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 x1y1x2y2 ⋯ xkykxk + 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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© Springer-Verlag GmbH Berlin Heidelberg 2014

Authors and Affiliations

  • Tim Smith
    • 1
  1. 1.Northeastern UniversityBostonUSA

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