The generalizability of PBE solvers is the key to the empirical synthesis performance. Despite the importance of generalizability, related studies on PBE solvers are still limited. In theory, few existing solvers provide theoretical guarantees on generalizability, and in practice, there is a lack of PBE solvers with satisfactory generalizability on important domains such as conditional linear integer arithmetic (CLIA). In this paper, we adopt a concept from the computational learning theory, Occam learning, and perform a comprehensive study on the framework of synthesis through unification (STUN), a state-of-the-art framework for synthesizing programs with nested if-then-else operators. We prove that Eusolver, a state-of-the-art STUN solver, does not satisfy the condition of Occam learning, and then we design a novel STUN solver, PolyGen, of which the generalizability is theoretically guaranteed by Occam learning. We evaluate PolyGen on the domains of CLIA and demonstrate that PolyGen significantly outperforms two state-of-the-art PBE solvers on CLIA, Eusolver and Euphony, on both generalizability and efficiency.

中文翻译：

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奥卡姆学习通过统一与综合相遇

PBE 求解器的通用性是经验综合性能的关键。尽管通用性很重要，但对 PBE 求解器的相关研究仍然有限。理论上，现有的求解器很少能提供泛化性的理论保证，而在实践中，缺乏对重要领域（如条件线性整数算法（CLIA））具有令人满意的泛化性的 PBE 求解器。在本文中，我们采用了计算学习理论中的概念，奥卡姆学习，并对统一合成框架（STUN）进行了全面的研究，这是一个用于合成具有嵌套 if-then 的程序的最新框架-else 运算符。我们证明了最先进的 STUN 求解器 Eusolver 不满足 Occam 学习的条件，然后我们设计了一个新颖的 STUN 求解器 PolyGen，其中，奥卡姆学习在理论上保证了泛化性。我们在 CLIA 的域上评估 PolyGen，并证明 PolyGen 在 CLIA、Eusolver 和 Euphony 上的普遍性和效率都显着优于两个最先进的 PBE 求解器。