On Residually Finite Semigroups of Cellullar Automata
نویسندگان
چکیده
We prove that if M is a monoid and A a finite set with more than one element, then the residual finiteness of M is equivalent to that of the monoid consisting of all cellular automata over M with alphabet A.
منابع مشابه
Groups and Semigroups Generated by Automata
In this dissertation we classify the metabelian groups arising from a restricted class of invertible synchronous automata over a binary alphabet. We give faithful, self-similar actions of Heisenberg groups and upper triangular matrix groups. We introduce a new class of semigroups given by a restricted class of asynchronous automata. We call these semigroups " expanding automaton semigroups ". W...
متن کاملFinite Aperiodic Semigroups with Commuting Idempotents and Generalizations
Among the most important and intensively studied classes of semigroups are finite semigroups, regular semigroups and inverse semigroups. Finite semigroups arise as syntactic semigroups of regular languages and as transition semigroups of finite automata. This connection has lead to a large and deep literature on classifying regular languages by means of algebraic properties of their correspondi...
متن کاملAn Effective Lower Bound for Group Complexity of Finite Semigroups and Automata
The question of computing the group complexity of finite semigroups and automata was first posed in K. Krohn and J. Rhodes, Complexity of finite semigroups, Annals of Mathematics (2) 88 (1968), 128–160, motivated by the Prime Decomposition Theorem of K. Krohn and J. Rhodes, Algebraic theory of machines, I: Prime decomposition theorem for finite semigroups and machines, Transactions of the Ameri...
متن کاملGeometric Semigroup Theory
Geometric semigroup theory is the systematic investigation of finitely-generated semigroups using the topology and geometry of their associated automata. In this article we show how a number of easily-defined expansions on finite semigroups and automata lead to simplifications of the graphs on which the corresponding finite semigroups act. We show in particular that every finite semigroup can b...
متن کاملGroups and Semigroups Defined by Colorings of Synchronizing Automata
In this paper we combine the algebraic properties of Mealy machines generating self-similar groups and the combinatorial properties of the corresponding deterministic finite automata (DFA). In particular, we relate bounded automata to finitely generated synchronizing automata and characterize finite automata groups in terms of nilpotency of the corresponding DFA. Moreover, we present a decidabl...
متن کامل