基本交互式算法：预览
Basic interactive algorithms: Preview
AI总结：
本文预览了基本交互式算法的公理化工作，回顾了基本算法的公理化及其在证明 Church-Turing 论题中的作用，并探讨了概率、非确定性和量子算法等扩展概念与预言机基本算法的关联。
摘要：
这篇对话性论文对即将发表的关于基本交互式算法公理化工作提供了预览和先导。现代算法概念在20世纪30年代至50年代得到阐明。它在四分之一个世纪前被公理化为“顺序算法”或“经典算法”的概念；我们现在更倾向于称之为“基本算法”。该公理化被用于证明，对于每个基本算法，都存在一个行为等价的抽象状态机。它也被用来证明逻辑学家所理解的 Church-Turing 论题。从20世纪60年代起，算法的概念不断扩展——概率算法、量子算法等——促使引入了一个更为宏大的 Church-Turing 论题版本，通常被称为“物理论题”。我们强调了 Church-Turing 论题两个版本之间的区别，并说明了非确定性和概率算法如何被视为带有适当预言机的基本算法。同样的观点也适用于量子电路算法和许多其他类别的算法。
英文摘要：
This dialog paper offers a preview and provides a foretaste of an upcoming work on the axiomatization of basic interactive algorithms. The modern notion of algorithm was elucidated in the 1930s--1950s. It was axiomatized a quarter of a century ago as the notion of ``sequential algorithm'' or ``classical algorithm''; we prefer to call it ``basic algorithm" now. The axiomatization was used to show that for every basic algorithm there is a behaviorally equivalent abstract state machine. It was also used to prove the Church-Turing thesis as it has been understood by the logicians. Starting from the 1960s, the notion of algorithm has expanded -- probabilistic algorithms, quantum algorithms, etc. -- prompting introduction of a much more ambitious version of the Church-Turing thesis commonly known as the ``physical thesis.'' We emphasize the difference between the two versions of the Church-Turing thesis and illustrate how nondeterministic and probabilistic algorithms can be viewed as basic algorithms with appropriate oracles. The same view applies to quantum circuit algorithms and many other classes of algorithms.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
