Continuous automaton

About: Continuous automaton is a research topic. Over the lifetime, 947 publications have been published within this topic receiving 17417 citations.

On Minimization of Deterministic Automaton with Rough Output

Abstract: The purpose of the present work is to introduce and study the concept of minimal deterministic automaton with rough output which recognizes the given rough languages. Specifically, we use two concepts for such construction, one is based on Myhill-Nerode’s theory and the other is on the basis of derivatives of the given rough language. Lastly, we discuss monoid representations of the given rough languages.

The hierarchical structure of graph searches

Abstract: Given a graph B , we show the existenee of a universal automaton U which “searches” B. U is universal in the sense that any automaton which searches B behaves as a subautomaton of U . Further, U is naturally filtered in a manner suggestive of hierarchical search depth: level 1 corresponds to simple rules for moving on B , level 2 to “meta-rules,” and so on. We show that if M is any finite state automaton which searches B , then M can in fact be embedded in some finite level U n of U . This leads naturally to a definition of “depth” of an arbitrary automaton which searches B , and we give several examples of such automata with varying depth. This notion of depth is independent of the state space structure of M . We further describe a resulting strategy for the construction of evolutionary learning systems which learn structural control hierarchies, based on our model of the universal automaton.

Factor automata and special factors

Abstract: The factor automaton of a nite word w is the minimal deter- ministic automaton recognizing the set of factors of w. It is a data structure allowing the search of a pattern in a text in time and space proportional to the length of the pattern. In this paper we link classical combinatorial parameters on words to the size and the structure of the factor automa- ton. As a main result, we give a characterization of the words having factor automaton with minimal number of states.

On the Existence of a Periodic Analog of a Finite Connected Automaton

Abstract: The solution of the problem of the existence of an analog with periodic-variable structure of a given fixed-structure connected automaton is presented. Using a Boolean approach, a necessary and sufficient condition for the existence of the periodic analog is proven, and an algorithm that enables us to actually find this analog is given. The saving of the memory capacity needed for the construction of a given automaton is the main interest of the existence of a periodic analog.

A Physically Universal Cellular Automaton.

Abstract: Several cellular automata (CA) are known to be universal in the sense that one can simulate arbitrary computations (e.g., circuits or Turing machines) by carefully encoding the computational device and its input into the cells of the CA. In this paper, we consider a different kind of universality proposed by Janzing. A cellular automaton is physically universal if it is possible to implement any transformation on a finite region of the CA by initializing the complement of the region and letting the system evolve. We give the first known example of a physically universal CA, answering an open problem of Janzing and opening the way for further research in this area.