A Probabilistic Higher-order Fixpoint Logic

Abstract

We introduce PHFL, a probabilistic extension of higher-order fixpoint logic, which can also be regarded as a higher-order extension of probabilistic temporal logics such as PCTL and the ${\mu }^p$-calculus. We show that PHFL is strictly more expressive than the ${\mu }^p$-calculus, and that the PHFL model-checking problem for finite Markov chains is undecidable even for the $\mu$-only, order-1 fragment of PHFL. Furthermore the full PHFL is far more expressive: we give a translation from Lubarsky's $\mu$-arithmetic to PHFL, which implies that PHFL model checking is ${\Pi }_1^1$-hard and ${\Sigma }_1^1$-hard. As a positive result, we characterize a decidable fragment of the PHFL model-checking problems using a novel type system.

References in corpus (2)

• Higher-Order Program Verification via HFL Model Checking
• A Probabilistic Higher-order Fixpoint Logic

Cited by in corpus (1)

• A Probabilistic Higher-order Fixpoint Logic