Gleason, Andrew Semigroups of shift register counting matrices. (English) Zbl 0790.20086 Math. Syst. Theory 25, No. 4, 253-267 (1992). 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. Cited in 2 Documents MSC: 20M35 Semigroups in automata theory, linguistics, etc. 15A30 Algebraic systems of matrices 94C10 Switching theory, application of Boolean algebra; Boolean functions (MSC2010) Keywords:Boolean sequences; binary functions; shift register; semigroup of counting matrices PDF BibTeX XML Cite \textit{A. Gleason}, Math. Syst. Theory 25, No. 4, 253--267 (1992; Zbl 0790.20086) Full Text: DOI References: [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 · doi:10.1007/BF01691062 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.