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.

研究了没有语言文法限制的综合技术，证明它可以被约化为DQF问题，通过DQF求解来设计综合程序并且克服了基于文法的综合技术的限制，实现了更好的性能。

计算机程序合成的依赖关系量化公式模 Theory