  This 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 brought 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,
hence expanding the variety of possible computations. We provide an overview of
PSMs, detailing their formal definitions as well as the computation mechanism
and their equivalence with Non-deterministic Shoenfield Machines (NSM).
