Skip to Main content Skip to Navigation
Conference papers

Homological computations for term rewriting systems

Abstract : An important problem in universal algebra consists in finding presentations of algebraic theories by generators and relations, which are as small as possible. Exhibiting lower bounds on the number of those generators and relations for a given theory is a difficult task because it a priori requires considering all possible sets of generators for a theory and no general method exists. In this article, we explain how homological computations can provide such lower bounds, in a systematic way, and show how to actually compute those in the case where a presentation of the theory by a convergent rewriting system is known. We also introduce the notion of coherent presentation of a theory in order to consider finer homotopical invariants. In some aspects, this work generalizes, to term rewriting systems, Squier’s celebrated homological and homotopical invariants for string rewriting systems.
Complete list of metadata

Cited literature [28 references]  Display  Hide  Download
Contributor : Philippe Malbos Connect in order to contact the contributor
Submitted on : Tuesday, January 9, 2018 - 12:13:26 AM
Last modification on : Tuesday, April 26, 2022 - 2:00:02 AM
Long-term archiving on: : Thursday, May 3, 2018 - 9:29:37 PM


Files produced by the author(s)


  • HAL Id : hal-01678175, version 1


Philippe Malbos, Samuel Mimram. Homological computations for term rewriting systems. 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016), Jun 2016, Porto, Portugal. pp.27:1-27:17. ⟨hal-01678175⟩



Record views


Files downloads