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A challenging problem for autonomous systems is to synthesize a reactivecontroller that conforms to a set of given correctness properties. Lineartemporal logic (LTL) provides a formal language to specify the desiredbehavioral properties of systems. In applications in which the specificationsoriginate from various aspects of the system design, or consist of a large setof formulas, the overall system specification may be unrealizable. Driven bythis fact, we develop an optimization variant of synthesis from LTL formulas,where the goal is to design a controller that satisfies a set of hardspecifications and minimally violates a set of soft specifications. To thatend, we introduce a value function that, by exploiting the LTL semantics,quantifies the level of violation of properties. Inspired by the idea ofbounded synthesis, we fix a bound on the implementation size and search for animplementation that is optimal with respect to the said value function. Wepropose a novel maximum satisfiability encoding of the search for an optimalimplementation (within the given bound on the implementation size). Weiteratively increase the bound on the implementation size until a terminationcriterion, such as a threshold over the value function, is met.

Reactive Synthesis with Maximum Realizability of Linear Temporal Logic Specifications