Reactive synthesis is an automated procedure to obtain a correct-by-construction reactive system from its temporal logic specification. Two of the main challenges in bringing reactive synthesis to practice are its very high worst-case complexity and the difficulty of writing declarative specifications using basic LTL operators. To address the first challenge, researchers have suggested the GR(1) fragment of LTL, which has an efficient poly-nomial time symbolic synthesis algorithm. To address the second challenge, specification languages include higher-level constructs that aim at allowing engineers to write succinct and readable specifications. One such construct is the triggers operator, as supported, e.g., in the Property Specification Language (PSL). In this work we introduce triggers into specifications for reactive synthesis. The effectiveness of our contribution relies on a novel encoding of regular expressions using symbolic finite automata (SFA) and on a novel semantics for triggers that, in contrast to PSL triggers, admits an efficient translation into GR(1). We show that our triggers are expressive and succinct, and prove that our encoding is optimal. We have implemented our ideas on top of the Spectra language and synthesizer. We demonstrate the usefulness and effectiveness of using triggers in specifications for synthesis, as well as the challenges involved in using them, via a study of more than 300 triggers written by undergraduate students who participated in a project class on writing specifications for synthesis. To the best of our knowledge, our work is the first to introduce triggers into specifications for reactive synthesis.

Abstract Reactive synthesis is an automated procedure to obtain a correct-by-construction reactive system from its temporal logic specification. GR(1) is an expressive assume-guarantee fragment of LTL that enables efficient synthesis and has been recently used in different contexts and application domains. A common form of providing system's requirements is through use cases, which are existential in nature. However, GR(1), as a fragment of LTL, is limited to universal properties. In this paper we introduce GR(1)*, which extends GR(1) with existential guarantees. We show that GR(1)* is strictly more expressive than GR(1) as it enables the expression of guarantees that are inexpressible in LTL. We solve the realizability problem for GR(1)* and present a symbolic strategy construction algorithm for GR(1)* specifications. Importantly, in comparison to GR(1), GR(1)* remains efficient: the time complexity of our realizability checking and synthesis procedures for GR(1)* is identical to the time complexity of the known corresponding procedures for GR(1).