Almost Sure Productivity

TL;DR

The paper introduces Almost Sure Productivity (ASP), a probabilistic extension of productivity for coinductive structures, with methods to verify ASP using syntactic criteria and model-checking, proving its decidability.

Contribution

It formalizes ASP for probabilistic streams and trees, and provides verification techniques including a syntactic criterion and a reduction to model-checking, establishing decidability.

Findings

ASP is defined using coalgebra semantics.

A core language for probabilistic streams and trees is introduced.

ASP verification is decidable via reduction to pCTL* model-checking.

Abstract

We define Almost Sure Productivity (ASP), a probabilistic generalization of the productivity condition for coinductively defined structures. Intuitively, a probabilistic coinductive stream or tree is ASP if it produces infinitely many outputs with probability 1. Formally, we define almost sure productivity using a final coalgebra semantics of programs inspired from Kerstan and K\"onig. Then, we introduce a core language for probabilistic streams and trees, and provide two approaches to verify ASP: a sufficient syntactic criterion, and a reduction to model-checking pCTL* formulas on probabilistic pushdown automata. The reduction shows that ASP is decidable for our core language.