🤖 AI Summary
This work addresses the challenge of solving complex string constraints that are poorly supported in current SMT solvers by proposing a novel string equation solving method. Building upon the classical Nielsen transformation, the approach uniquely integrates string exponentiation with generalized Parikh images and introduces an equality decomposition technique, thereby substantially extending the scope of traditional methods. Experimental results demonstrate that the proposed method effectively solves intricate string equations, including those involving rare SMT string inputs, significantly enhancing the capability to handle expressive string constraints.
📝 Abstract
Commonly used proof strategies by automated reasoners organise proof search either by ordering-based saturation or by reducing goals to subgoals. In this paper, we combine these two approaches and advocate a SAT-based method with symmetry breaking for connection calculi in first-order logic, with the purpose of further pushing the automation in first-order classical logic proofs. In contrast to classical ways of reducing first-order logic to propositional logic, our method encodes the structure of the proof search itself. We present three distinct SAT encodings for connection calculi, analyse their theoretical properties, and discuss the effect of using SAT/SMT solvers on these encodings. We implemented our work in the new solver upCoP and showcase its practical feasibility.