Work

A Nominal Approach to Equational Problems in Languages with Binders

Year: 2025

Type: article

Abstract: Equational problems are fundamental in computer science, frequently arising as subproblems across diverse domains, including program analysis and learning from examples and counterexamples. This article focuses on equational problems in languages with binding operators, formulating them within the nominal framework and referring to them as Nominal Equational Problems . We provide a comprehensive definition of solutions for nominal equational problems and introduce a set of simplification rules for computing these solutions within the nominal ground term algebra. We rigorously prove that the simplification rules are sound , solution-preserving and complete . Moreover, we establish that, under a specific strategy for rule application, the simplification process always terminates, thereby providing an effective algorithm for solving nominal equational problems. Finally, we demonstrate the practical relevance of our results by showcasing how nominal equational problems can serve as a framework for learning from examples and counterexamples. We also illustrate their applicability in addressing sufficient completeness problems, emphasising their utility in theoretical and practical contexts.

Source: ACM Transactions on Computational Logic

DOI: 10.1145/3767744

Authors: Daniele Nantes-Sobrinho, Maribel Fernández, Deivid Vale, Mauricio Ayala-Rincón

Institutions: Universidade de Brasília, Imperial College London, King's College London, Augusta University

Language: English

Topic: Logic, programming, and type systems

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: bronze

Funder: National Science Foundation

Award: SHF:Small:Concurrency In Reversible Computations