Reconciling Enumerative and Symbolic Search in Syntax-Guided Synthesis.

Syntax-guided synthesis aims to find a program satisfying semantic specification as well as user-provided structural hypothesis. For syntax-guided synthesis there are two main search strategies: concrete search, which systematically or stochastically enumerates all possible solutions, and symbolic search, which interacts with a constraint solver to solve the synthesis problem. In this paper, we propose a concolic synthesis framework which combines the best of the two worlds. Based on a decision tree representation, our framework works by enumerating tree heights from the smallest possible one to larger ones. For each fixed height, the framework symbolically searches a solution through the counterexample-guided inductive synthesis approach. To compensate the exponential blow-up problem with the concolic synthesis framework, we identify two fragments of synthesis problems and develop purely symbolic and more efficient procedures. The two fragments are decidable as these procedures are terminating and complete. We implemented our synthesis procedures and compared with state-of-the-art synthesizers on a range of benchmarks. Experiments show that our algorithms are promising.