Abstract We generalize an efficient automata-based approach to string solving, the stabilization-based method behind the solver Z3-Noodler , to support relational constraints represented by finite-state transducers (useful for modeling constraints, etc.). We focus on efficient handling of length constraints by reducing the need for expensive concatenation elimination, a major bottleneck in automata-based string solving. We also propose heuristics that significantly improve performance in practice. Implemented on top of Z3-Noodler , our method clearly outperforms other solvers on benchmarks with relational constraints: it solves more instances and runs orders of magnitude faster.

Abstract Z3-Noodler is a fork of the Z3 SMT solver replacing its string theory implementation with a portfolio of decision procedures and a selection mechanism for choosing among them based on the features of the input formula. In this paper, we give an overview of the used decision procedures, including a novel length-based procedure, and their integration into a robust solver with a good overall performance, as witnessed by Z3-Noodler winning the string division of SMT-COMP’24 by a large margin. We also extended the solver with a support for model generation, which is essential for the use of the solver in practice.

Abstract Z3-Noodleris a fork ofZ3that replaces its string theory solver with a custom solver implementing the recently introduced stabilization-based algorithm for solving word equations with regular constraints. An extensive experimental evaluation shows thatZ3-Noodleris a fully-fledged solver that can compete with state-of-the-art solvers, surpassing them by far on many benchmarks. Moreover, it is often complementary to other solvers, making it a suitable choice as a candidate to a solver portfolio.

Abstract Mata is a well-engineered automata library written in C++ that offers a unique combination of speed and simplicity. It is meant to serve in applications such as string constraint solving and reasoning about regular expressions, and as a reference implementation of automata algorithms. Besides basic algorithms for (non)deterministic automata, it implements a fast simulation reduction and antichain-based language inclusion checking. The simplicity allows a straightforward access to the low-level structures, making it relatively easy to extend and modify. Besides the C++ API, the library also implements a Python binding. The library comes with a large benchmark of automata problems collected from relevant applications such as string constraint solving, regular model checking, and reasoning about regular expressions. We show that Mata is on this benchmark significantly faster than all libraries from a wide range of automata libraries we collected. Its usefulness in string constraint solving is demonstrated by the string solver Z3-Noodler, which is based on Mata and outperforms the state of the art in string constraint solving on many standard benchmarks.

We present a new algorithm for solving string constraints. The algorithm builds upon a recent method for solving word equations and regular constraints that interprets string variables as languages rather than strings and, consequently, mitigates the combinatorial explosion that plagues other approaches. We extend the approach to handle linear integer arithmetic length constraints by combination with a known principle of equation alignment and splitting, and by extension to other common types of string constraints, yielding a fully-fledged string solver. The ability of the framework to handle unrestricted disequalities even extends one of the largest decidable classes of string constraints, the chain-free fragment. We integrate our algorithm into a DPLL-based SMT solver. The performance of our implementation is competitive and even significantly better than state-of-the-art string solvers on several established benchmarks obtained from applications in verification of string programs.