article

State complexity of operations on two-way finite automata over a unary alphabet

Authors:

Alexander OkhotinAuthors Info & Claims

Theoretical Computer Science, Volume 449

Pages 106 - 118

https://doi.org/10.1016/j.tcs.2012.04.010

Published: 01 August 2012 Publication History

Abstract

The paper determines the number of states in two-way deterministic finite automata (2DFA) over a one-letter alphabet sufficient and in the worst case necessary to represent the results of basic language-theoretic operations on 2DFAs with a certain number of states. It is proved that (i) intersection of an m-state 2DFA and an n-state 2DFA requires between m+n and m+n+1 states; (ii) union of an m-state 2DFA and an n-state 2DFA, between m+n and 2m+n+4 states; (iii) Kleene star of an n-state 2DFA, (g(n)+O(n))^2 states, where g(n)=e^(^1^+^o^(^1^)^)^n^l^n^n is the maximum value of lcm(p"1,...,p"k) for @__ __p"i=

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Cited By

Martynova OOkhotin A(2022)Homomorphisms on Graph-Walking AutomataImplementation and Application of Automata10.1007/978-3-031-07469-1_14(177-188)Online publication date: 28-Jun-2022
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Bianchi MMereghetti CPalano B(2019)Quantum finite automataTheoretical Computer Science10.1016/j.tcs.2016.01.045664:C(39-53)Online publication date: 6-Jan-2019
https://dl.acm.org/doi/10.1016/j.tcs.2016.01.045
Jirskov GOkhotin A(2019)On the state complexity of operations on two-way finite automataInformation and Computation10.1016/j.ic.2016.12.007253:P1(36-63)Online publication date: 4-Jan-2019
https://dl.acm.org/doi/10.1016/j.ic.2016.12.007
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State complexity of operations on two-way finite automata over a unary alphabet
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cover image Theoretical Computer Science

Theoretical Computer Science Volume 449, Issue

August, 2012

150 pages

ISSN:0304-3975

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Copyright © Elsevier B.V. © 2012.

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Elsevier Science Publishers Ltd.

United Kingdom

Publication History

Published: 01 August 2012

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Cited By

Martynova OOkhotin A(2022)Homomorphisms on Graph-Walking AutomataImplementation and Application of Automata10.1007/978-3-031-07469-1_14(177-188)Online publication date: 28-Jun-2022
https://dl.acm.org/doi/10.1007/978-3-031-07469-1_14
Bianchi MMereghetti CPalano B(2019)Quantum finite automataTheoretical Computer Science10.1016/j.tcs.2016.01.045664:C(39-53)Online publication date: 6-Jan-2019
https://dl.acm.org/doi/10.1016/j.tcs.2016.01.045
Jirskov GOkhotin A(2019)On the state complexity of operations on two-way finite automataInformation and Computation10.1016/j.ic.2016.12.007253:P1(36-63)Online publication date: 4-Jan-2019
https://dl.acm.org/doi/10.1016/j.ic.2016.12.007
Kutrib MPighizzini GWendlandt M(2018)Descriptional complexity of limited automataInformation and Computation10.1016/j.ic.2017.09.005259:P2(259-276)Online publication date: 1-Apr-2018
https://dl.acm.org/doi/10.1016/j.ic.2017.09.005
Jirásková GOkhotin A(2018)State Complexity of Unambiguous Operations on Deterministic Finite AutomataDescriptional Complexity of Formal Systems10.1007/978-3-319-94631-3_16(188-199)Online publication date: 25-Jul-2018
https://dl.acm.org/doi/10.1007/978-3-319-94631-3_16

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