Abstract
The notion of state is fundamental to the design and analysis of virtually all computational systems. The Myhill-Nerode Theorem of Finite Automata theory—and the concepts underlying the Theorem—is a source of sophisticated fundamental insights about a large class of state-based systems, both finite-state and infinite-state systems. The Theorem’s elegant algebraic characterization of the notion of state often allows one to analyze the behaviors and resource requirements of such systems. This paper reviews the Theorem and illustrates its application to a variety of formal computational systems and problems, ranging from the design of circuits, to the analysis of data structures, to the study of state-based formalisms for machine-learning systems. It is hoped that this survey will awaken many to, and remind others of, the importance of the Theorem and its fundamental insights.
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Rosenberg, A.L. (2006). State. In: Goldreich, O., Rosenberg, A.L., Selman, A.L. (eds) Theoretical Computer Science. Lecture Notes in Computer Science, vol 3895. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11685654_16
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DOI: https://doi.org/10.1007/11685654_16
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