Topic
Continuous automaton
About: Continuous automaton is a research topic. Over the lifetime, 947 publications have been published within this topic receiving 17417 citations.
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TL;DR: In this paper, the authors studied the word problem for automaton semigroups and automaton groups from a complexity point of view, and showed that the uniform word problem is NP-hard.
14 citations
TL;DR: The main results are that a multi-tilde-bar expression of width n can be converted into an (n+1)-state position-like automaton and that any acyclic n-state automaton can be turned into an extended expression ofwidth O(n).
13 citations
TL;DR: This work considers the finite homogeneous Markov chain induced by a class of one-dimensional asynchronous cellular automata—automata that are allowed to change only one cell per iteration, and shows that if the local transition rule is exponential, the stationary probability is the Boltzmann distribution of the Ising model.
Abstract: We consider the finite homogeneous Markov chain induced by a class of one-dimensional asynchronous cellular automata—automata that are allowed to change only one cell per iteration. Furthermore, we confine to totalistic automata, where transitions depend only on the number of 1s in the neighborhood of the current cell. We consider three different cases: (i) size of neighborhood equals length of the automaton; (ii) size of neighborhood two, length of automaton arbitrary; and (iii) size of neighborhood three, length of automaton arbitrary. For each case, the associated Markov chain proves to be ergodic. We derive simple-form stationary distributions, in case (i) by lumping states with respect to the number of 1s in the automaton, and in cases (ii) and (iii) by considering the number of 0–1 borders within the automaton configuration. For the three-neighborhood automaton, we analyze also the Markov chain at the boundary of the parameter domain, and the symmetry of the entropy. Finally, we show that if the local transition rule is exponential, the stationary probability is the Boltzmann distribution of the Ising model.
13 citations
Journal Article•
TL;DR: A new model, a neural network pushdown automaton (NNPDA), which is a hybrid system that couples a recurrent network to an external stack memory and should be capable of learning and recognizing some class of context-free grammars.
Abstract: In particular this paper develops a new model, a neural network pushdown automaton (NNPDA), which is a hybrid system that couples a recurrent network to an external stack memory. More importantly, a NNPDA should be capable of learning and recognizing some class of context-free grammars. We explore the capabilities of such a model by inferring automata from sample strings-the problem of grammatical inference.
13 citations
18 Jun 2007
TL;DR: This paper studies conditions for a sofic subshift to be the trace of a cellular automaton.
Abstract: The trace subshift of a cellular automaton is the subshift of all possible columns that may appear in a space-time diagram. In this paper we study conditions for a sofic subshift to be the trace of a cellular automaton.
13 citations