Compositional Verification of Concurrency Using Past-Time Temporal Epistemic Logic

Reasoning about shared variable concurrent programs poses significant challenges due to the need to account for interference between concurrently executing threads. Traditional verification approaches often fall short in terms of modularity and composability, which are essential for scalable and maintainable verification. We present a method for modular and compositional verification of concurrent programs using past-time temporal epistemic logic. Our approach builds on Halpern and Moses' epistemic logic framework and incorporates past-time temporal operators to capture the temporal context of thread interactions. We formalize the semantics of our logic, introduce a compositional proof system for reasoning about concurrent programs, and demonstrate its application. The expressiveness of our proposed logic provides a rigorous foundation to verify concurrent systems compositionally.