👉 Probabilistic Boolean Algebra (PBA) is a mathematical framework designed to model and analyze Boolean functions, particularly those used in digital logic design. Unlike classical Boolean Algebra, which operates on binary values (0 and 1), PBA extends this concept to handle probabilistic elements, allowing for the representation of uncertainty and randomness in logical operations. In PBA, Boolean variables are associated with real-valued probability distributions rather than fixed binary states. This enables the modeling of systems where the truth values are not deterministic but rather governed by probability distributions, making it especially useful in areas like machine learning, artificial intelligence, and stochastic digital systems. By leveraging concepts from measure theory and probability, PBA provides a powerful tool for designing and analyzing complex, probabilistic digital circuits and systems.
