Compositional Synthesis of Piece-Wise Functions by Learning Classifiers

Abstract

We present a novel general technique that uses classifier learning to synthesize piece-wise functions (functions that split the domain into regions and apply simpler functions to each region) against logical synthesis specifications. Our framework works by combining a synthesizer of functions for fixed 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 integer arithmetic, combining leaf expression synthesis using constraint-solving with predicate synthesis using enumeration, and tie them together using a decision tree classifier. We demonstrate that this compositional approach is competitive compared to existing synthesis engines on a set of synthesis specifications.