2,113 research outputs found
On insertion-deletion systems over relational words
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
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
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 of pairs of ergodic, Lebesgue measure
preserving diffeomorphisms of the 2-torus that are isomorphic is a
complete analytic set in the - topology (and hence not Borel).Comment: 97 pages, 4 figure
Describing the set of words generated by interval exchange transformation
Let be an infinite word over finite alphabet . 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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