Abstract
Reactive synthesis is an automated procedure to obtain acorrect-by-construction reactive system from its temporal logicspecification. GR(1) is an expressive assume-guarantee fragment ofLTL that enables efficient synthesis and has been recently used indifferent contexts and application domains. A common form ofproviding system's requirements is through use cases, which areexistential in nature. However, GR(1), as a fragment of LTL, islimited 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 expressionof guarantees that are inexpressible in LTL. We solve therealizability problem for GR(1)* and present a symbolic strategyconstruction algorithm for GR(1)* specifications. Importantly, incomparison to GR(1), GR(1)* remains efficient: the time complexityof our realizability checking and synthesis procedures for GR(1)* isidentical to the time complexity of the known correspondingprocedures for GR(1).
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