无选择多项式时间
Choiceless polynomial time
摘要：
图灵机在字符串上定义了多项式时间（PTime），但不能直接处理像图这样的结构，并且没有已知的、容易计算的结构同构类的字符串编码。是否存在一种计算模型，其机器不区分同构结构并精确计算PTime属性？这个问题可以改写为：是否存在一个逻辑，捕捉多项式时间（不假设存在线性顺序）？早些时候，我们中的一个人否认了否定的答案。这个问题激发了对越来越强的PTime逻辑的追求。所有这些逻辑都避免了任意选择。在这里，我们试图捕捉PTime的无选择片段。我们的计算模型是抽象状态机（以前称为进化代数）的一个版本。这个想法是用并行执行取代任意选择。由此产生的逻辑比其他PTime逻辑在文献中更有表现力。一个更困难的定理表明，逻辑并不能捕获所有的PTime。
英文摘要：
Turing machines define polynomial time (PTime) on strings but cannot deal with structures like graphs directly, and there is no known, easily computable string encoding of isomorphism classes of structures. Is there a computation model whose machines do not distinguish between isomorphic structures and compute exactly PTime properties? This question can be recast as follows: Does there exist a logic that captures polynomial time (without presuming the presence of a linear order)? Earlier, one of us conjectured the negative answer. The problem motivated a quest for stronger and stronger PTime logics. All these logics avoid arbitrary choice. Here we attempt to capture the choiceless fragment of PTime. Our computation model is a version of abstract state machines (formerly called evolving algebras). The idea is to replace arbitrary choice with parallel execution. The resulting logic is more expressive than other PTime logics in the literature. A more difficult theorem shows that the logic does not capture all PTime.
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。
