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Extensions of an idea of McNaughton

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Abstract

Two important measures of the computational complexity of a regular language are the type of finite automaton needed to recognize it and the type of logical expression needed to describe it. Important connections between these measures were studied by Büchi and McNaughton as early as 1960. In this survey we describe the logical formalism used, outline these early results, and describe modern extensions of this work. In particular, we show how the formalism is extended by the use of new quantifiers and atomic predicates to express many of the fundamental classes of boolean circuit complexity.

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Authors and Affiliations

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

    David A. Mix Barrington

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  1. David A. Mix Barrington
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Former name David A. Barrington. Supported by NSF Computer and Computation Theory Grant CCR-8714714.

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Mix Barrington, D.A. Extensions of an idea of McNaughton. Math. Systems Theory 23, 147–164 (1990). https://doi.org/10.1007/BF02090772

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