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A Pumping Lemma for Two-Way Finite Transducers

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Mathematical Foundations of Computer Science 2014 (MFCS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8634))

Abstract

A two-way nondeterministic finite transducer (2-NFT) is a finite automaton with a two-way input tape and a one-way output tape. The generated language of a 2-NFT is the set of all strings it can output (across all inputs). Whereas two-way nondeterministic finite acceptors (2-NFAs) accept only regular languages, 2-NFTs can generate languages which are not even context-free, e.g. \(\{\texttt{a}^n \texttt{b}^n \texttt{c}^n \mid n \geq 0\}\). We prove a pumping lemma for 2-NFT languages which strengthens and generalizes previous results. Our pumping lemma states that every 2-NFT language L is k-iterative for some k ≥ 1. That is, every string in L above a certain length can be expressed in the form x 1 y 1 x 2 y 2 ⋯ x k y k x k + 1, where the ys can be “pumped” to produce new strings in L of the form \(x_1 y_1^i x_2 y_2^i \dotsm x_k y_k^i x_{k+1}\).

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Authors and Affiliations

  1. Northeastern University, Boston, MA, USA

    Tim Smith

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  1. Tim Smith
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Editors and Affiliations

  1. Faculty of Informatics, Eötvös Loránd University, Pázmány Péter sétány 1/C, 1117, Budapest, Hungary

    Erzsébet Csuhaj-Varjú

  2. Fakultät für Informatik und Automatisierung, Technische Universität Ilmenau, Helmholtzplatz, 598693, Ilmenau, Germany

    Martin Dietzfelbinger

  3. Institute of Informatics, Szeged University, Tisza Lajos krt. 103, 6720, Szeged, Hungary

    Zoltán Ésik

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Smith, T. (2014). A Pumping Lemma for Two-Way Finite Transducers. In: Csuhaj-Varjú, E., Dietzfelbinger, M., Ésik, Z. (eds) Mathematical Foundations of Computer Science 2014. MFCS 2014. Lecture Notes in Computer Science, vol 8634. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44522-8_44

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  • DOI: https://doi.org/10.1007/978-3-662-44522-8_44

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44521-1

  • Online ISBN: 978-3-662-44522-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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