Decidable Synthesis of Programs with Uninterpreted Functions

TL;DR

This paper introduces a decidable synthesis method for a class of programs with unbounded size, conditionals, iteration, and uninterpreted functions over infinite domains, leveraging a coherence restriction.

Contribution

It formulates a syntax-guided synthesis problem for coherent uninterpreted programs, proves its decidability, and determines its exact complexity.

Findings

Decidability of the synthesis problem for coherent uninterpreted programs.

Precise complexity characterization of the synthesis problem.

Analysis of various problem variants.

Abstract

We identify a decidable synthesis problem for a class of programs of unbounded size with conditionals and iteration that work over infinite data domains. The programs in our class use uninterpreted functions and relations, and abide by a restriction called coherence that was recently identified to yield decidable verification. We formulate a powerful grammar-restricted (syntax-guided) synthesis problem for coherent uninterpreted programs, and we show the problem to be decidable, identify its precise complexity, and also study several variants of the problem.