Title: Probabilistic Shoenfield Machines Show Chinese title

Title: 概率Shoenfield机

Abstract: The article provides the theoretical framework of Probabilistic Shoenfield Machines (PSMs), an extension of the classical Shoenfield Machine that models randomness in the computation process. PSMs are introduced in contexts where deterministic computation is insufficient, such as randomized algorithms. By allowing transitions to multiple possible states with certain probabilities, PSMs can solve problems and make decisions based on probabilistic outcomes, thus expanding the variety of possible computations. We provide an overview of PSMs, detailing their formal definitions, the computation mechanism, and their equivalence with Non-deterministic Shoenfield Machines (NSMs) Show Chinese abstract

Abstract: 本文提供了概率Shoenfield机（PSMs）的理论框架，这是经典Shoenfield机的一个扩展，用于在计算过程中建模随机性。PSMs在确定性计算不足的背景下被引入，例如随机算法。通过允许以一定概率向多个可能状态的转换，PSMs可以根据概率结果解决问题和做出决策，从而扩展了可能计算的多样性。我们概述了PSMs，详细介绍了它们的形式定义、计算机制以及与非确定性Shoenfield机（NSMs）的等价性。