Work

Probabilistic Concurrent Reasoning in Outcome Logic: Independence, Conditioning, and Invariants

Year: 2026

Type: article

Abstract: Although randomization has long been used in distributed computing, formal methods for reasoning aboutprobabilistic concurrent programs have lagged behind. No existing program logics can express specificationsabout the full distributions of outcomes resulting from programs that are both probabilistic and concurrent. To address this, we introduce Probabilistic Concurrent Outcome Logic ( pcOL ), which incorporates ideas fromconcurrent and probabilistic separation logics into Outcome Logic to introduce new compositional reasoningprinciples. At its core, pcOL reinterprets the rules of Concurrent Separation Logic in a setting where separationmodels probabilistic independence, so as to compositionally describe joint distributions over variables inconcurrent threads. Reasoning about outcomes also proves crucial, as case analysis is often necessary to deriveprecise information about threads that rely on randomized shared state. We demonstrate pcOL on a variety ofexamples, including to prove almost sure termination of unbounded loops.

Source: Proceedings of the ACM on Programming Languages

DOI: 10.1145/3776651

Authors: Noam Zilberstein, Alexandra Silva, Joseph Tassarotti

Institutions: Cornell University, New York University

Language: English

Topic: Logic, programming, and type systems

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funder: National Science Foundation

Awards: Collaborative Research: SHF: Medium: Probabilistic Concurrent Outcome Logic (pcOL) -- Expressive Specifications for Concurrent Randomized Programs, Collaborative Research: SHF: Medium: Probabilistic Concurrent Outcome Logic (pcOL) -- Expressive Specifications for Concurrent Randomized Programs