Details:
Title  Applications of Rewriting Systems and Groebner Bases to Computing Kan Extensions and Identities Among Relations  Author(s)  Anne Heyworth  Type  Article in Journal  Abstract  This thesis concentrates on the development and application of rewriting and Groebner basis methods to a range of combinatorial problems. Chapter Two contains the most important result, which is the application of KnuthBendix procedures to Kan extensions, showing how rewriting provides a useful method for attempting to solve a variety of combinatorial problems which can be phrased in terms of Kan extensions. Chapter Three shows that the standard KnuthBendix algorithm is stepforstep a special case of Buchberger's algorithm. The onesided cases and higher dimensions are considered. Chapter Four relates rewrite systems, Groebner bases and automata. Automata which only accept irreducibles, and automata which output reduced forms are discussed for presentations of Kan extensions. Reduction machines for rewrite systems are identified with standard output automata and the reduction machines devised for algebras are expressed as Petri nets. Chapter Five uses the completion of a group rewriting system to algorithmically determine a contracting homotopy necessary in order to compute the set of generators for the module of identities among relations using the covering groupoid methods devised by Brown and Razak Salleh. Reducing the resulting set of submodule generators is identified as a Groebner basis problem. Algorithms are implemented in GAP3.  Keywords  presentation, congruence, category, Kan extension, rewrite System, Gröbner basis, normal form, automaton, regular expression, Peiffer relation, module, crossed module, identities among relations, covering groupoid, contracting homotopy  Length  84 
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 Language  English  Journal  eprint arXiv: math/9812097  Year  1998  Translation 
No  Refereed 
No 
