Removing nondeterminism in constant height pushdown automata

Bednárová, Zuzana; Geffert, Viliam; Mereghetti, Carlo; Palano, Beatrice

doi:10.1016/j.ic.2014.03.002

Cited by 10 publications

(5 citation statements)

References 15 publications

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“…However, pdas in that form can be turned into the form we consider here with a polynomial increase in size and by preserving the property of being constant height. For a further discussion on this point, we address the reader to [4].…”

Section: Preliminariesmentioning

confidence: 99%

“…Further properties of these devices have been recently considered. A double-exponential size increase when converting a nondeterministic constant-height pushdown automaton into an equivalent deterministic one, which cannot be avoided in the worst case, has been proven in [4]. A double-exponential size gap also holds for the conversion of deterministic and nondeterministic constant-height pushdown automata with a two-way input head into equivalent one-way devices [3].…”

Section: Introductionmentioning

confidence: 99%

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Pushdown automata and constant height: decidability and bounds

Pighizzini

Prigioniero

2022

Acta Informatica

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It cannot be decided whether a pushdown automaton accepts using a pushdown height, which does not depend on the input length, i.e., when it accepts using constant height. Furthermore, when a pushdown automaton accepts in constant height, the height can be arbitrarily large with respect to the size of the description of the machine, namely it does not exist any recursive function in the size of the description of the machine bounding the height of the pushdown. In contrast, in the restricted case of pushdown automata over a one-letter input alphabet, i.e., unary pushdown automata, the situation is different. First, acceptance in constant height is decidable. Moreover, in the case of acceptance in constant height, the height is at most exponential with respect to the size of the description of the pushdown automaton. We also prove a matching lower bound. Finally, if a unary pushdown automaton uses nonconstant height to accept, then the height should grow at least as the logarithm of the input length. This bound is optimal.

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Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Pushdown automata and constant height: decidability and bounds

Pighizzini

Prigioniero

2022

Acta Informatica

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“…With this being said, we would also like to quickly comment on the language L m from a Theoretical Computer Science viewpoint. Notwithstanding its simplicity, the language L m plays a crucial role in Descriptional Complexity Theory (see, e.g., in [17][18][19][20][21]), the area of Formal Language Theory in which the size of computational models is investigated. In particular, a well-consolidated trend in Descriptional Complexity is devoted to study the size of several types of finite automata.…”

Section: Formal Languages Finite Automata and Quantum Computingmentioning

confidence: 99%

An Enhanced Photonic Quantum Finite Automaton

et al. 2021

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In a recent paper we have described an optical implementation of a measure-once one-way quantum finite automaton recognizing a well-known family of unary periodic languages, accepting words not in the language with a given error probability. To process input words, the automaton exploits the degree of polarization of single photons and, to reduce the acceptance error probability, a technique of confidence amplification using the photon counts is implemented. In this paper, we show that the performance of this automaton may be further improved by using strategies that suitably consider both the orthogonal output polarizations of the photon. In our analysis, we also take into account how detector dark counts may affect the performance of the automaton.

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“…It is undecidable whether a pda accepts in constant height. 2 Proof. (outline) We give a reduction from the halting problem.…”

Section: Undecidability and Non-recursive Boundsmentioning

confidence: 99%

“…In some papers pdas are presented in different forms. As pointed out in[2], it is possible to turn the definition of pdas into these equivalent forms, with a polynomial increase in size and by preserving the property of being constant height.…”

mentioning

confidence: 99%

Pushdown Automata and Constant Height: Decidability and Bounds

Pighizzini

Prigioniero

2019

Descriptional Complexity of Formal Systems

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It cannot be decided whether a pushdown automaton accepts using constant pushdown height, with respect to the input length, or not. Furthermore, in the case of acceptance in constant height, the height cannot be bounded by any recursive function in the size of the description of the machine. In contrast, in the restricted case of pushdown automata over a one-letter input alphabet, i.e., unary pushdown automata, the above property becomes decidable. Moreover, if the height is bounded by a constant in the input length, then it is at most exponential with respect to the size of the description of the pushdown automaton. This bound cannot be reduced. Finally, if a unary pushdown automaton uses nonconstant height to accept, then the height should grow at least as the logarithm of the input length. This bound is optimal.

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Removing nondeterminism in constant height pushdown automata

Cited by 10 publications

References 15 publications

Pushdown automata and constant height: decidability and bounds

Pushdown automata and constant height: decidability and bounds

An Enhanced Photonic Quantum Finite Automaton

Pushdown Automata and Constant Height: Decidability and Bounds

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