Algorithm selection is important in satisfiability and constraint solving, since no single solver performs best across all instances. Traditional learning-based approaches represent problem instances using expert-designed features to predict solver performance, while recent work explores graph representations derived from ASTs. However, most existing approaches overlook high-level contextual information, such as the application domain or the benchmark origin. In practice, such cues often help practitioners choose an appropriate solver. We present SMT-Select, a multimodal framework for SMT algorithm selection. It learns graph representations from formula ASTs and textual representations from natural-language context descriptions. These representations are then combined to guide solver selection. Evaluated across nine SMT logics, SMT-Select consistently outperforms existing selectors and SMT-COMP winning solvers. Across all evaluated logics, it closes at least 30% of the performance gap between the competition winner and the virtual best solver (VBS), and nearly matches the VBS in two logics.

Constraint satisfaction problems involving strings have been a subject of theoretical study for decades, but the recent years have seen an increased interest in the development of practical solving methods. This interest in solving string constraints led to the development of various techniques and solvers, often accompanied by specific benchmark sets. As a result, there is now a substantial corpus of publicly available, yet largely unclassified, such benchmarks. In this context, we present SMTQuery , a framework for maintaining and analyzing benchmarks for SMT string problems. SMTQuery enables the execution of user-defined queries to extract domain-specific information from these benchmarks, facilitating a deeper analysis of the underlying problems. We demonstrate its utility by analyzing over 100,000 benchmarks and training an algorithm selection model to match benchmarks with suitable solvers.

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.

Abstract We consider the longest common subsequence problem in the context of subsequences with gap constraints. In particular, following Day et al. (2022), we consider the setting when the distance (i. e., the gap) between two consecutive symbols of the subsequence has to be between a lower and an upper bound (which may depend on the position of those symbols in the subsequence or on the symbols bordering the gap) as well as the case where the entire subsequence is found in a bounded range (defined by a single upper bound), considered by Kosche et al. (2022). In all these cases, we present efficient algorithms for determining the length of the longest common constrained subsequence between two given strings, and discuss lower bounds for the respective problems.