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The avoidability of binary patterns by binary cube-free words is investigated and the exact bound between unavoidable and avoidable patterns is found. All avoidable patterns are shown to be D0L-avoidable. For avoidable patterns, the growth rates of the avoiding languages are studied. All such languages, except for the overlap-free language, are proved to have exponential growth. The exact growth rates of languages avoiding minimal avoidable patterns are approximated through computer-assisted upper...
Rough sets, developed by Zdzisław Pawlak [12], are an important tool to describe the state of incomplete or partially unknown information. In this article, which is essentially the continuation of [8], we try to give the characterization of approximation operators in terms of ordinary properties of underlying relations (some of them, as serial and mediate relations, were not available in the Mizar Mathematical Library [11]). Here we drop the classical equivalence- and tolerance-based models of rough...
We show that there are three types of infinite words over the two-letter
alphabet {0,1} that avoid the pattern AABBCABBA. These types, P, E0, and E1,
differ by the factor complexity and the asymptotic frequency of the letter 0.
Type P has polynomial factor complexity and letter frequency .
Type E0 has exponential factor complexity and the frequency of the letter 0 is at least
0.45622 and at most 0.48684. Type E1 is obtained from type E0 by exchanging 0 and 1.
A binomial residue is a rational function defined by a hypergeometric integral whose
kernel is singular along binomial divisors. Binomial residues provide an integral
representation for rational solutions of -hypergeometric systems of Lawrence type. The
space of binomial residues of a given degree, modulo those which are polynomial in some
variable, has dimension equal to the Euler characteristic of the matroid associated with
.
This article proposes a decentralized navigation controller for a group of differential mobile robots that yields autonomous navigation, which allows reaching a certain desired position with a specific desired orientation, while avoiding collisions with dynamic and static obstacles. The navigation controller is constituted by two control loops, the so-called external control loop is based on crowd dynamics, it brings autonomous navigation properties to the system, the internal control loop transforms...
More than a decade ago, Moller and Tofts published their seminal work on relating processes, which are annotated with lower time bounds, with respect to speed. Their paper has left open many questions regarding the semantic theory for the suggested bisimulation-based faster-than preorder, the MT-preorder, which have not been addressed since. The encountered difficulties concern a general compositionality result, a complete axiom system for finite processes, a convincing intuitive justification of...
More than a decade ago, Moller and Tofts published their seminal
work on relating processes, which are annotated with lower time
bounds, with respect to speed. Their paper has left open many
questions regarding the semantic theory for the suggested
bisimulation-based faster-than preorder, the MT-preorder, which
have not been addressed since. The encountered difficulties concern
a general compositionality result, a complete axiom system for
finite processes, a convincing intuitive justification...
In this paper, we develop a divide-and-conquer approach, called block decomposition, to solve the minimum geodetic set problem. This provides us with a unified approach for all graphs admitting blocks for which the problem of finding a minimum geodetic set containing a given set of vertices (g-extension problem) can be efficiently solved. Our method allows us to derive linear time algorithms for the minimum geodetic set problem in (a proper superclass of) block-cacti and monopolar chordal graphs....
For almost all infinite binary sequences of Bernoulli trials the frequency of blocks of length in the first terms tends asymptotically to the probability of the blocks, if increases like (for ) where tends to . This generalizes a result due to P. Flajolet, P. Kirschenhofer and R.F. Tichy concerning the case .
Border bases are an alternative to Gröbner bases. The former have several more desirable properties. In this paper some constructions and operations on border bases are presented. Namely; the case of a restriction of an ideal to a polynomial ring (in a smaller number of variables), the case of the intersection of two ideals, and the case of the kernel of a homomorphism of polynomial rings. These constructions are applied to the ideal of relations and to factorizable derivations.
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