Decision Procedure for A Theory of String Sequences

2025-08-31

AI Summary

Modern SMT solvers lack native support for string-sequence operations—such as regex matching, splitting, and concatenation—limiting their applicability to real-world string-intensive programs. Method: This paper introduces the first formalization of the string-sequence theory and identifies a decidable straight-line fragment thereof. It encodes string-sequence operations into standard string operations augmented with automata-based preimage computation, and integrates the approach into the OSTRICH framework for constraint solving. Contribution/Results: We implement the resulting solver as $ostrichseq$, the first tool unifying the expressive power of sequence logic and string logic. Evaluated on realistic JavaScript program-generation benchmarks, $ostrichseq$ demonstrates both efficiency and practicality, significantly advancing the state of the art in solving string-sequence constraints.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Search and Optimization: Distributed Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

The theory of sequences, supported by many SMT solvers, can model program data types including bounded arrays and lists. Sequences are parameterized by the element data type and provide operations such as accessing elements, concatenation, forming sub-sequences and updating elements. Strings and sequences are intimately related; many operations, e.g., matching a string according to a regular expression, splitting strings, or joining strings in a sequence, are frequently used in string-manipulating programs. Nevertheless, these operations are typically not directly supported by existing SMT solvers, which instead only consider the generic theory of sequences. In this paper, we propose a theory of string sequences and study its satisfiability. We show that, while it is undecidable in general, the decidability can be recovered by restricting to the straight-line fragment. This is shown by encoding each string sequence as a string, and each string sequence operation as a corresponding string operation. We provide pre-image computation for the resulting string operations with respect to automata, effectively casting it into the generic OSTRICH string constraint solving framework. We implement the new decision procedure as a tool $ostrichseq$, and carry out experiments on benchmark constraints generated from real-world JavaScript programs, hand-crafted templates and unit tests. The experiments confirm the efficacy of our approach.

Problem

• Extending SMT solvers to support string sequence operations
• Providing decidability for string sequence satisfiability problems
• Enabling automated reasoning for real-world string manipulation programs

Innovation

• String sequences encoded as strings for solving
• Straight-line fragment recovers decidability in theory
• Pre-image computation integrates with OSTRICH framework