scholarly journals Succinctness of two-way probabilistic and quantum finite automata

2010 ◽  
Vol Vol. 12 no. 4 ◽  
Author(s):  
Abuzer Yakaryilmaz ◽  
A. C. Cem Say
Keyword(s):  
Finite Automaton ◽  
Finite Automata ◽  
Quantum Computers ◽  
Constant Number ◽  
Special Issue ◽  
Mixed States ◽  
New Model ◽  
Quantum Finite Automata ◽  
International Audience ◽  
Bounded Error

special issue dedicated to the second edition of the conference AutoMathA: from Mathematics to Applications International audience We introduce a new model of two-way finite automaton, which is endowed with the capability of resetting the position of the tape head to the left end of the tape in a single move during the computation. Several variants of this model are examined, with the following results: The weakest known model of computation where quantum computers recognize more languages with bounded error than their classical counterparts is identified. We prove that two-way probabilistic and quantum finite automata (2PFAs and 2QFAs) can be considerably more concise than both their one-way versions (1PFAs and 1QFAs), and two-way nondeterministic finite automata (2NFAs). For this purpose, we demonstrate several infinite families of regular languages which can be recognized with some fixed probability greater than 1 2 by just tuning the transition amplitudes of a 2QFA (and, in one case, a 2PFA) with a constant number of states, whereas the sizes of the corresponding 1PFAs, 1QFAs and 2NFAs grow without bound. We also show that 2QFAs with mixed states can support highly efficient probability amplification.

On the power of two-way multihead quantum finite automata

2019 ◽  
Vol 53 (1-2) ◽  
pp. 19-35 ◽  
Author(s):  
Amandeep Singh Bhatia ◽  
Ajay Kumar
Keyword(s):  
Prime Number ◽  
Finite Automaton ◽  
Finite Automata ◽  
Language Recognition ◽  
Quantum Finite Automata ◽  
Recognition Capability

This paper introduces a variant of two-way quantum finite automata named two-way multihead quantum finite automata. A two-way quantum finite automaton is more powerful than classical two-way finite automata. However, the generalizations of two-way quantum finite automata have not been defined so far as compared to one-way quantum finite automata model. We have investigated the newly introduced automata from two aspects: the language recognition capability and its comparison with classical and quantum counterparts. It has been proved that a language which cannot be recognized by any one-way and multi-letter quantum finite automata can be recognized by two-way quantum finite automata. Further, it has been shown that a language which cannot be recognized by two-way quantum finite automata can be recognized by two-way multihead quantum finite automata with two heads. Furthermore, it has been investigated that quantum variant of two-way deterministic multihead finite automata takes less number of heads to recognize a language containing of all words whose length is a prime number.

scholarly journals Languages recognized by nondeterministic quantum finite automata

2010 ◽  
Vol 10 (9&10) ◽  
pp. 747-770
Author(s):  
Abuzer Yakaryilmaz ◽  
A.C. Cem Say
Keyword(s):  
Finite Automaton ◽  
Finite Automata ◽  
Space Complexity ◽  
Complexity Classes ◽  
Language Recognition ◽  
Closure Properties ◽  
Quantum Finite Automata ◽  
Sublogarithmic Space

The nondeterministic quantum finite automaton (NQFA) is the only known case where a one-way quantum finite automaton (QFA) model has been shown to be strictly superior in terms of language recognition power to its probabilistic counterpart. We give a characterization of the class of languages recognized by NQFAs, demonstrating that it is equal to the class of exclusive stochastic languages. We also characterize the class of languages that are recognized necessarily by two-sided error by QFAs. It is shown that these classes remain the same when the QFAs used in their definitions are replaced by several different model variants that have appeared in the literature. We prove several closure properties of the related classes. The ramifications of these results about classical and quantum sublogarithmic space complexity classes are examined.

