Validity-Guided Synthesis of Reactive Systems from Assume-Guarantee Contracts
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Automated synthesis of reactive systems from spe- cifications has been a topic of research for decades. Recently, a variety of approaches have been proposed to extend synt- hesis of reactive systems from propositional specifications to- wards specifications over rich theories. Such approaches include inductive synthesis, template-based synthesis, counterexample- guided synthesis, and predicate abstraction techniques. In this paper, we propose a novel approach to program synthesis based on the validity of forall-exists formulas. The approach is inspired by verification techniques that construct inductive invariants, like IC3 / Property Directed Reachability, and is completely automated. The original problem space is recursively refined by blocking out regions of unsafe states, with the goal being the discovery of a fixpoint that describes safe reactions. If such a fixpoint is found, we construct a witness that is directly translated into an implementation. We have implemented the algorithm in the JKIND model checker, and exercised it against contracts written using the Lustre specification language. Experimental results show how the new algorithm yields better performance as well as soundness for "unrealizable" results when compared to JKIND's existing synthesis procedure, an approach based on the construction of k-inductive proofs of realizability.
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