🤖 AI Summary
This work proposes a native bounded structural model finding approach within the Maude rewriting logic framework, circumventing the reliance on external SAT/SMT solvers that hinders direct verification of software designs in their original formal setting. The method leverages symbolic reachability to automatically generate finite object configurations from class declarations and graph/data constraints, eliminating the need for custom generators. It introduces an obligation-driven bounded calculus that decouples object creation from reference assignment and integrates ACU matching for symmetry reduction. Correctness of folding is ensured via coverage-preserving entailment checks. By unifying symbolic rewriting, SMT-based pruning, and state exploration modulo equational theories, the approach guarantees termination, bounded completeness, and soundness. A prototype implementation demonstrates its effectiveness and expressiveness in generating structural models.
📝 Abstract
Bounded model finding is a key technique for validating software designs, usually obtained by translating high-level specifications into SAT/SMT problems. Although effective, such translations introduce a semantic gap and a dependency on external tools. We present the \emph{Maude Model Finder} (MMF), a native approach that brings bounded model finding to the Maude rewriting logic framework. MMF provides a schema-parametric engine that repurposes symbolic reachability for structural solving, generating finite object configurations from class declarations and graph and data constraints without bespoke generators. Technically, MMF explores a constrained symbolic rewriting system over runtime states modulo an equational theory; SMT is used only to prune states by constraint satisfiability and to discharge entailment checks for subsumption and folding. We contribute a bounded, obligation-driven calculus that separates object creation from reference assignment and supports symmetry reduction by folding via Maude's ACU matching. We establish termination, soundness, and completeness of the bounded construction within the declared bounds, and justify folding via a coverage-preserving subsumption test. We focus on the calculus and its properties, illustrating it on running examples supported by a Maude prototype.