A pumping lemma for two-way finite transducers

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. 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. © 2014 Springer-Verlag Berlin Heidelberg.