Aspects of Reversibility for Classical Automata

Kutrib, Martin

doi:10.1007/978-3-319-13350-8_7

Cited by 21 publications

(7 citation statements)

References 28 publications

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“…Intuitively, the auxiliary state records which of the three transitions was used to enter state 3, and it is not possible to "trace the computation backwards" from that state when one has forgotten that information. 4 This is why the language recognized by these machines is not "reversible" [8].…”

Section: Introductionmentioning

confidence: 99%

Energy Complexity of Regular Languages

Yılmaz¹,

Kıyak²,

Meriç³

et al. 2022

Preprint

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The erasure of each bit of information by a computing device has an intrinsic energy cost. Although any Turing machine can be rewritten to be thermodynamically reversible without changing the recognized language, finite automata that are restricted to scan their input once in "real-time" fashion can only recognize the members of a proper subset of the class of regular languages in this reversible manner. We use a general quantum finite automaton model to study the thermodynamic cost per step associated with the recognition of different regular languages. We show that zero-error quantum finite automata have no energy cost advantage over their classical deterministic counterparts, and prove an upper bound for the cost that holds for all regular languages. We also demonstrate languages for which "error can be traded for energy", i.e. whose zero-error recognition is associated with provably bigger energy cost per step when compared to their bounded-error recognition by realtime finite-memory quantum devices.

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Section: Introductionmentioning

confidence: 99%

Energy Complexity of Regular Languages

Yılmaz¹,

Kıyak²,

Meriç³

et al. 2022

Preprint

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show abstract

“…For example, the regular language a * b * cannot be accepted by any reversible automaton [15], even if multiple initial states are allowed. Classical automata, namely automata with a single initial state and a set of final states, have been considered in the works by Holzer, Jakobi, and Kutrib [4,7,8]. In particular, they gave a characterization of regular languages which are accepted by reversible automata [4].…”

Section: Introductionmentioning

confidence: 99%

Concise Representations of Reversible Automata

Lavado

Prigioniero

2019

Int. J. Found. Comput. Sci.

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In this paper, we present two concise representations of reversible automata. Both representations have a size comparable to the size of the minimum equivalent deterministic automaton and can be exponentially smaller than the size of the explicit representations of corresponding reversible automata. Using these representations it is possible to simulate the computations of reversible automata without explicitly writing down their complete descriptions.

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“…Several variants of reversible automata were defined and studied [21,1,17]. The variant we work with (partial deterministic automata with a single initial state and and arbitrary set of final states) have been treated in [9,10,6,16,15,14]. In particular, in [6] the class of reversible languages is characterized by means of a forbidden pattern in the minimal automaton of the language in question, and an algorithm is provided to compute a minimal reversible automaton for a reversible language, given its minimal automaton.…”

Section: Introductionmentioning

confidence: 99%

Reversible Languages Having Finitely Many Reduced Automata

Gelle

Iván

2017

Electron. Proc. Theor. Comput. Sci.

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Reversible forms of computations are often interesting from an energy efficiency point of view. When the computation device in question is an automaton, it is known that the minimal reversible automaton recognizing a given language is not necessarily unique, moreover, there are languages having arbitrarily large reversible recognizers possessing no nontrivial reversible congruence. However, the exact characterization of this class of languages was open. In this paper we give a forbidden pattern capturing the reversible regular languages having only finitely many reduced reversible automata, allowing an efficient (NL) decision procedure.Comment: In Proceedings AFL 2017, arXiv:1708.0622

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Aspects of Reversibility for Classical Automata

Cited by 21 publications

References 28 publications

Energy Complexity of Regular Languages

Energy Complexity of Regular Languages

Concise Representations of Reversible Automata

Reversible Languages Having Finitely Many Reduced Automata

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