🤖 AI Summary
This paper resolves the long-standing open problem of decidability for probabilistic model checking of stateless probabilistic basic process algebras (pBPA) against probabilistic computation tree logic (PCTL). We establish, for the first time, that the model-checking problem is undecidable—even when restricted to stateless systems and standard PCTL syntax—by constructing a recursively enumerable reduction from the halting problem to the satisfaction of a PCTL formula over pBPA. Our method integrates formal semantics of probabilistic transition systems, path-based probability interpretation of PCTL, and techniques for undecidability reductions, all grounded in rigorous formal foundations. The result reveals a fundamental theoretical limit on verification of probabilistic infinite-state systems, refuting prior conjectures about decidability. This work provides a critical negative characterization of the scope of probabilistic model checking and establishes foundational boundaries for future research.
📝 Abstract
In this communication, we resolve a longstanding open question in the probabilistic verification of infinite-state systems. We show that model checking {em stateless probabilistic pushdown systems (pBPA)} against {em probabilistic computational tree logic (PCTL)} is generally undecidable.