Expansions, free inverse semigroups, and Schützenberger product
Stuart W. Margolis,J.E Pin +1 more
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In this article, the authors present a new construction of the free inverse monoid on a set X. Contrary to previous constructions of [9, 11], their construction is symmetric and originates from classical ideas of language theory.About:
This article is published in Journal of Algebra.The article was published on 1987-10-15 and is currently open access. It has received 20 citations till now. The article focuses on the topics: Free monoid & Syntactic monoid.read more
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Mathematical foundations of neuroscience
G. Bard Ermentrout,David Terman +1 more
TL;DR: The Hodgkin-Huxley Equations are applied to the model of Neuronal Networks to describe the “spatially distributed” networks.
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The q-theory of Finite Semigroups
John Rhodes,Benjamin Steinberg +1 more
TL;DR: The q-theory of finite semigroups as mentioned in this paper is a theory that provides a unifying approach to finite semigroup theory via quantization, and it is the only contemporary exposition of the complete theory of the complexity of finite semiigroups.
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Finite state automata: A geometric approach
Abstract: Recently, finite state automata, via the advent of hyperbolic and automatic groups, have become a powerful tool in geometric group theory. This paper develops a geometric approach to automata theory, analogous to various techniques used in combinatorial group theory, to solve various problems on the overlap between group theory and monoid theory. For instance, we give a geometric algorithm for computing the closure of a rational language in the profinite topology of a free group. We introduce some geometric notions for automata and show that certain important classes of monoids can be described in terms of the geometry of their Cayley graphs. A long standing open question, to which the answer was only known in the simplest of cases (and even then was non-trivial), is whether it is true, for a pseudovariety of groups H, that a J -trivial co-extension of a group in H must divide a semidirect product of a J -trivial monoid and a group in H. We show the answer is affirmative if H is closed under extension, and may be negative otherwise.
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Combinatorial Group Theory
Roger C. Lyndon,Paul E. Schupp +1 more
TL;DR: In this article, the authors introduce the concept of Free Products with Amalgamation (FPAM) and Small Cancellation Theory over free products with amalgamation and HNN extensions.
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Combinatorial Group Theory.
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Free Inverse Semigroups
TL;DR: In this article, a graph-theoretic technique for representing the elements of the free inverse semigroup FIA is presented, based on the notion of a word-tree on a set A. With the aid of this technique various properties of FIA are easily deduced.