Novel tree-search method for synthesizing SMT strategies

Abstract

Modern SMT solvers, such as Z3, allow solver users to customize strategies to improve performance on their specific use cases. However, handcrafting an optimized strategy for a specific class of SMT instances remains a complex and demanding task for both solver developers and users alike. In this paper, we address the problem of automated SMT strategy synthesis via a novel method based on Monte-Carlo Tree Search (MCTS). We formulate strategy synthesis as a sequential decision-making process, where the search tree corresponds to the strategy space. Subsequently, we employ MCTS to navigate this vast search space. Compared to the conventional MCTS, we introduce two heuristics—layered and staged search—that enable our method to identify effective strategies with lower costs. We implement our method, dubbed Z3alpha, upon the Z3 SMT solver. Our experiments demonstrate that Z3alpha outperforms the default Z3 solver and the state-of-the-art synthesis tool Fastsmt on the majority of the evaluated benchmark sets, while producing more interpretable strategies than FastSMT. At SMT-COMP’24, among the 16 participating logics, Z3alpha improved upon the default Z3 in 12 cases and helped solve hundreds more instances in QF_NIA and QF_NRA, winning their respective divisions.