Almost Sure Productivity

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 König. 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. 1998 ACM Subject Classification F.3.1 Specifying and Verifying and Reasoning about Programs, F.3.2 Semantics of Programming Languages, D.3.1 Formal Definitions and Theory