Search results for "complexi"

showing 10 items of 1116 documents

Machine-Independent Characterizations and Complete Problems for Deterministic Linear Time

2002

This article presents two algebraic characterizations and two related complete problems for the complexity class DLIN that was introduced in [E. Grandjean, Ann. Math. Artif. Intell., 16 (1996), pp. 183--236]. DLIN is essentially the class of all functions that can be computed in linear time on a Random Access Machine which uses only numbers of linear value during its computations. The algebraic characterizations are in terms of recursion schemes that define unary functions. One of these schemes defines several functions simultaneously, while the other one defines only one function. From the algebraic characterizations, we derive two complete problems for DLIN under new, very strict, and mac…

Discrete mathematicsGeneral Computer ScienceUnary operationGeneral Mathematics[INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS]Recursion (computer science)[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS]0102 computer and information sciences02 engineering and technologyFunction (mathematics)01 natural sciencesRandom-access machine010201 computation theory & mathematicsCompleteness (order theory)0202 electrical engineering electronic engineering information engineeringComplexity class020201 artificial intelligence & image processingAlgebraic numberTime complexityMathematics
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Application of kolmogorov complexity to inductive inference with limited memory

1995

A b s t r a c t . We consider inductive inference with limited memory[l]. We show that there exists a set U of total recursive functions such that U can be learned with linear long-term memory (and no short-term memory); U can be learned with logarithmic long-term memory (and some amount of short-term memory); if U is learned with sublinear long-term memory, then the short-term memory exceeds arbitrary recursive function. Thus an open problem posed by Freivalds, Kinber and Smith[l] is solved. To prove our result, we use Kolmogorov complexity.

Discrete mathematicsHardware_MEMORYSTRUCTURESKolmogorov complexityLogarithmSublinear functionKolmogorov structure functionChain rule for Kolmogorov complexityOpen problemInductive probabilityInductive reasoningMathematics
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Nondeterministic Unitary OBDDs

2017

We investigate the width complexity of nondeterministic unitary OBDDs (NUOBDDs). Firstly, we present a generic lower bound on their widths based on the size of strong 1-fooling sets. Then, we present classically “cheap” functions that are “expensive” for NUOBDDs and vice versa by improving the previous gap. We also present a function for which neither classical nor unitary nondeterminism does help. Moreover, based on our results, we present a width hierarchy for NUOBDDs. Lastly, we provide the bounds on the widths of NUOBDDs for the basic Boolean operations negation, union, and intersection.

Discrete mathematicsHierarchy (mathematics)Intersection (set theory)010102 general mathematics0102 computer and information sciencesFunction (mathematics)Computer Science::Computational Complexity01 natural sciencesUpper and lower boundsUnitary stateNondeterministic algorithmCombinatoricsNegation010201 computation theory & mathematicsBoolean operations in computer-aided design0101 mathematicsMathematics
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Very Narrow Quantum OBDDs and Width Hierarchies for Classical OBDDs

2014

In the paper we investigate a model for computing of Boolean functions – Ordered Binary Decision Diagrams (OBDDs), which is a restricted version of Branching Programs. We present several results on the comparative complexity for several variants of OBDD models. We present some results on the comparative complexity of classical and quantum OBDDs. We consider a partial function depending on a parameter k such that for any k > 0 this function is computed by an exact quantum OBDD of width 2, but any classical OBDD (deterministic or stable bounded-error probabilistic) needs width 2 k + 1. We consider quantum and classical nondeterminism. We show that quantum nondeterminism can be more efficient …

Discrete mathematicsImplicit functionBinary decision diagram010102 general mathematics02 engineering and technologyFunction (mathematics)Computer Science::Artificial IntelligenceComputer Science::Computational Complexity01 natural sciencesCombinatoricsNondeterministic algorithmComputer Science::Logic in Computer SciencePartial function0202 electrical engineering electronic engineering information engineering020201 artificial intelligence & image processing0101 mathematicsBoolean functionQuantumQuantum computerMathematics
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The computational complexity of the relative robust shortest path problem with interval data

2004

Abstract The paper deals with the relative robust shortest path problem in a directed arc weighted graph, where arc lengths are specified as intervals containing possible realizations of arc lengths. The complexity status of this problem has been unknown in the literature. We show that the problem is NP -hard.

