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Machines that Can Output Empty Words

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Abstract

We propose the e-model for leaf languages which complements the known balanced and unbalanced concepts. Inspired by the neutral behavior of rejecting paths of NP machines, we allow transducers to output empty words.

The paper explains several advantages of the new model. A central aspect is that it allows us to prove strong gap theorems: For any class \(\mathcal{C}\) that is definable in the e-model, either \(\mathrm{coUP}\subseteq\mathcal{C}\) or \(\mathcal{C}\subseteq\mathrm{NP}\) . For the existing models, gap theorems, where they exist at all, only identify gaps for the definability by regular languages. We prove gaps for the general case, i.e., for the definability by arbitrary languages. We obtain such general gaps for NP, coNP, 1NP, and co1NP. For the regular case we prove further gap theorems for Σ P2 , Π P2 , and Δ P2 . These are the first gap theorems for Δ P2 .

This work is related to former work by Bovet, Crescenzi, and Silvestri, Vereshchagin, Hertrampf et al., Burtschick and Vollmer, and Borchert et al.

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Authors and Affiliations

  1. Theoretische Informatik, Universität Würzburg, Am Hubland, 97074, Würzburg, Germany

    Christian Glaßer & Stephen Travers

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  1. Christian Glaßer
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  2. Stephen Travers
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Correspondence to Christian Glaßer.

Additional information

An extended abstract of this paper was presented at the 31st International Symposium on Mathematical Foundations of Computer Science (MFCS 2006).S. Travers supported by the Konrad-Adenauer-Stiftung.

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Glaßer, C., Travers, S. Machines that Can Output Empty Words. Theory Comput Syst 44, 369–390 (2009). https://doi.org/10.1007/s00224-007-9087-5

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