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.

中文翻译：

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形式语言的扩展复杂性

在本文中，我们从形式语言的角度进行了扩展复杂性的研究。我们定义了一种自然的方式来将多聚体家族与二进制语言相关联。这使我们能够定义形式语言的扩展复杂性的概念。我们证明了允许紧凑扩展的语言的几种封闭特性。此外，我们对紧凑型语言进行了充分的机器表征。我们通过获取非确定性对数空间中问题的多边形上限来证明该机器表征的实用性。流模型的下限；和几个多态性的延伸复杂性的上限。