder binary decision diagrams during strategy construction, in order to prevent the exponential blowup observed in previous work.Comment: In Proceedings SYNT 2015, arXiv:1602.0078

How to Handle Assumptions in Synthesis

The increased interest in reactive synthesis over the last decade has led to many improved solutions but also to many new questions. In this paper, we discuss the question of how to deal with assumptions on environment behavior. We present four goals that we think should be met and review several different possibilities that have been proposed. We argue that each of them falls short in at least one aspect.Comment: In Proceedings SYNT 2014, arXiv:1407.493

On the complexity of heterogeneous multidimensional quantitative games

In this paper, we study two-player zero-sum turn-based games played on a finite multidimensional weighted graph. In recent papers all dimensions use the same measure, whereas here we allow to combine different measures. Such heterogeneous multidimensional quantitative games provide a general and natural model for the study of reactive system synthesis. We focus on classical measures like the Inf, Sup, LimInf, and LimSup of the weights seen along the play, as well as on the window mean-payoff (WMP) measure. This new measure is a natural strengthening of the mean-payoff measure. We allow objectives defined as Boolean combinations of heterogeneous constraints. While multidimensional games with Boolean combinations of mean-payoff constraints are undecidable, we show that the problem becomes EXPTIME-complete for DNF/CNF Boolean combinations of heterogeneous measures taken among {WMP, Inf, Sup, LimInf, LimSup} and that exponential memory strategies are sufficient for both players to win. We provide a detailed study of the complexity and the memory requirements when the Boolean combination of the measures is replaced by an intersection. EXPTIME-completeness and exponential memory strategies still hold for the intersection of measures in {WMP, Inf, Sup, LimInf, LimSup}, and we get PSPACE-completeness when WMP measure is no longer considered. To avoid EXPTIME-or PSPACE-hardness, we impose at most one occurrence of WMP measure and fix the number of Sup measures, and we propose several refinements (on the number of occurrences of the other measures) for which we get polynomial algorithms and lower memory requirements. For all the considered classes of games, we also study parameterized complexity