Semigroups of shift register counting matrices. (English) Zbl 0790.20086

Summary: This is a revised and corrected version of notes from lectures by Andrew Gleason. The goal of the paper is a structure theorem about “onto maps” from the space of infinite Boolean sequences to itself, induced by binary functions on a shift register. The methods of proof involve a close study of the semigroup of counting matrices.


20M35 Semigroups in automata theory, linguistics, etc.
15A30 Algebraic systems of matrices
94C10 Switching theory, application of Boolean algebra; Boolean functions (MSC2010)
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[1] Hedlund, G., Endomorphisms and automorphisms of the shift dynamical system,Mathematical Systems Theory, Vol. 3, No. 4, 1969, pp. 320-375. · Zbl 0182.56901
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