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Organizers: Klaus Madlener (Chair), Susan Hermiller, Ben Keller, Birgit Reinert
Deadline for abstracts: February 15, 1999
Description:
This workshop aims at strengthening the connections between Gröbner bases and rewriting techniques.
Gröbner bases in commutative polynomial rings are an important tool for studying ideal theoretic questions by means of reduction relations and have various applications, e.g. deciding ideal membership, solving algebraic equations or proving theorems in Euclidean geometry. Connections between Gröbner basis techniques and term rewriting systems as well as Buchberger's algorithm and the Knuth-Bendix completion procedure have been studied intensively in the past and have influenced the fields of computer algebra and term rewriting.
The connections between methods from Gröbner basis theory and string rewriting will be particularly highlighted, with participants from both areas brought together to discuss current research. The workshop will address theoretical and application oriented aspects, with an emphasis on the following topics:
Generalizations of the algebraic setting in which Gröbner basis methods are applied. Connections between techniques in Gröbner basis theory and rewriting systems. Implementational aspects and applications.
Agenda
The workshop will consist of three tutorials and six paper sessions.
The tutorials will introduce workshop participants to the areas of both rewriting systems and non-commutative Gröbner bases, so that researchers in each of these areas can learn more about the other field:
String rewriting systems and extensions of Gröbner bases (Susan Hermiller) Gröbner bases in monoid and group rings (Birgit Reinert) Implementing Groebner basis methods (Ben Keller)
The central part of the workshop will consist of six one-hour sessions, each covering a specific topic. Topics of interest include all aspects related to non-commutative Gröbner basis theory with emphasis on connections to rewriting, in particular:
Extensions of Gröbner basis theory and the corresponding completion based procedures to more general algebras. Applications of general Gröbner basis methods (ranging from group theory to control theory). Adaption of geometric techniques from group theory in the context of Gröbner basis methods. Integration of Gröbner basis methods into theorem proving methods. Existing implementations and strategies for speeding up the procedures (ranging from critical pair criteria to special data structures). Characterizations of orderings: admissible and non-admissible orderings.
For each of these sessions experts in the area are invited to apply to give a position talk on the work that has been done as well as open problems in the area. The second half of each session will consist of an open discussion directly following the talk.
Date received: February 07, 1999
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