2,113 research outputs found

    On insertion-deletion systems over relational words

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    We introduce a new notion of a relational word as a finite totally ordered set of positions endowed with three binary relations that describe which positions are labeled by equal data, by unequal data and those having an undefined relation between their labels. We define the operations of insertion and deletion on relational words generalizing corresponding operations on strings. We prove that the transitive and reflexive closure of these operations has a decidable membership problem for the case of short insertion-deletion rules (of size two/three and three/two). At the same time, we show that in the general case such systems can produce a coding of any recursively enumerable language leading to undecidabilty of reachability questions.Comment: 24 pages, 8 figure

    Knuth-Bendix algorithm and the conjugacy problems in monoids

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    We present an algorithmic approach to the conjugacy problems in monoids, using rewriting systems. We extend the classical theory of rewriting developed by Knuth and Bendix to a rewriting that takes into account the cyclic conjugates.Comment: This is a new version of the paper 'The conjugacy problems in monoids and semigroups'. This version will appear in the journal 'Semigroup forum

    Measure Preserving Diffeomorphisms of the Torus are Unclassifiable

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    The isomorphism problem in ergodic theory was formulated by von Neumann in 1932 in his pioneering paper Zur Operatorenmethode in der klassischen Mechanik (Ann. of Math. (2), 33(3):587--642, 1932). The problem has been solved for some classes of transformations that have special properties, such as the collection of transformations with discrete spectrum or Bernoulli shifts. This paper shows that a general classification is impossible (even in concrete settings) by showing that the collection EE of pairs of ergodic, Lebesgue measure preserving diffeomorphisms (S,T)(S,T) of the 2-torus that are isomorphic is a complete analytic set in the CC^\infty- topology (and hence not Borel).Comment: 97 pages, 4 figure

    Describing the set of words generated by interval exchange transformation

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    Let WW be an infinite word over finite alphabet AA. We get combinatorial criteria of existence of interval exchange transformations that generate the word W.Comment: 17 pages, this paper was submitted at scientific council of MSU, date: September 21, 200
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