Synthesizing Piece-Wise Functions by Learning Classifiers

We present a novel general technique that classifier learning to synthesize piece-wise functions (functions that split the domain into regions, applying simpler functions to each region), working in combination with a synthesizer of the simpler functions for concrete inputs and a synthesizer of predicates that can be used to define regions. We develop a theory of single-point refutable specifications that facilitate generating concrete counterexamples using constraint solvers. We implement the framework for synthesizing piece-wise functions in linear arithmetic, combining leaf expression synthesis using constraint-solving and predicate synthesis using enumeration, and tie them together using a decision tree classifier. We demonstrate that this approach is competitive compared to existing synthesis engines on a set of specifications.