research-article

Converting two-way nondeterministic unary automata into simpler automata

Authors:

Viliam Geffert,

Carlo Mereghetti,

Giovanni PighizziniAuthors Info & Claims

Theoretical Computer Science, Volume 295, Issue 1

Pages 189 - 203

Published: 24 February 2003 Publication History

Abstract

We show that, on inputs of length exceeding 5n2, any n-state unary two-way nondeterministic finite automaton (2nfa) can be simulated by a (2n+2)-state quasi-sweeping 2nfa. Such a result, besides providing a “normal form” for 2nfa's, enables us to get a subexponential simulation of unary 2nfa's by two-way deterministic finite automata (2dfa's). In fact, we prove that any n-state unary 2nfa can be simulated by a sweeping 2dfa with O(n log2(n+1)+3 ) states.

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Cited By

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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
Yamakami T(2018)State Complexity Characterizations of Parameterized Degree-Bounded Graph Connectivity, Sub-Linear Space Computation, and the Linear Space HypothesisDescriptional Complexity of Formal Systems10.1007/978-3-319-94631-3_20(237-249)Online publication date: 25-Jul-2018
https://dl.acm.org/doi/10.1007/978-3-319-94631-3_20
Jirskov GOkhotin A(2017)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: 1-Apr-2017
https://dl.acm.org/doi/10.1016/j.ic.2016.12.007
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Index Terms

Converting two-way nondeterministic unary automata into simpler automata
1. Software and its engineering
  1. Software notations and tools
    1. Formal language definitions
2. Theory of computation
  1. Formal languages and automata theory
  2. Models of computation

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We show that, on inputs of length exceeding 5n², any n- state unary 2nfa (two-way nondeterministic finite automaton) can be simulated by a (2n+2)-state quasi sweeping 2nfa. Such a result, besides providing a "normalform" for 2nfa's, enables us to get a ...

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cover image Theoretical Computer Science

Theoretical Computer Science Volume 295, Issue 1

February 2003

397 pages

ISSN:0304-3975

Issue’s Table of Contents

Publisher

Elsevier Science Publishers Ltd.

United Kingdom

Publication History

Published: 24 February 2003

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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
Yamakami T(2018)State Complexity Characterizations of Parameterized Degree-Bounded Graph Connectivity, Sub-Linear Space Computation, and the Linear Space HypothesisDescriptional Complexity of Formal Systems10.1007/978-3-319-94631-3_20(237-249)Online publication date: 25-Jul-2018
https://dl.acm.org/doi/10.1007/978-3-319-94631-3_20
Jirskov GOkhotin A(2017)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: 1-Apr-2017
https://dl.acm.org/doi/10.1016/j.ic.2016.12.007
Kapoutsis CPighizzini G(2015)Two-Way Automata Characterizations of L/poly Versus NLTheory of Computing Systems10.1007/s00224-014-9560-x56:4(662-685)Online publication date: 1-May-2015
https://dl.acm.org/doi/10.1007/s00224-014-9560-x
Geffert VGuillon BPighizzini G(2014)Two-way automata making choices only at the endmarkersInformation and Computation10.1016/j.ic.2014.08.009239:C(71-86)Online publication date: 1-Dec-2014
https://dl.acm.org/doi/10.1016/j.ic.2014.08.009
Kapoutsis C(2014)Two-Way Automata Versus Logarithmic SpaceTheory of Computing Systems10.1007/s00224-013-9465-055:2(421-447)Online publication date: 1-Aug-2014
https://dl.acm.org/doi/10.1007/s00224-013-9465-0
Pighizzini G(2013)Two-Way Finite AutomataFundamenta Informaticae10.5555/2637657.2637663126:2-3(225-246)Online publication date: 1-Apr-2013
https://dl.acm.org/doi/10.5555/2637657.2637663
Hromkovič JKrálovič RKrálovič RŠtefanec R(2012)Determinism vs. nondeterminism for two-way automataProceedings of the 16th international conference on Developments in Language Theory10.1007/978-3-642-31653-1_4(24-39)Online publication date: 14-Aug-2012
https://dl.acm.org/doi/10.1007/978-3-642-31653-1_4
Bednárová ZGeffert VMereghetti CPalano B(2012)Removing nondeterminism in constant height pushdown automataProceedings of the 14th international conference on Descriptional Complexity of Formal Systems10.1007/978-3-642-31623-4_6(76-88)Online publication date: 23-Jul-2012
https://dl.acm.org/doi/10.1007/978-3-642-31623-4_6
Geffert VGuillon BPighizzini G(2012)Two-Way automata making choices only at the endmarkersProceedings of the 6th international conference on Language and Automata Theory and Applications10.1007/978-3-642-28332-1_23(264-276)Online publication date: 5-Mar-2012
https://dl.acm.org/doi/10.1007/978-3-642-28332-1_23
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Abstract

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Cited By

Index Terms

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