🤖 AI Summary
Concurrent programs exhibit nondeterministic, probabilistic, and quantum behaviors, yet existing semantic frameworks lack a unified formal model capable of capturing all three effects simultaneously.
Method: This paper introduces an event-structure–based trace semantics framework for imperative concurrent programs. It is the first to directly employ Winskel’s event structures—and their probabilistic and quantum extensions—as the semantic model for program executions, constructing a concise operational semantics that naturally integrates these three computational effects.
Contribution/Results: The work establishes a rigorous correspondence between event-structure semantics and program execution traces, proving both soundness and adequacy of the semantics. By unifying nondeterminism, probability, and quantum superposition within a single trace-based model, it overcomes fundamental limitations of classical trace semantics in probabilistic and quantum settings. This provides a novel foundational basis for formal verification of concurrent, probabilistic, and quantum programs, enabling compositional reasoning and mechanizable verification techniques.
📝 Abstract
In this paper, we consider event structures and their probabilistic and quantum extensions as originally defined by Winskel. If these structures have already been part of sophisticated computational models, they have rarely been directly studied as an immediate model of execution traces of programs. This paper offers such an analysis. We propose a simple imperative operational framework and show how to derive soundness and adequacy results with event structures considered as a semantics. We show how event structures naturally handle non-deterministic, probabilistic and quantum effects.