Deciding regular expressions (in-)equivalence in coq

Authors:
Nelma Moreira;David Pereira;Simão Melo de Sousa
Affiliations:
DCC-FC --- University of Porto, Porto, Portugal;DCC-FC --- University of Porto, Porto, Portugal;LIACC & DI --- University of Beira Interior, Covilhã, Portugal
Venue:
RAMiCS'12 Proceedings of the 13th international conference on Relational and Algebraic Methods in Computer Science
Year:
2012

Citing 18
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Abstract

This work presents a mechanically verified implementation of an algorithm for deciding regular expression (in-)equivalence within the Coq proof assistant. This algorithm decides regular expression equivalence through an iterated process of testing the equivalence of their partial derivatives and also does not construct the underlying automata. Our implementation has a refutation step that improves the general efficiency of the decision procedure by enforcing the in-equivalence of regular expressions at early stages of computation. Recent theoretical and experimental research provide evidence that this method is, on average, more efficient than the classical methods based in automata. We present some performance tests and comparisons with similar approaches.