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dc.contributor.authorKozen, Dexteren_US
dc.description.abstractKleene algebras are an important class of algebraic structures that arise in diverse areas of computer science: program logic and semantics, relational algebra, automata theory, and the design and analysis of algorithms. The literature contains at several inequivalent definitions of Kleene algebras and related algebraic structures [2, 13, 14, 5, 6, 1, 9, 7]. In this paper we establish some new relationships among these structures. Our main results are: (1) There is a Kleene algebra in the sense of [6] that is not *-continuous. (2) The categories of *-continuous Kleene algebras [5, 6], closed semirings [1, 9] and S-algebras [2] are strongly related by adjunctions. (3) The axioms of Kleene algebra in the sense of [6] are not complete for the universal Horn theory of the regular events. This refutes a conjecture of Conway [2, p. 103]. (4) Right-handed Kleene algebras are not necessarily left-handed Kleene algebras. This verifies a weaker version of a conjecture of Pratt [14].en_US
dc.format.extent150652 bytes
dc.format.extent296332 bytes
dc.publisherCornell Universityen_US
dc.subjectcomputer scienceen_US
dc.subjecttechnical reporten_US
dc.titleOn Kleene Algebras and Closed Semiringsen_US
dc.typetechnical reporten_US

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