Details of Grant 

EPSRC Reference:	GR/S56085/01
Title:	Semigroups & Monoids in GAP
Principal Investigator:	Ruskuc, Professor N
Other Investigators:	Linton, Professor S Robertson, Professor E
Researcher Co-Investigators:
Project Partners:
Department:	Mathematics and Statistics
Organisation:	University of St Andrews
Scheme:	Standard Research (Pre-FEC)
Starts:	01 June 2004	Ends:	31 May 2007	Value (£):	144,327
EPSRC Research Topic Classifications:	Fundamentals of Computing Logic & Combinatorics
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
Related Grants:
Panel History:
Summary on Grant Application Form
Semigroups and monoids are among the most fundamental mathematical objects, arising naturally as semigroups of transformations of sets or words over an alphabet, and also providing a bridge between mathematics and computer science. Therefore the availability of computational tools for these algebraic structures will influence the development of a variety of seemingly disconnected scientific disciplines, going well beyond mainstream semigroup theory. Although there is a significant body of work in this area, it is fragmented and imbalanced, with theoretical results outnumbering fully described algorithms and practical implementations. The aim of this project is to address these problems. The proposers will use their combined expertise in different areas of algebra, and experiences of their pioneering GAP package MONOID dealing with transformation monoids, to build an integrated GAP library of data structures and algorithms, bringing together all the existing major algorithms. The project will then proceed to address a second negative consequence of fragmentation: the lack of understanding of connections between different methods and algorithms. This will result in the development of a series of new, more powerful and integrated algorithms. Finally, the developed computational tools will be used to advance the understanding of a number of open problems. such as one relation semigroups. Cernv's conjecture for reset automata etc.
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Organisation Website:	http://www.st-and.ac.uk