Energy Complexity of Regular Language Recognition

Yılmaz, Öykü; Kıyak, Fırat; Meriç, Üngör,; Say, A. C. Cem

doi:10.1007/978-3-031-07469-1_16

Cited by 4 publications

(5 citation statements)

References 12 publications

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“…They do not capture the regular languages either. This is in contrast to modified recent definitions that lead to quantum finite automata which recognize all and only the regular languages with bounded error [8,23,24]. See [18] and the references therein for a recent survey on quantum automata.…”

Section: Introductionmentioning

confidence: 91%

Reversible Computations of One-Way Counter Automata

Kutrib

Malcher

2022

Electron. Proc. Theor. Comput. Sci.

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Deterministic one-way time-bounded multi-counter automata are studied with respect to their ability to perform reversible computations, which means that the automata are also backward deterministic and, thus, are able to uniquely step the computation back and forth. We study the computational capacity of such devices and obtain separation results between irreversible and reversible k-counter automata for superpolynomial time. For exponential time we obtain moreover an infinite and tight hierarchy with respect to the number of counters. This hierarchy is shown with Kolmogorov complexity and incompressibility arguments. In this way, on passing we can prove this hierarchy also for ordinary counter automata. This improves the known hierarchy for ordinary counter automata in the sense that here we consider a weaker acceptance condition. Then, it turns out that k + 1 reversible counters are not better than k ordinary counters and vice versa. Finally, almost all usually studied decidability questions turn out to be undecidable and not even semidecidable for reversible multi-counter automata, if at least two counters are provided.

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Section: Introductionmentioning

confidence: 91%

Reversible Computations of One-Way Counter Automata

Kutrib

Malcher

2022

Electron. Proc. Theor. Comput. Sci.

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show abstract

“…They do not capture the regular languages either. This is in contrast to modified recent definitions that lead to quantum finite automata which recognize all and only the regular languages with bounded error [10][11][12]. See [13] and the references therein for a recent survey on quantum automata.…”

Section: Introductionmentioning

confidence: 92%

“…Then, transitions (2) and (3) are used to count the difference one. Transitions (5), ( 7) and ( 10), (12) increase the difference by one and transitions (8) and (11) decrease the difference by one. Finally, if the difference is one, then transitions ( 6) and ( 9) can be used to decrease the difference to zero, to enter state q 1 , and to enter an accepting state when reading the right endmarker with transition (4).…”

Section: Preliminariesmentioning

confidence: 99%

“…Thus, for δ ← we have to increase the difference when reading a b (transitions ( 6) and ( 8)) and to decrease the difference when reading an a (transitions ( 5) and ( 7)). The transitions (2)-( 3) and ( 9)- (12) can analogously be translated. To translate the transitions (1) , respectively.…”

Section: Preliminariesmentioning

confidence: 99%

“…By construction, after the second phase of an accepting computation, M is in state s i , where the factor $ i z 2 has been processed. In order to reach state s i by Transition (12) or ( 13) the auxiliary counter must be empty. As above, before we continue the construction with the third phase, we consider the reversibility of M in the second phase.…”

Section: State Qmentioning

confidence: 99%

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Reversible Computations of One-Way Counter Automata

Kutrib,

Malcher

2024

RAIRO-Theor. Inf. Appl.

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Deterministic one-way time-bounded multi-counter automata are studied with respect to their ability to perform reversible computations, which means that the automata are also backward deterministic and, thus, are able to uniquely step the computation back and forth. We study the computational capacity of such devices and obtain separation results between irreversible and reversible k-counter automata for polynomial and superpolynomial time. For polynomial time and exponential time we obtain moreover infinite and tight hierarchies with respect to the number of counters. These hierarchies are shown with Kolmogorov complexity and incompressibility arguments. In this way, on passing we can prove these hierarchies also for ordinary counter automata. This improves the known hierarchies for ordinary counter automata in the sense that we consider here a weaker acceptance condition. Then, it turns out that k +1 reversible counters are not better than k ordinary counters and vice versa. Finally, almost all usually studied decidability questions turn out to be undecidable and not even semidecidable for reversible multi-counter automata, if at least two counters are provided. In case of reversible one-counter automata, it is possible to show that the inclusion problem is also not even semidecidable.

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Energy Complexity of Computation

Say

2023

Lecture Notes in Computer Science

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Energy Complexity of Regular Language Recognition

Cited by 4 publications

References 12 publications

Reversible Computations of One-Way Counter Automata

Reversible Computations of One-Way Counter Automata

Reversible Computations of One-Way Counter Automata

Energy Complexity of Computation

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