Combining word problems through rewriting in categories with products

Authors:
Camillo Fiorentini;Silvio Ghilardi
Affiliations:
Dipartimento di Scienze dell'Informazione, Università degli Studi di Milano, via Comelico 39, 20135 Milano, Italy;Dipartimento di Scienze dell'Informazione, Università degli Studi di Milano, via Comelico 39, 20135 Milano, Italy
Venue:
Theoretical Computer Science - Category theory and computer science
Year:
2003

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Abstract

We give an algorithm solving combined word problems (over non-necessarily disjoint signatures) based on rewriting of equivalence classes of terms. The canonical rewriting system we introduce consists of few transparent rules and is obtained by applying Knuth-Bendix completion procedure to presentations of pushouts among categories with products. It applies to pairs of theories which are both constructible over their common reduct (on which we do not make any special assumption).