Parallelism, Communication and Randomness in Models of Computation, and Efficient Computation in Permutation Groups

研究正在进行的权力的基本 根据各种不同的计算方法进行计算的特点 模型 PI和其他人最近定义了新的 类在通信复杂性理论，也在 图灵复杂性 在这些新的类别中， 亚瑟王-梅林协议的近亲 交互式证明系统 既相互作用又随机 在大多数新课程中扮演重要角色。 这些新类别的分离特性正在 研究了 特别感兴趣的是分离问题 在通信复杂度中的多项式时间层次 理论和语言类的关系确定 通过亚瑟-梅林协议， 语言 私家侦探也在继续调查 异步分布式网络中的可靠性问题。 PI最近完成了证明， 组成员资格属于NC类。 他们的方法似乎 对连续的情况有影响， 探索获得实质性加速的可能性 对于连续的情况。 计算中的相互作用和随机性的作用是 这是理论界目前最关心的问题。 的 PI是开发的领导人物， 了解这些角色。

Research is being conducted into the power of fundamental features of computation carried out according to various models. The PIs and others have recently defined new classes in communication complexity theory and also in Turing Complexity. Among such new classes are those defined by Arthur-Merlin protocols which are close relatives of interactive proof systems. Both interaction and randomness play important roles in most of these new classes. Separation properties for these new classes are being studied. Of particular interest are the separation problem of the polynomial time hierarchy in communication complexity theory and the relation of the class of languages determined by Arthur-Merlin protocols to the class of almost-NP languages. The PIs are also continuing their investigation of reliability problems in asynchronous distributed networks. The PIs have recently completed the proof that permutation group membership is in the class NC. Their methods appear to have implications for the sequential case and they are exploring the possibility of obtaining a substantial speedup for the sequential situation. The roles of interaction and randomness in computation are of crucial interest to the theory community at this time. The PIs are leading figures in the development of the understanding of these roles.