Program Synthesis as Dependency Quantified Formula Modulo Theory

Given a specification varphi(X,Y) over inputs X and output Y, defined over a background theory mathbbT, 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 mathbbT-constrained synthesis. We show that mathbbT-constrained synthesis can be reduced to DQF(mathbbT), 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 mathbbT-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.