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Exposing graph uniformities via algebraic specification

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Abstract

This survey acknowledges an intellectual debt to Bob McNaughton. In 1968 I turned my research focus to the study of structural uniformities in graphs, motivated by the desire to study theoretical aspects of data structures. The approach that I took in this study was influenced heavily by the algebra-based study of structure in finite automata initiated in the mid-1960s by Bob and others. Their successes in using the syntactic monoid of an automaton to study its structure convinced me to base my study on a monoid-theoretic specification of graphs. The study of what I termeddata graphs occupied me for the next 4–5 years; the insights garnered during that period have served me well since, in a variety of disparate contexts. Indeed, when I began to focus on the study of structural uniformities in the interconnection networks of parallel architectures, in the mid-1980s, it was second nature to me to base this study also on a monoid-theoretic specification of the graphs underlying the interconnection networks. This paper is a brief survey of the highlights of my studies of uniformities in algebraically specified graphs. It is both fitting and pleasureful to dedicate this survey to Bob McNaughton, a wise mentor and a man of vision.

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Authors and Affiliations

  1. Department of Computer and Information Science, University of Massachusetts, 01003, Amherst, MA, USA

    Arnold L. Rosenberg

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  1. Arnold L. Rosenberg
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This work was partially supported by NSF Grant CCR-88-12567.

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Rosenberg, A.L. Exposing graph uniformities via algebraic specification. Math. Systems Theory 23, 227–244 (1990). https://doi.org/10.1007/BF02090777

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  • DOI: https://doi.org/10.1007/BF02090777

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