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.

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 SUBLINEARLY SPACE BOUNDED ITERATIVE ARRAYS

2010 ◽  
Vol 21 (05) ◽  
pp. 843-858 ◽  
Author(s):  
ANDREAS MALCHER ◽  
CARLO MEREGHETTI ◽  
BEATRICE PALANO
Keyword(s):  
Lower Bound ◽  
Computational Model ◽  
Regular Language ◽  
Finite Automata ◽  
Complexity Classes ◽  
Language Recognition ◽  
Deterministic Finite Automata ◽  
One Dimensional ◽  
Sequential Processing ◽  
Trade Offs

Iterative arrays (IAs) are a parallel computational model with a sequential processing of the input. They are one-dimensional arrays of interacting identical deterministic finite automata. In this paper, realtime-IAs with sublinear space bounds are used to recognize formal languages. The existence of an infinite proper hierarchy of space complexity classes between logarithmic and linear space bounds is proved. Some decidability questions on logarithmically space bounded realtime-IAs are investigated, and an optimal logarithmic space lower bound for non-regular language recognition on realtime-IAs is shown. Finally, some non-recursive trade-offs between space bounded realtime-IAs are emphasized.

Quantum Automata with Open Time Evolution

2012 ◽  
pp. 74-89
Author(s):  
Mika Hirvensalo
Keyword(s):  
Time Evolution ◽  
Finite Automaton ◽  
Finite Automata ◽  
Quantum Evolution ◽  
Closure Properties ◽  
Probabilistic Measure ◽  
Quantum Automata ◽  
Open Quantum ◽  
Quantum Measure ◽  
Open Time

In this paper, a model for finite automaton with an open quantum evolution is introduced, and its basic properties are studied. It is shown that the (fuzzy) languages accepted by open evolution quantum automata obey various closure properties. More importantly, it is shown that major other models of finite automata, including probabilistic, measure once quantum, measure many quantum, and Latvian quantum automata can be simulated by the open quantum evolution automata without increasing the number of the states.

Automata theory based on unsharp quantum logic

2009 ◽  
Vol 19 (4) ◽  
pp. 737-756 ◽  
Author(s):  
YUN SHANG ◽  
XIAN LU ◽  
RUQIAN LU
Keyword(s):  
Quantum Logic ◽  
Finite Automata ◽  
Automata Theory ◽  
Quantum Structures ◽  
Closure Properties ◽  
Mv Algebra ◽  
Quantum Finite Automata ◽  
Distributive Law ◽  
Qmv Algebras ◽  
Mv Algebras

By studying two unsharp quantum structures, namely extended lattice ordered effect algebras and lattice ordered QMV algebras, we obtain some characteristic theorems of MV algebras. We go on to discuss automata theory based on these two unsharp quantum structures. In particular, we prove that an extended lattice ordered effect algebra (or a lattice ordered QMV algebra) is an MV algebra if and only if a certain kind of distributive law holds for the sum operation. We introduce the notions of (quantum) finite automata based on these two unsharp quantum structures, and discuss closure properties of languages and the subset construction of automata. We show that the universal validity of some important properties (such as sum, concatenation and subset constructions) depend heavily on the above distributive law. These generalise results about automata theory based on sharp quantum logic.

Quantum Automata with Open Time Evolution

2010 ◽  
Vol 1 (1) ◽  
pp. 70-85 ◽  
Author(s):  
Mika Hirvensalo
Keyword(s):  
Time Evolution ◽  
Finite Automaton ◽  
Finite Automata ◽  
Quantum Evolution ◽  
Closure Properties ◽  
Probabilistic Measure ◽  
Quantum Automata ◽  
Open Quantum ◽  
Quantum Measure ◽  
Open Time

In this paper, a model for finite automaton with an open quantum evolution is introduced, and its basic properties are studied. It is shown that the (fuzzy) languages accepted by open evolution quantum automata obey various closure properties. More importantly, it is shown that major other models of finite automata, including probabilistic, measure once quantum, measure many quantum, and Latvian quantum automata can be simulated by the open quantum evolution automata without increasing the number of the states.

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 SOME RELATIONS BETWEEN THE LATTICES R-nat, R-conat AND R-tors AND THE RINGS THEY CHARACTERIZE

2013 ◽  
Vol 12 (05) ◽  
pp. 1250214
Author(s):  
HUGO A. RINCÓN-MEJÍA ◽  
MANUEL G. ZORRILLA-NORIEGA
Keyword(s):  
Lattice Isomorphism ◽  
Torsion Class ◽  
Closure Properties

This article consists of two sections. In the first one, the concepts of spanning and cospanning classes of modules, both hereditarily and cohereditarily, are explained, and some closure properties of the class of modules hereditarily cospanned by a conatural class are established, which amount to its being a hereditary torsion class. This gives a function from R-conat to R-tors and it is proven that its being a lattice isomorphism is part of a characterization of bilaterally perfect rings. The second section begins considering a description of pseudocomplements in certain lattices of module classes. The idea is generalized to define an inclusion-reversing operation on the collection of classes of modules. Restricted to R-nat, it is shown to be a function onto R-tors, and its being an anti-isomorphism is equivalent to R being left semiartinian. Lastly, another characterization of R being left semiartinian is given, in terms solely of R-tors.

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