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On the Fine-Structure of Regular Algebra.

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Title: On the Fine-Structure of Regular Algebra.
Authors: Foster, Simon1 simon.foster@york.ac.uk, Struth, Georg2 g.struth@sheffield.ac.uk
Source: Journal of Automated Reasoning. Feb2015, Vol. 54 Issue 2, p165-197. 33p.
Subjects: Algebra, Mathematical analysis, Axioms, Mathematics theorems, Automation
Abstract: Regular algebra is the algebra of regular expressions as induced by regular language identity. We use Isabelle/HOL for a detailed systematic study of the regular algebra axioms given by Boffa, Conway, Kozen and Salomaa. We investigate the relationships between these systems, formalise a soundness proof for the smallest class (Salomaa's) and obtain completeness for the largest one (Boffa's) relative to a deep result by Krob. As a case study in formalised mathematics, our investigations also shed some light on the power of theorem proving technology for reasoning with algebras and their models, including proof automation and counterexample generation. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Automated Reasoning is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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  Data: Regular algebra is the algebra of regular expressions as induced by regular language identity. We use Isabelle/HOL for a detailed systematic study of the regular algebra axioms given by Boffa, Conway, Kozen and Salomaa. We investigate the relationships between these systems, formalise a soundness proof for the smallest class (Salomaa's) and obtain completeness for the largest one (Boffa's) relative to a deep result by Krob. As a case study in formalised mathematics, our investigations also shed some light on the power of theorem proving technology for reasoning with algebras and their models, including proof automation and counterexample generation. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Journal of Automated Reasoning is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s10817-014-9318-9
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      – Code: eng
        Text: English
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      – SubjectFull: Mathematical analysis
        Type: general
      – SubjectFull: Axioms
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      – SubjectFull: Mathematics theorems
        Type: general
      – SubjectFull: Automation
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      – TitleFull: On the Fine-Structure of Regular Algebra.
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              Text: Feb2015
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