This paper presents a wpâ€“style calculus for obtaining bounds on the expected runâ€“time of probabilistic programs. Its application includes determining the (possibly infinite) expected termination timeâ€¦ (More)

Separation Logic with inductive predicate definitions (SL) and hyperedge replacement grammars (HRG) are established formalisms to describe the abstract shape of data structures maintained byâ€¦ (More)

We study weakest precondition reasoning about the (co)variance of outcomes and the variance of runâ€“times of probabilistic programs with conditioning. For outcomes, we show that approximatingâ€¦ (More)

Bayesian networks (BNs) are probabilistic graphical models for describing complex joint probability distributions. The main problem for BNs is inference: Determine the probability of an event givenâ€¦ (More)

We present quantitative separation logic (QSL). In contrast to classical separation logic, QSL employs quantities which evaluate to real numbers instead of predicates which evaluate to booleanâ€¦ (More)

We study the hardness of deciding probabilistic termination as well as the hardness of approximating expected values (e.g. of program variables) and (co)variances for probabilistic programs.â€¦ (More)

The aim of shape analysis is to discover precise abstractions of the reachable data structures in a programâ€™s heap. This paper develops a shape analysis for reasoning about relational properties ofâ€¦ (More)

This paper presents a wp--style calculus for obtaining expectations on the outcomes of (mutually) recursive probabilistic programs. We provide several proof rules to derive one-- and two--sidedâ€¦ (More)