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Complement for Two-Way Alternating Automata

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Computer Science – Theory and Applications (CSR 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10846))

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Abstract

We consider the problem of converting a two-way alternating finite automaton (2AFA) with n states to a 2AFA accepting the complement of the original language. Complementing is trivial for halting 2AFAs, by inverting the roles of existential and universal decisions and the roles of accepting and rejecting states. However, since 2AFAs do not have resources to detect infinite loops by counting executed steps, the best construction known so far required \(\varOmega (4^n)\) states. Here we shall show that the cost of complementing is polynomial in n. This complementary simulation does not eliminate infinite loops.

V. Geffert—Supported by the Slovak grant contracts VEGA 1/0056/18 and APVV-15-0091.

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Notes

  1. 1.

    Throughout the paper, m denotes the length of the input and n the number of states.

  2. 2.

    Such configuration has no sons and the entire subtree degenerates into a single node.

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Authors and Affiliations

  1. Department of Computer Science, P. J. Šafárik University, Jesenná 5, 04154, Košice, Slovakia

    Viliam Geffert

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  1. Viliam Geffert
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Correspondence to Viliam Geffert .

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Editors and Affiliations

  1. Department of Informatics, University of Bergen, Bergen, Norway

    Fedor V. Fomin

  2. Steklov Mathematical Institute, Moscow, Russia

    Vladimir V. Podolskii

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Geffert, V. (2018). Complement for Two-Way Alternating Automata. In: Fomin, F., Podolskii, V. (eds) Computer Science – Theory and Applications. CSR 2018. Lecture Notes in Computer Science(), vol 10846. Springer, Cham. https://doi.org/10.1007/978-3-319-90530-3_12

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  • DOI: https://doi.org/10.1007/978-3-319-90530-3_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-90529-7

  • Online ISBN: 978-3-319-90530-3

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