Michal Šedý | Searcharxiv

arXiv2026

String Solving with Stabilization and Transducers (Technical Report)

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

cs.FL↗

arXiv2025

Automata Size Reduction by Procedure Finding

We introduce a novel paradigm for reducing the size of finite automata by compressing repeating sub-graphs. These repeating sub-graphs can be viewed as invocations of a single procedure. Instead of representing each invocation explicitly, they can be replaced by a single procedure that uses a small runtime memory to remember the call context. We elaborate on the technical details of a basic implementation of this idea, where the memory used by the procedures is a simple finite-state register. We propose methods for identifying repetitive sub-graphs, collapsing them into procedures, and measuring the resulting reduction in automata size. Already this basic implementation of reduction by procedure finding yields practically relevant results, particularly in the context of FPGA-accelerated pattern matching, where automata size is a primary bottleneck. We achieve a size reduction of up to 70\% in automata that had already been minimized using existing advanced methods.

cs.FL↗