Program Synthesis as Dependency Quantified Formula Modulo Theory

TL;DR

This paper introduces a new approach to program synthesis that avoids the need for grammars by reducing the problem to Dependency Quantified Formula problems, leveraging advances in DQBF solving for improved performance.

Contribution

It demonstrates that T-constrained synthesis can be reduced to DQF, and further to DQBF, enabling the use of DQBF solvers for more efficient program synthesis without grammars.

Findings

DQF reduction enables grammar-free synthesis.

DQBF solvers outperform domain-specific techniques.

General-purpose DQBF solvers match specialized methods.

Abstract

Given a specification $\varphi(X,Y)$ over inputs $X$ and output $Y$, defined over a background theory $\mathbb{T}$, the problem of program synthesis is to design a program $f$ such that $Y=f(X)$ satisfies the specification $\varphi$. Over the past decade, syntax-guided synthesis (SyGuS) has emerged as a dominant approach for program synthesis where in addition to the specification $\varphi$, the end-user also specifies a grammar $L$ to aid the underlying synthesis engine. This paper investigates the feasibility of synthesis techniques without grammar, a sub-class defined as $\mathbb{T}$-constrained synthesis. We show that $\mathbb{T}$-constrained synthesis can be reduced to DQF($\mathbb{T}$), i.e., to the problem of finding a witness of a Dependency Quantified Formula Modulo Theory. When the underlying theory is the theory of bitvectors, the corresponding DQF(BV) problem can be further reduced to Dependency Quantified Boolean Formulas (DQBF). We rely on the progress in DQBF solving to design DQBF-based synthesizers that outperform the domain-specific program synthesis techniques, thereby positioning DQBF as a core representation language for program synthesis. Our empirical analysis shows that $\mathbb{T}$-constrained synthesis can achieve significantly better performance than syntax-guided approaches. Furthermore, the general-purpose DQBF solvers perform on par with domain-specific synthesis techniques.