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Solving Second-Order Constraints with Program Synthesis

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In this talk I’ll summarise my work on expressing and solving program analysis problems as second-order satisfiability with an emphasis on the solving part. I’ll start by introducing a decidable fragment of second-order logic that is expressive enough to capture numerous program analysis problems (e.g. safety proving, bug finding, termination and non-termination proving, superoptimisation, complexity analysis). Subsequently, I will describe the solver we have built for this fragment, which is based on program synthesis. In particular, we rely on the synthesis of finite state programs, which we showed to be NEXPTIME -complete. Our synthesiser is an instance of the Counterexample Guided Inductive Synthesis (CEGIS) framework and can be used to synthesise C programs from a specification written in a subset of C. For this purpose it makes use of explicit proof search, symbolic bounded model checking and genetic programming. I’ll conclude with some experimental results.

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