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Linear Cellular Automata via de Bruijn Diagrams
, 1991
"... Graph theory plays several important roles in the theory of cellular automata, one of which consists in describing the evolution of the automaton, and another of which consists in relating local properties to global properties. Evolution is described by local rules mapping cell neighborhoods into it ..."
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Cited by 18 (8 self)
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Graph theory plays several important roles in the theory of cellular automata, one of which consists in describing the evolution of the automaton, and another of which consists in relating local properties to global properties. Evolution is described by local rules mapping cell neighborhoods into its subsequent state; because successive neighborhoods overlap it is important to be able to take the overlap into account when relating the behavior of successive cells to one another. In illustration, the de Bruijn diagram and its subdiagrams are applied to the study of cellular automata in one dimension. 1 Introduction An automaton has states and mappings between its states. The concept arose from electrical switching theory, but thanks to the pioneering work of Claude Shannon #1#, boolean algebra and probability theory were seen to haveanimportant role in the theory of switching networks. Speculation concerning the relationship between logical processes and the physiology of the nervous s...
On the Completeness of the Equations for the Kleene Star in bisimulation
"... A classical result from Redko [14] says that there does not exist a complete finite equational axiomatization for the Kleene star modulo trace equivalence. Fokkink and Zantema [9] showed that there does exist a complete finite equational axiomatization for the Kleene star up to strong bisimulation e ..."
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Cited by 9 (3 self)
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A classical result from Redko [14] says that there does not exist a complete finite equational axiomatization for the Kleene star modulo trace equivalence. Fokkink and Zantema [9] showed that there does exist a complete finite equational axiomatization for the Kleene star up to strong bisimulation equivalence. Their proof is based on a sophisticated term rewriting analysis. In this paper, we present amuch simpler and shorter completeness proof. Furthermore, we show that the three equations for the Kleene star are all essential for this completeness result.
Elements of stream calculus
 In MFPS 2001, ENTCS 45
, 2001
"... CWI is a founding member of ERCIM, the European Research Consortium for Informatics and Mathematics. CWI's research has a themeoriented structure and is grouped into four clusters. Listed below are the names of the clusters and in parentheses their acronyms. ..."
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Cited by 1 (1 self)
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CWI is a founding member of ERCIM, the European Research Consortium for Informatics and Mathematics. CWI's research has a themeoriented structure and is grouped into four clusters. Listed below are the names of the clusters and in parentheses their acronyms.