正则语言的非确定性通信复杂性
Non-Deterministic Communication Complexity of Regular Languages
摘要：
在这篇论文中，我们研究了正则语言在通信复杂性中的地位。特别地，我们对正则语言的非确定性通信复杂性感兴趣。我们证明了一个正则语言具有O（1）或Omega（log n）的非确定性复杂度。我们得到了几个线性下界的结果，涵盖了广泛的正则语言具有线性非确定性的复杂性。这些下界结果也暗示了半群理论中的一个结果：我们得到了不属于正簇Pol（Com）的充分条件。为了得到我们的结果，我们使用代数技巧。在正则语言的研究中，由Eilenberg（\cite{Eil74}）开创的代数观点导致了许多有趣的结果。从半群理论和形式语言的角度来看，将半群看作是识别语言的计算设备已经被证明是多产的。在这篇论文中，我们提供了更多的例子，这种互惠。
英文摘要：
In this thesis, we study the place of regular languages within the communication complexity setting. In particular, we are interested in the non-deterministic communication complexity of regular languages. We show that a regular language has either O(1) or Omega(log n) non-deterministic complexity. We obtain several linear lower bound results which cover a wide range of regular languages having linear non-deterministic complexity. These lower bound results also imply a result in semigroup theory: we obtain sufficient conditions for not being in the positive variety Pol(Com). To obtain our results, we use algebraic techniques. In the study of regular languages, the algebraic point of view pioneered by Eilenberg (\cite{Eil74}) has led to many interesting results. Viewing a semigroup as a computational device that recognizes languages has proven to be prolific from both semigroup theory and formal languages perspectives. In this thesis, we provide further instances of such mutualism.
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