0000000000164015

AUTHOR

Janis Buls

showing 6 related works from this author

Machine Morphisms And Simulation

2012

This paper examines the concept of simulation from a modelling viewpoint. How can one Mealy machine simulate the other one? We create formalism for simulation of Mealy machines. The injective s–morphism of the machine semigroups induces the simulation of machines [1]. We present the example of s–morphism such that it is not a homomorphism of semigroups. The story for the surjective s–morphisms is quite different. These are homomorphisms of semigroups but there exists the surjective s–morphism such that it does not induce the simulation.

Mathematics::Algebraic GeometryMealy machineMathematics::Category Theorysurjective s–morphisms.injective s–morphismsimulationmachine semigroup
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On the Existence of 1-Bounded Bi-ideals with the WELLDOC Property

2015

A combinatorial condition called well distributedoccurrences, or WELLDOC for short, has been introducedrecently. The proofs that WELLDOC property holds for thefamily of Sturmian words, and more generally, for Arnoux-Rauzy words are given in two papers by Balkova et al. The WELLDOC property for bounded bi-ideals is analysed inthis paper. The existence of a 1-bounded bi-ideal over thefinite alphabet that satisfies the WELLDOC property has beenproved by the authors.

Discrete mathematicsAlgebraProperty (philosophy)Computer scienceBounded functionAlphabetComputer-aided software engineeringMathematical proofElectronic mail2015 17th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)
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Partial Finitely Generated Bi-Ideals

2016

Partial words have been studied by Blanchet-Sadri et al., but bi-ideals or reccurrent words have been studied for centuries by many researchers. This paper gives a solution for some problems for partial reccurrent words. This paper gives an algorithm for a given finitely generated bi-ideal, how to construct a new basis of ultimately finitely generated bi-ideal, which generates the same given bi-ideal. The paper states that it is always possible to find a basis for a given finitely generated bi-ideal. The main results of this paper are presented in third section. At first, we show that if two irreduciable bi-ideals are different, they will differ in infinitely many places. This led to the st…

Discrete mathematicsStatement (computer science)Mathematics::Commutative Algebra020207 software engineering0102 computer and information sciences02 engineering and technologyBasis (universal algebra)01 natural sciencesElectronic mailSection (category theory)Stallings theorem about ends of groups010201 computation theory & mathematics0202 electrical engineering electronic engineering information engineeringFinitely-generated abelian groupFinite setCounterexampleMathematics2016 18th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)
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Bounded Bi-ideals and Linear Recurrence

2013

Bounded bi-ideals are a subclass of uniformly recurrent words. We introduce the notion of completely bounded bi-ideals by imposing a restriction on their generating base sequences. We prove that a bounded bi-ideal is linearly recurrent if and only if it is completely bounded.

CombinatoricsCombinatorics on wordsMathematics::Commutative AlgebraBounded setBounded functionBase (topology)Bounded inverse theoremBounded operatorMathematics2013 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
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On a Non-periodic Shrinking Generator

2011

We present a new non-periodic random number generator based on the shrinking generator. The A-sequence is still generated using a LFSR, but the S-sequence is replaced by a finitely generated bi-ideal - a non-periodic sequence. The resulting pseudo-random sequence performs well in statistical tests. We show a method for the construction of an infinite number of finitely generated bi-ideals from a given A-sequence, such that the resulting sequence of the shrinking generator is nonperiodic. Further we prove the existence of what we call universal finitely generated bi-ideals that produce non-periodic words when used as the S-sequence of a shrinking generator for all non-trivial periodic A-sequ…

Discrete mathematicsPseudorandom number generatorSequenceRandom number generationSelf-shrinking generatorAutomata theoryTopologyElectronic mailStatistical hypothesis testingMathematicsShrinking generator2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
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Representation of Autonomous Automata

2001

An autonomous automaton is a finite automaton with output in which the input alphabet has cardinality one when special reduced. We define the transition from automata to semigroups via a representation successful if given two incomparable automata (neither simulate the other), the semigroups representing the automata are distinct. We show that representation by the transition semigroup is not successful. We then consider a representation of automata by semigroups of partial transformations. We show that in general transition from automata to semigroups by this representation is not successful either. In fact, the only successful transition presented is the transiton to this semigroup of par…

Krohn–Rhodes theoryDiscrete mathematicsNested wordFinite-state machineMathematics::Operator AlgebrasComputer scienceSemigroupTimed automatonω-automatonNonlinear Sciences::Cellular Automata and Lattice GasesMobile automatonAutomatonNondeterministic finite automaton with ε-movesStochastic cellular automatonDeterministic finite automatonDFA minimizationDeterministic automatonContinuous spatial automatonSpecial classes of semigroupsQuantum finite automataAutomata theoryTwo-way deterministic finite automatonNondeterministic finite automatonComputer Science::Formal Languages and Automata Theory
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