Probabilistic Shoenfield Machines

TL;DR

This paper introduces Probabilistic Shoenfield Machines (PSMs), extending classical models to incorporate randomness, enabling probabilistic decision-making and expanding computational capabilities in contexts requiring stochastic processes.

Contribution

It formalizes PSMs, demonstrating their equivalence with Non-deterministic Shoenfield Machines and providing a foundational framework for probabilistic computation models.

Findings

PSMs can simulate randomized algorithms effectively.

PSMs are equivalent to NSMs in computational power.

The framework broadens the scope of Shoenfield Machines to probabilistic contexts.

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)