Search results for "rete"

showing 10 items of 3470 documents

On extremal cases of Hopcroft’s algorithm

2010

AbstractIn this paper we consider the problem of minimization of deterministic finite automata (DFA) with reference to Hopcroft’s algorithm. Hopcroft’s algorithm has several degrees of freedom, so there can exist different executions that can lead to different sequences of refinements of the set of the states up to the final partition. We find an infinite family of binary automata for which such a process is unique, whatever strategy is chosen. Some recent papers (cf. Berstel and Carton (2004) [3], Castiglione et al. (2008) [6] and Berstel et al. (2009) [1]) have been devoted to find families of automata for which Hopcroft’s algorithm has its worst execution time. They are unary automata as…

Discrete mathematicsFinite-state machineGeneral Computer ScienceUnary operationWord treesStandard treesAutomatonTheoretical Computer ScienceCombinatoricsDeterministic finite automatonDFA minimizationDeterministic automatonHopcroft’s minimization algorithmTree automatonDeterministic finite state automataTime complexityAlgorithmComputer Science::Formal Languages and Automata TheoryMathematicsComputer Science(all)Theoretical Computer Science
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Counting with Probabilistic and Ultrametric Finite Automata

2014

We investigate the state complexity of probabilistic and ultrametric finite automata for the problem of counting, i.e. recognizing the one-word unary language \(C_n=\left\{ 1^n \right\} \). We also review the known results for other types of automata.

Discrete mathematicsFinite-state machineState complexityUnary languageProbabilistic logicQuantum finite automataNonlinear Sciences::Cellular Automata and Lattice GasesUltrametric spaceComputer Science::Formal Languages and Automata TheoryMathematicsAutomaton
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Superiority Of One-Way And Realtime Quantum Machines

2012

In automata theory, quantum computation has been widely examined for finite state machines, known as quantum finite automata (QFAs), and less attention has been given to QFAs augmented with counters or stacks. In this paper, we focus on such generalizations of QFAs where the input head operates in one-way or realtime mode, and present some new results regarding their superiority over their classical counterparts. Our first result is about the nondeterministic acceptance mode: Each quantum model architecturally intermediate between realtime finite state automaton and one-way pushdown automaton (one-way finite automaton, realtime and one-way finite automata with one-counter, and realtime push…

Discrete mathematicsFinite-state machineTheoryofComputation_COMPUTATIONBYABSTRACTDEVICESGeneral MathematicsPushdown automaton0102 computer and information sciences02 engineering and technologyω-automaton01 natural sciencesComputer Science ApplicationsNondeterministic algorithmTheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES010201 computation theory & mathematics0202 electrical engineering electronic engineering information engineeringQuantum finite automataAutomata theory020201 artificial intelligence & image processingAlgorithmSoftwareComputer Science::Formal Languages and Automata TheoryQuantum cellular automatonMathematicsQuantum computer
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Affine Automata Verifiers

2021

We initiate the study of the verification power of Affine finite automata (AfA) as a part of Arthur-Merlin (AM) proof systems. We show that every unary language is verified by a real-valued AfA verifier. Then, we focus on the verifiers restricted to have only integer-valued or rational-valued transitions. We observe that rational-valued verifiers can be simulated by integer-valued verifiers, and their protocols can be simulated in nondeterministic polynomial time. We show that this upper bound is tight by presenting an AfA verifier for NP-complete problem SUBSETSUM. We also show that AfAs can verify certain non-affine and non-stochastic unary languages.

Discrete mathematicsFinite-state machineUnary operationComputer scienceUnary languageSubset sum problemAffine transformationUpper and lower boundsNPAutomaton
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A natural and rigid model of quantum groups

1992

We introduce a natural (Frechet-Hopf) algebra A containing all generic Jimbo algebras U t (sl(2)) (as dense subalgebras). The Hopf structures on A extend (in a continuous way) the Hopf structures of generic U t (sl(2)). The Universal R-matrices converge in A\(\hat \otimes \)A. Using the (topological) dual of A, we recover the formalism of functions of noncommutative arguments. In addition, we show that all these Hopf structures on A are isomorphic (as bialgebras), and rigid in the category of bialgebras.

