An Improved Algorithm for E-Generalization

TL;DR

This paper introduces an improved algorithm for E-generalization, enhancing efficiency and scalability, with proven correctness and completeness, and demonstrates its implementation in C for larger problem handling.

Contribution

The paper presents novel algorithmic improvements for E-generalization, along with correctness proofs and an efficient C implementation for large-scale problems.

Findings

Algorithmic improvements increase efficiency significantly.

Implementation in C enables handling larger problems.

Proofs confirm correctness and completeness of the new approach.

Abstract

E-generalization computes common generalizations of given ground terms w.r.t. a given equational background theory E. In 2005 [arXiv:1403.8118], we had presented a computation approach based on standard regular tree grammar algorithms, and a Prolog prototype implementation. In this report, we present algorithmic improvements, prove them correct and complete, and give some details of an efficiency-oriented implementation in C that allows us to handle problems larger by several orders of magnitude.