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Abstract. Program synthesis is the mechanised construction of software. One of the main difficulties is the efficient exploration of the very large solution space, and tools often require a user-provided syntactic restriction of the search space. We propose a new approach to program synthesis that combines the strengths of a counterexample-guided inductive synthesizer with those of a theory solver, exploring the solution space more efficiently without relying on user guidance. We call this approach CEGIS(T ), where T is a first-order theory. In this paper, we focus on one particular challenge for program synthesizers, namely the generation of programs that require non-trivial constants. This is a fundamentally difficult task for state-of-the-art synthesizers. We present two exemplars, one based on Fourier-Motzkin (FM) variable elimination and one based on first-order satisfiability. We demonstrate the practical value of CEGIS(T ) by automatically synthesizing programs for a set of intricate benchmarks.
Modern control is implemented with digital microcontrollers, embedded within a dynamical plant that represents physical components. We present a new algorithm based on counterexample guided inductive synthesis that automates the design of digital controllers that are correct by construction. The synthesis result is sound with respect to the complete range of approximations, including time discretization, quantization effects, and finite-precision arithmetic and its rounding errors. We have implemented our new algorithm in a tool called DSSynth, and are able to automatically generate stable controllers for a set of intricate plant models taken from the literature within minutes.
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