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Symbolic Dynamics and Finite Automata
, 1999
"... this paper, based on notes by R. Beals and M. Spivak, methods of nite semigroups were introduced to obtain some of the results of G. Hedlund. ..."
Abstract

Cited by 26 (9 self)
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this paper, based on notes by R. Beals and M. Spivak, methods of nite semigroups were introduced to obtain some of the results of G. Hedlund.
Linear Cellular Automata and Fischer Automata
 Parallel Computing
, 1997
"... Introduction Every linear cellular automaton ae can be associated with a regular language L(ae) of finite words: L(ae) is the collection of all finite subwords of configurations that arise after one application of the global map of the cellular automaton. Discussions of the language theoretic aspec ..."
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Cited by 14 (9 self)
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Introduction Every linear cellular automaton ae can be associated with a regular language L(ae) of finite words: L(ae) is the collection of all finite subwords of configurations that arise after one application of the global map of the cellular automaton. Discussions of the language theoretic aspects of linear cellular automata and sofic systems, in particular with respect to their relation to the topology of the space of configurations, can be found in [8], [10] and [7]. In this paper, we will study two measures of complexity associated with L(ae) that are based on minimal finite state machines of a certain type. The first is simply the size of the minimal automaton for L(ae), or, equivalently, the number of left quotients of this language. For the second measure, one can exploit the fact that the languages L(ae) are no
The Size of Power Automata
 Mathematical Foundations of Computer Science, volume 2136 of SLNCS
, 1994
"... We describe a class of simple transitive semiautomata that exhibit full exponential blowup during deterministic simulation. For arbitrary semiautomata we show that it is PSPACEcomplete to decide whether the size of the accessible part of their power automata exceeds a given bound. 1 Motivation C ..."
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Cited by 13 (6 self)
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We describe a class of simple transitive semiautomata that exhibit full exponential blowup during deterministic simulation. For arbitrary semiautomata we show that it is PSPACEcomplete to decide whether the size of the accessible part of their power automata exceeds a given bound. 1 Motivation Consider the following semiautomaton A = h[n]; ; i where [n] = f1; : : : ; ng, = fa; b; cg and the transition function is given by a a cyclic shift on [n]; b the transposition that interchanges 1 and 2, c sends 1 and 2 to 2, identity elsewhere. It is wellknown that A has a transition semigroup of maximal size n n , see [13]. In other words, every function f : [n] ! [n] is already of the form w for some word w. Note that a ; b can be replaced by any other pair of generators for the symmetric group on n points, and c can be replaced by any function whose range has cardinality n 1. It was shown by Salomaa that, for a threeletter alphabet , those are the only choices that produ...
A hierarchy of shift equivalent sofic shifts
"... We define new subclasses of the class of irreducible sofic shifts. These classes form an infinite hierarchy where the lowest class is the class of almost finite type shifts introduced by B. Marcus. We give effective characterizations of these classes with the syntactic semigroups of the shifts. We p ..."
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Cited by 7 (3 self)
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We define new subclasses of the class of irreducible sofic shifts. These classes form an infinite hierarchy where the lowest class is the class of almost finite type shifts introduced by B. Marcus. We give effective characterizations of these classes with the syntactic semigroups of the shifts. We prove that these classes define invariants shift equivalence (and thus for conjugacy). Finally, we extend the result to the case of reducible sofic shifts.
PSEUDOVARIETIES DEFINING CLASSES OF SOFIC SUBSHIFTS CLOSED FOR TAKING SHIFT EQUIVALENT
, 2005
"... For a pseudovariety V of ordered semigroups, let S (V) be the class of sofic subshifts whose syntactic semigroup lies in V. It is proved that if V contains Sl − then S (V∗D) is closed for taking shift equivalent subshifts, and conversely, if S (V) is closed for taking conjugate subshifts then V con ..."
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Cited by 1 (1 self)
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For a pseudovariety V of ordered semigroups, let S (V) be the class of sofic subshifts whose syntactic semigroup lies in V. It is proved that if V contains Sl − then S (V∗D) is closed for taking shift equivalent subshifts, and conversely, if S (V) is closed for taking conjugate subshifts then V contains LSl − and S (V) = S (V∗D). Almost finite type subshifts are characterized as the irreducible elements of S (LInv), which gives a new proof that the class of almost finite type subshifts is closed for taking shift equivalent subshifts.
The syntactic graph of a sofic shift
 in STACS 2004
, 2004
"... invariant under shift equivalence ..."
Linear Cellular Automata and Finite Automata
"... Linear cellular automata have a canonical representation in terms of labeled de Bruijn graphs. We will show that these graphs, construed as semiautomata, provide a natural setting for the study of cellular automata. For example, we give a simple algorithm to determine reversibility and surjectivity ..."
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Linear cellular automata have a canonical representation in terms of labeled de Bruijn graphs. We will show that these graphs, construed as semiautomata, provide a natural setting for the study of cellular automata. For example, we give a simple algorithm to determine reversibility and surjectivity of the global maps. We also comment on Wolfram’s question about the growth rates of the minimal finite state machines associated with iterates of a cellular automaton. 1
Author manuscript, published in "29th International Symposium on Mathematical Foundations of Computer Science 2004, Czech Republic (2004)"
, 2011
"... Abstract. We define new subclasses of the class of irreducible sofic shifts. These classes form an infinite hierarchy where the lowest class is the class of almost finite type shifts introduced by B. Marcus. We give effective characterizations of these classes with the syntactic semigroups of the sh ..."
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Abstract. We define new subclasses of the class of irreducible sofic shifts. These classes form an infinite hierarchy where the lowest class is the class of almost finite type shifts introduced by B. Marcus. We give effective characterizations of these classes with the syntactic semigroups of the shifts.