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Dynamic algebras as a well-behaved fragment of relation algebras

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Algebraic Logic and Universal Algebra in Computer Science (ALUACS 1988)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 425))

Abstract

The varieties RA of relation algebras and DA of dynamic algebras are similar with regard to definitional capacity, admitting essentially the same equational definitions of converse and star. They differ with regard to completeness and decidability. The RA definitions that are incomplete with respect to representable relation algebras, when expressed in their DA form are complete with respect to representable dynamic algebras. Moreover, whereas the theory of RA is undecidable, that of DA is decidable in exponential time. These results follow from representability of the free intensional dynamic algebras.

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Authors and Affiliations

  1. Dept. of Computer Science, 94305, Stanford, CA

    Vaughan Pratt

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  1. Vaughan Pratt
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Clifford H. Bergman Roger D. Maddux Don L. Pigozzi

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Pratt, V. (1990). Dynamic algebras as a well-behaved fragment of relation algebras. In: Bergman, C.H., Maddux, R.D., Pigozzi, D.L. (eds) Algebraic Logic and Universal Algebra in Computer Science. ALUACS 1988. Lecture Notes in Computer Science, vol 425. Springer, New York, NY. https://doi.org/10.1007/BFb0043079

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  • DOI: https://doi.org/10.1007/BFb0043079

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  • Print ISBN: 978-0-387-97288-6

  • Online ISBN: 978-0-387-34804-9

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