Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.607191
Title: Computing relatively large algebraic structures by automated theory exploration
Author: Mahesar, Quratul-ain
ISNI:       0000 0004 5362 3797
Awarding Body: University of Birmingham
Current Institution: University of Birmingham
Date of Award: 2014
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Abstract:
Automated reasoning technology provides means for inference in a formal context via a multitude of disparate reasoning techniques. Combining different techniques not only increases the effectiveness of single systems but also provides a more powerful approach to solving hard problems. Consequently combined reasoning systems have been successfully employed to solve non-trivial mathematical problems in combinatorially rich domains that are intractable by traditional mathematical means. Nevertheless, the lack of domain specific knowledge often limits the effectiveness of these systems. In this thesis we investigate how the combination of diverse reasoning techniques can be employed to pre-compute additional knowledge to enable mathematical discovery in finite and potentially infinite domains that is otherwise not feasible. In particular, we demonstrate how we can exploit bespoke symbolic computations and automated theorem proving to automatically compute and evolve the structural knowledge of small size finite structures in the algebraic theory of quasigroups. This allows us to increase the solvability horizon of model generation systems to find solution models for large size finite algebraic structures previously unattainable. We also present an approach to exploring infinite models using a mixture of automated tools and user interaction to iteratively inspect the structure of solutions and refine search. A practical implementation combines a specialist term rewriting system with bespoke graph algorithms and visualization tools and has been applied to solve the generalized version of Kuratowski's classical closure-complement problem from point-set topology that had remained open for several years.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.607191  DOI: Not available
Keywords: QA75 Electronic computers. Computer science
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