Synthesis of Infinite-State Systems with Random Behavior

Diversity in the exhibited behavior of a given system is a desirable characteristic in a variety of application contexts. Synthesis of conformant implementations often proceeds by discovering witnessing Skolem functions, which are traditionally deterministic. In this paper, we present a novel Skolem extraction algorithm to enable synthesis of witnesses with random behavior and demonstrate its applicability in the context of reactive systems. The synthesized solutions are guaranteed by design to meet the given specification, while exhibiting a high degree of diversity in their responses to external stimuli. Case studies demonstrate how our proposed framework unveils a novel application of synthesis in model-based fuzz testing to generate fuzzers of competitive performance to general-purpose alternatives, as well as the practical utility of synthesized controllers in robot motion planning problems.