scholarly journals p-box: a new graph model

2015 ◽  
Vol Vol. 17 no. 1 (Graph Theory) ◽  
Author(s):  
Mauricio Soto ◽  
Christopher Thraves-Caro
Keyword(s):  
Graph Theory ◽  
Graph Model ◽  
Directed Path ◽  
Outerplanar Graphs ◽  
New Model ◽  
Model Based ◽  
Representative Element ◽  
International Audience ◽  
Graph Families

Graph Theory International audience In this document, we study the scope of the following graph model: each vertex is assigned to a box in ℝd and to a representative element that belongs to that box. Two vertices are connected by an edge if and only if its respective boxes contain the opposite representative element. We focus our study on the case where boxes (and therefore representative elements) associated to vertices are spread in ℝ. We give both, a combinatorial and an intersection characterization of the model. Based on these characterizations, we determine graph families that contain the model (e. g., boxicity 2 graphs) and others that the new model contains (e. g., rooted directed path). We also study the particular case where each representative element is the center of its respective box. In this particular case, we provide constructive representations for interval, block and outerplanar graphs. Finally, we show that the general and the particular model are not equivalent by constructing a graph family that separates the two cases.

scholarly journals Combinatorics of k-shapes and Genocchi numbers

2011 ◽  
Vol DMTCS Proceedings vol. AO,... (Proceedings) ◽  
Author(s):  
Florent Hivert ◽  
Olivier Mallet
Keyword(s):  
Symmetric Functions ◽  
New Model ◽  
Work In Progress ◽  
Genocchi Numbers ◽  
Combinatorial Model ◽  
International Audience

International audience In this paper we present a work in progress on a conjectural new combinatorial model for the Genocchi numbers. This new model called irreducible k-shapes has a strong algebraic background in the theory of symmetric functions and leads to seemingly new features on the theory of Genocchi numbers. In particular, the natural q-analogue coming from the degree of symmetric functions seems to be unknown so far. Dans cet article, nous présentons un travail en cours sur un nouveau modèle combinatoire conjectural pour les nombres de Genocchi. Ce nouveau modèle est celui des k-formes irréductibles, qui repose sur de solides bases algébriques en lien avec la théorie des fonctions symétriques et qui conduit à des aspects apparemment nouveaux de la théorie des nombres de Genocchi. En particulier, le q-analogue naturel venant du degré des fonctions symétriques semble inconnu jusqu'ici.

scholarly journals Implementing Quantum Finite Automata Algorithms on Noisy Devices

2021 ◽  
pp. 3-16
Author(s):  
Utku Birkan ◽  
Özlem Salehi ◽  
Viktor Olejar ◽  
Cem Nurlu ◽  
Abuzer Yakaryılmaz
Keyword(s):  
Finite Automata ◽  
Quantum Finite Automata

scholarly journals Special Issue on Visualisations in Historical Linguistics: Introduction

2020 ◽  
Vol Special issue on... ◽  
Author(s):  
Benjamin Molineaux ◽  
Bettelou Los ◽  
Martti Mäkinen
Keyword(s):  
Historical Linguistics ◽  
Data Visualisation ◽  
Complex Materials ◽  
Special Issue ◽  
The Core ◽  
Methodological Research ◽  
International Audience ◽  
Introductory Paper ◽  
The Individual ◽  
Historical Periods

International audience The advent of ever-larger and more diverse historical corpora for different historical periods and linguistic varieties has led to the impossibility of obtaining simple, direct-and yet balancedrepresentations of the core patterns in the data. In order to draw insights from heterogeneous and complex materials of this type, historical linguists have begun to reach for a growing number of data visualisation techniques, from the statistical, to the cartographical, the network-based and beyond. An exploration of the state of this art was the objective of a workshop at the 2018 International Conference on English Historical Linguistics, from whence most of the materials of this Special Issue are drawn. This brief introductory paper outlines the background and relevance of this line of methodological research and presents a summary of the individual papers that make up the collection.

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