Discrete mathematicsInformation Systems and ManagementGeneral Computer ScienceManagement Science and Operations ResearchIndustrial and Manufacturing EngineeringLongest path problemWidest path problemEuclidean shortest pathShortest Path Faster AlgorithmTheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITYModeling and SimulationShortest path problemK shortest path routingCanadian traveller problemDistanceMathematicsofComputing_DISCRETEMATHEMATICSMathematicsEuropean Journal of Operational Research
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The computational complexity of the criticality problems in a network with interval activity times

2002

Abstract The paper analyzes the criticality in a network with interval activities duration times. A natural generalization of the criticality notion (for a path, an activity and an event) for the case of network with interval activity duration times is given. The computation complexity of five problems linked to the introduced criticality notion is presented.

Discrete mathematicsInformation Systems and ManagementTheoretical computer scienceGeneral Computer ScienceComputational complexity theoryGeneralizationEvent (relativity)Interval (mathematics)Management Science and Operations ResearchIndustrial and Manufacturing EngineeringCriticalityModeling and SimulationPath (graph theory)Computation complexityDuration (project management)MathematicsEuropean Journal of Operational Research
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Periodicity and repetitions in parameterized strings

2008

AbstractOne of the most beautiful and useful notions in the Mathematical Theory of Strings is that of a Period, i.e., an initial piece of a given string that can generate that string by repeating itself at regular intervals. Periods have an elegant mathematical structure and a wealth of applications [F. Mignosi and A. Restivo, Periodicity, Algebraic Combinatorics on Words, in: M. Lothaire (Ed.), Cambridge University Press, Cambridge, pp. 237–274, 2002]. At the hearth of their theory, there are two Periodicity Lemmas: one due to Lyndon and Schutzenberger [The equation aM=bNcP in a free group, Michigan Math. J. 9 (1962) 289–298], referred to as the Weak Version, and the other due to Fine and …

Discrete mathematicsLemma (mathematics)Algebraic combinatoricsCombinatorics on wordsSettore INF/01 - InformaticaApplied MathematicsParameterized complexityParameterized stringsString searching algorithmString (physics)Periodic functionCombinatoricsCombinatorics on wordsDiscrete Mathematics and CombinatoricsString periodicityUniquenessCombinatorics on Words AlgorithmsMathematics
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Quantum Finite Automata and Logics

2006

The connection between measure once quantum finite automata (MO-QFA) and logic is studied in this paper. The language class recognized by MO-QFA is compared to languages described by the first order logics and modular logics. And the equivalence between languages accepted by MO-QFA and languages described by formulas using Lindstrom quantifier is shown.

Discrete mathematicsLindström quantifierNested wordAbstract family of languagesComputer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing)Computer Science::Computational ComplexityComputer Science::Digital LibrariesAlgebraTheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESMonoidal t-norm logicComputer Science::Programming LanguagesQuantum finite automataEquivalence (formal languages)T-norm fuzzy logicsComputer Science::Formal Languages and Automata TheoryAND gateMathematics
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Logics with counting and equivalence

2014

We consider the two-variable fragment of first-order logic with counting, subject to the stipulation that a single distinguished binary predicate be interpreted as an equivalence. We show that the satisfiability and finite satisfiability problems for this logic are both NEXPTIME-complete. We further show that the corresponding problems for two-variable first-order logic with counting and two equivalences are both undecidable.

Discrete mathematicsLogical equivalenceComplexityHigher-order logicSatisfiabilityUndecidable problemStipulationCombinatoricsBinary predicateTheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESEquivalence relationComputer Science::Logic in Computer ScienceEquivalence relationSatisfiabilityEquivalence (formal languages)MathematicsProceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
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Minimal Morse flows on compact manifolds

2006

Abstract In this paper we prove, using the Poincare–Hopf inequalities, that a minimal number of non-degenerate singularities can be computed in terms only of abstract homological boundary information. Furthermore, this minimal number can be realized on some manifold with non-empty boundary satisfying the abstract homological boundary information. In fact, we present all possible indices and types (connecting or disconnecting) of singularities realizing this minimal number. The Euler characteristics of all manifolds realizing this minimal number are obtained and the associated Lyapunov graphs of Morse type are described and shown to have the lowest topological complexity.

Discrete mathematicsLyapunov functionTopological complexityBoundary (topology)Type (model theory)Morse codeManifoldLyapunov graphslaw.inventionsymbols.namesakePoincaré–Hopf inequalitieslawEuler's formulasymbolsGravitational singularityGeometry and TopologyMathematics::Symplectic GeometryConley indexMathematicsTopology and its Applications
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