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Extension Complexity of Formal Languages

  • Hans Raj TiwaryEmail author
Article
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Abstract

In this article we undertake a study of extension complexity from the perspective of formal languages. We define a natural way to associate a family of polytopes with binary languages. This allows us to define the notion of extension complexity of formal languages. We prove several closure properties of languages admitting compact extended formulations. Furthermore, we give a sufficient machine characterization of compact languages. We demonstrate the utility of this machine characterization by obtaining upper bounds for polytopes for problems in nondeterministic logspace; lower bounds in streaming models; and upper bounds on extension complexities of several polytopes.

Keywords

Extended formulations Formal languages 

Notes

Acknowledgments

The author would like to acknowledge the support of grant GA15-11559S of GAČR. We also thank Mateus De Oliveira Oliveira for finding a critical flaw in a previous proof of Theorem 7 and the anonymous referees for many valuable suggestions.

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.KAM/ITICharles UniversityPrague 1Czech Republic

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