Affine Computation and Affine Automaton

Díaz-Caro, Alejandro; Yakaryılmaz, Abuzer

doi:10.1007/978-3-319-34171-2_11

Cited by 15 publications

(27 citation statements)

References 13 publications

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“…In previous research we studied alternating finite state automata. In this work we studied QFAs, and in the extended version of this paper [3] we consider the novel model of affine automata [6,15]. We think that these questions are interesting in their own rigth, and that they deserve further investigation.…”

Section: Discussionmentioning

confidence: 99%

Looking for Pairs that Hard to Separate: A Quantum Approach

Belovs

Montoya

Yakaryılmaz

2016

Implementation and Application of Automata

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Abstract. Determining the minimum number of states required by a deterministic finite automaton to separate a given pair of different words (to accept one word and to reject the other) is an important challenge. In this paper, we ask the same question for quantum finite automata (QFAs). We classify such pairs as easy and hard ones. We show that 2-state QFAs with real amplitudes can separate any easy pair with zero-error but cannot separate some hard pairs even in nondeterministic acceptance mode. When using complex amplitudes, 2-state QFAs can separate any pair in nondeterministic acceptance mode, and here we conjecture that they can separate any pair also with zero-error. Then, we focus on (a more general problem) separating a pair of two disjoint finite set of words. We show that QFAs can separate them efficiently in nondeterministic acceptance mode, i.e., the number of states is two to the power of the size of the small set.

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Section: Discussionmentioning

confidence: 99%

Looking for Pairs that Hard to Separate: A Quantum Approach

Belovs

Montoya

Yakaryılmaz

2016

Implementation and Application of Automata

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“…Recently, the same question has been investigated in [1,2] for different models such as probabilistic, quantum, and affine finite automata (respectively, PFA, QFA, AfA). (We refer the reader to [6,24] for details of these models.) As these models are capable of storing information in their probabilities or amplitudes, they can be much more state-efficient than DFAs.…”

Section: The String Separation Problemmentioning

confidence: 99%

New Results on Vector and Homing Vector Automata

Salehi

Yakaryılmaz

Say

2019

Int. J. Found. Comput. Sci.

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We present several new results and connections between various extensions of finite automata through the study of vector automata and homing vector automata. We show that homing vector automata outperform extended finite automata when both are defined over 2 × 2 integer matrices. We study the string separation problem for vector automata and demonstrate that generalized finite automata with rational entries can separate any pair of strings using only two states. Investigating stateless homing vector automata, we prove that a language is recognized by stateless blind deterministic realtime version of finite automata with multiplication iff it is commutative and its Parikh image is the set of nonnegative integer solutions to a system of linear homogeneous Diophantine equations.

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“…Proof. It is known that AfAs can recognize PAL with one-sided bounded-error [15,19] and so we can design a Las Vegas automaton for PAL-NPAL by using similar ideas given in [11,6].…”

Section: Las Vegas Algorithmsmentioning

confidence: 99%

“…This is mainly because quantum models are allowed to use negative amplitudes, by which interference can occur between configurations. In order to mimic quantum interference classically, recently a new concept called affine computation was introduced [4] and its finite automata versions (AfAs) have been examined [4,15,2,8]. Some underlying results are as follows: (i) they are more powerful than their probabilistic and quantum counterparts (PFAs and QFAs) with bounded and unbounded error; (ii) one-sided bounded-error AfAs and nondeterministic QFAs define the same class when using rational number transitions; and, (iii) AfAs can distinguish any given pair of strings by using two states with zero-error.…”

Section: Introductionmentioning

confidence: 99%

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Exact Affine Counter Automata

Nakanishi

Khadiev

Prūsis

et al. 2017

Electron. Proc. Theor. Comput. Sci.

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We introduce an affine generalization of counter automata, and analyze their ability as well as affine finite automata. Our contributions are as follows. We show that there is a language that can be recognized by exact realtime affine counter automata but by neither 1-way deterministic pushdown automata nor realtime deterministic k-counter automata. We also show that a certain promise problem, which is conjectured not to be solved by two-way quantum finite automata in polynomial time, can be solved by Las Vegas affine finite automata. Lastly, we show that how a counter helps for affine finite automata by showing that the language MANYTWINS, which is conjectured not to be recognized by affine, quantum or classical finite state models in polynomial time, can be recognized by affine counter automata with one-sided bounded-error in realtime.Comment: In Proceedings AFL 2017, arXiv:1708.0622

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Affine Computation and Affine Automaton

Cited by 15 publications

References 13 publications

Looking for Pairs that Hard to Separate: A Quantum Approach

Looking for Pairs that Hard to Separate: A Quantum Approach

New Results on Vector and Homing Vector Automata

Exact Affine Counter Automata

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