Discrete mathematicsFormalism (philosophy of mathematics)Pure mathematicsRigid modelQuantum groupMathematics::Quantum AlgebraMathematics::Rings and AlgebrasStatistical and Nonlinear PhysicsHopf algebraNoncommutative geometryQuantumMathematical PhysicsMathematicsLetters in Mathematical Physics
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A Graph Based Algorithm For Intersection Of Subdivision Surfaces

2003

Computing surface intersections is a fundamental problem in geometric modeling. Any boolean operation can be seen as an intersection calculation followed by a selection of the parts necessary for building the surface of the resulting object. A robust and efficient algorithm to compute intersection on subdivision surfaces (surfaces generated by the Loop scheme) is proposed here. This algorithm relies on the concept of a bipartite graph which allows the reduction of the number of faces intersection tests. Intersection computations are accelerated by the use of the bipartite graph and the neighborhood of intersecting faces at a given level of subdivision to deduce intersecting faces at the fol…

Discrete mathematicsFoster graph[INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS][INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS][ INFO.INFO-DM ] Computer Science [cs]/Discrete Mathematics [cs.DM][INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]Intersection number (graph theory)Intersection graphlaw.inventionCombinatorics[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]IntersectionlawHomeomorphism (graph theory)Subdivision surfaceCircle graphAlgorithmComputingMilieux_MISCELLANEOUS[ INFO.INFO-DS ] Computer Science [cs]/Data Structures and Algorithms [cs.DS]ComputingMethodologies_COMPUTERGRAPHICSMathematicsDistance-hereditary graph
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Single-valued extension property at the points of the approximate point spectrum

2003

Abstract A localized version of the single-valued extension property is studied at the points which are not limit points of the approximate point spectrum, as well as of the surjectivity spectrum. In particular, we shall characterize the single-valued extension property at a point λ o ∈ C in the case that λoI−T is of Kato type. From this characterizations we shall deduce several results on cluster points of some distinguished parts of the spectrum.

Discrete mathematicsFredholm theoryFredholm operatorApplied MathematicsSpectrum (functional analysis)Banach spaceExtension (predicate logic)Type (model theory)Fredholm theorySingle valued extension propertysymbols.namesakeLimit pointsymbolsPoint (geometry)AnalysisMathematicsJournal of Mathematical Analysis and Applications
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Operators Which Do Not Have the Single Valued Extension Property

2000

Abstract In this paper we shall consider the relationships between a local version of the single valued extension property of a bounded operator T  ∈  L ( X ) on a Banach space X and some quantities associated with T which play an important role in Fredholm theory. In particular, we shall consider some conditions for which T does not have the single valued extension property at a point λ o  ∈  C .

Discrete mathematicsFredholm theoryProperty (philosophy)Applied MathematicsFredholm operatorBanach spaceExtension (predicate logic)Fredholm theoryBounded operatorLinear mapsymbols.namesakesingle valued extension propertysymbolsAnalysisMathematicsResolventJournal of Mathematical Analysis and Applications
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Banach spaces which are somewhat uniformly noncreasy

2003

AbstractWe consider a family of spaces wider than r-UNC spaces and we give some fixed point results in the setting of these spaces.

Discrete mathematicsFréchet spaceApplied MathematicsLocally convex topological vector spaceInterpolation spaceUniformly convex spaceBirnbaum–Orlicz spaceBanach manifoldReflexive spaceLp spaceQuantitative Biology::GenomicsAnalysisMathematicsJournal of Mathematical Analysis and Applications
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Holomorphic Mappings of Bounded Type on (DF)-Spaces

1992

We study the holomorphic functions of bounded type defined on (DF)-spaces. We prove that they are of uniformly bounded type. The space of all these functions is a Frechet space with its natural topology. Some consequences and related results are obtained.

Discrete mathematicsFréchet spaceBounded functionHolomorphic functionUniform boundednessTotally bounded spaceNatural topologyIdentity theoremBounded typeMathematics
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