From LTL and Limit-Deterministic B\"uchi Automata to Deterministic Parity Automata

Controller synthesis for general linear temporal logic (LTL) objectives is a challenging task. The standard approach involves translating the LTL objective into a deterministic parity automaton (DPA) by means of the Safra-Piterman construction. One of the challenges is the size of the DPA, which often grows very fast in practice, and can reach double exponential size in the length of the LTL formula. In this paper we describe a single exponential translation from limit-deterministic B\"uchi automata (LDBA) to DPA, and show that it can be concatenated with a recent efficient translation from LTL to LDBA to yield a double exponential, \enquote{Safraless} LTL-to-DPA construction. We also report on an implementation, a comparison with the SPOT library, and performance on several sets of formulas, including instances from the 2016 SyntComp competition

Exploiting the Temporal Logic Hierarchy and the Non-Confluence Property for Efficient LTL Synthesis

The classic approaches to synthesize a reactive system from a linear temporal logic (LTL) specification first translate the given LTL formula to an equivalent omega-automaton and then compute a winning strategy for the corresponding omega-regular game. To this end, the obtained omega-automata have to be (pseudo)-determinized where typically a variant of Safra's determinization procedure is used. In this paper, we show that this determinization step can be significantly improved for tool implementations by replacing Safra's determinization by simpler determinization procedures. In particular, we exploit (1) the temporal logic hierarchy that corresponds to the well-known automata hierarchy consisting of safety, liveness, Buechi, and co-Buechi automata as well as their boolean closures, (2) the non-confluence property of omega-automata that result from certain translations of LTL formulas, and (3) symbolic implementations of determinization procedures for the Rabin-Scott and the Miyano-Hayashi breakpoint construction. In particular, we present convincing experimental results that demonstrate the practical applicability of our new synthesis procedure

One Theorem to Rule Them All: A Unified Translation of LTL into {\omega}-Automata

We present a unified translation of LTL formulas into deterministic Rabin automata, limit-deterministic B\"uchi automata, and nondeterministic B\"uchi automata. The translations yield automata of asymptotically optimal size (double or single exponential, respectively). All three translations are derived from one single Master Theorem of purely logical nature. The Master Theorem decomposes the language of a formula into a positive boolean combination of languages that can be translated into {\omega}-automata by elementary means. In particular, Safra's, ranking, and breakpoint constructions used in other translations are not needed

Experimental Aspects of Synthesis

We discuss the problem of experimentally evaluating linear-time temporal logic (LTL) synthesis tools for reactive systems. We first survey previous such work for the currently publicly available synthesis tools, and then draw conclusions by deriving useful schemes for future such evaluations. In particular, we explain why previous tools have incompatible scopes and semantics and provide a framework that reduces the impact of this problem for future experimental comparisons of such tools. Furthermore, we discuss which difficulties the complex workflows that begin to appear in modern synthesis tools induce on experimental evaluations and give answers to the question how convincing such evaluations can still be performed in such a setting.Comment: In Proceedings iWIGP 2011, arXiv:1102.374

Approximating Optimal Bounds in Prompt-LTL Realizability in Doubly-exponential Time

We consider the optimization variant of the realizability problem for Prompt Linear Temporal Logic, an extension of Linear Temporal Logic (LTL) by the prompt eventually operator whose scope is bounded by some parameter. In the realizability optimization problem, one is interested in computing the minimal such bound that allows to realize a given specification. It is known that this problem is solvable in triply-exponential time, but not whether it can be done in doubly-exponential time, i.e., whether it is just as hard as solving LTL realizability. We take a step towards resolving this problem by showing that the optimum can be approximated within a factor of two in doubly-exponential time. Also, we report on a proof-of-concept implementation of the algorithm based on bounded LTL synthesis, which computes the smallest implementation of a given specification. In our experiments, we observe a tradeoff between the size of the implementation and the bound it realizes. We investigate this tradeoff in the general case and prove upper bounds, which reduce the search space for the algorithm, and matching lower bounds.Comment: In Proceedings GandALF 2016, arXiv:1609.0364

Synthesizing Dominant Strategies for Liveness

Reactive synthesis automatically derives a strategy that satisfies a given specification. However, requiring a strategy to meet the specification in every situation is, in many cases, too hard of a requirement. Particularly in compositional synthesis of distributed systems, individual winning strategies for the processes often do not exist. Remorsefree dominance, a weaker notion than winning, accounts for such situations: dominant strategies are only required to be as good as any alternative strategy, i.e.they are allowed to violate the specification if no other strategy would have satisfied it in the same situation. The composition of dominant strategies is only guaranteed to be dominant for safety properties, though; preventing the use of dominance in compositional synthesis for liveness specifications. Yet, safety properties are often not expressive enough. In this paper, we thus introduce a new winning condition for strategies, called delay-dominance, that overcomes this weakness of remorsefree dominance: we show that it is compositional for many safety and liveness specifications, enabling a compositional synthesis algorithm based on delay-dominance for general specifications. Furthermore, we introduce an automaton construction for recognizing delay-dominant strategies and prove its soundness and completeness. The resulting automaton is of single-exponential size in the squared length of the specification and can immediately be used for safraless synthesis procedures. Thus, synthesis of delay-dominant strategies is, as synthesis of winning strategies, in 2EXPTIME