TL;DR
This paper explores the extension complexity of formal languages by associating polytopes with languages, establishing closure properties, and providing machine characterizations to analyze computational and polyhedral bounds.
Contribution
It introduces a novel framework linking formal languages with polyhedral extension complexity and offers new bounds and characterizations for various computational models.
Findings
Closure properties of languages with compact extended formulations
Upper bounds for polytopes in nondeterministic logspace
Lower bounds in streaming models
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.
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