A Behavioural Theory of Probabilistic Algorithms Using Probabilistic Abstract State Machines

2026-06-22

AI Summary

This work addresses the lack of a formal behavioral theory for probabilistic algorithms, which has hindered rigorous characterization of their semantics and execution. Building upon four axiomatic assumptions—stochastic branching time, abstract states, background, and stochastic bounded exploration—the study introduces the first axiomatic behavioral framework for probabilistic algorithms and proposes probabilistic Abstract State Machines (pASMs) as a formal modeling tool. The paper establishes that any algorithm satisfying this framework can be step-by-step behaviorally simulated by a pASM with identical signature and background. This result provides a rigorous behavioral theory for probabilistic algorithms and achieves a semantics-preserving mapping from abstract specifications to concrete computational models.

Abstract

We motivate an axiomatic definition of probabilistic algorithms (PAs) by four postulates covering random branching time, abstract states, background, and random bounded exploration. Then, we introduce probabilistic Abstract State Machines (pASMs) and show that they specify PAs. Finally, we prove that every PA satisfying these postulates can be simulated step-by-step by a behaviourally equivalent pASM with the same signature and background.

Problem

• probabilistic algorithms
• behavioural theory
• abstract state machines
• axiomatic definition
• randomness

Innovation

• probabilistic algorithms
• probabilistic Abstract State Machines
• axiomatic definition
• behavioral equivalence
• random bounded exploration