Related papers: Quantitative Weakest Hyper Pre: Unifying Correctne…
We present a novel strongest-postcondition-style calculus for quantitative reasoning about non-deterministic programs with loops. Whereas existing quantitative weakest pre allows reasoning about the value of a quantity after a program…
We present a weakest-precondition-style calculus for reasoning about the expected values (pre-expectations) of \emph{mixed-sign unbounded} random variables after execution of a probabilistic program. The semantics of a while-loop is…
Auto-active program verification rests on the ability to effectively the translation from annotated programs into verification conditions that are then discharged by automated theorem provers in the background. Characteristic such tools,…
We develop a notion of predicate transformer and, in particular, the weakest precondition, appropriate for quantum computation. We show that there is a Stone-type duality between the usual state-transformer semantics and the weakest…
Weakest preconditions are a useful notion for program verification as they reduce a problem of program verification to a problem of constraint solving. Category-theoretic generalisations of weakest preconditions have been studied to capture…
In this paper, we prove existence of \emph{very weak solutions} to nonhomogeneous quasilinear parabolic equations beyond the duality pairing. The main ingredients are a priori esitmates in suitable weighted spaces combined with the…
Reasoning about program correctness has been a central topic in static analysis for many years, with Hoare logic (HL) playing an important role. The key notions in HL are partial and total correctness. Both require that program executions…
We study weakest precondition reasoning about the (co)variance of outcomes and the variance of run-times of probabilistic programs with conditioning. For outcomes, we show that approximating (co)variances is computationally more difficult…
We address the problem of reasoning on graph transformations featuring actions such as \emph{addition} and \emph{deletion} of nodes and edges, node \emph{merging} and \emph{cloning}, node or edge \emph{labelling} and edge…
An important problem when modeling gene networks lies in the identification of parameters, even if we consider a purely discrete framework as the one of Ren\'e Thomas. Here we are interested in the exhaustive search of all parameter values…
In this paper, we present a Hoare-style logic for reasoning about quantum programs with classical variables. Our approach offers several improvements over previous work: (1) Enhanced expressivity of the programming language: Our logic…
This paper presents a wp-style calculus for obtaining bounds on the expected run-time of probabilistic programs. Its application includes determining the (possibly infinite) expected termination time of a probabilistic program and proving…
In this article we investigate the relationships between the classical notions of weakest precondition and weakest liberal precondition, and provide several results, namely that in general, weakest liberal precondition is neither stronger…
Refinement calculus provides a structured framework for the progressive and modular development of programs, ensuring their correctness throughout the refinement process. This paper introduces a refinement calculus tailored for quantum…
Statistical paradoxes such as the Hardy paradox and the enhancement of phase estimation via post-selection both draw upon the same non-classical features of quantum statistics described by non-positive quasi-probabilities. In this paper, we…
We study weighted programming, a programming paradigm for specifying mathematical models. More specifically, the weighted programs we investigate are like usual imperative programs with two additional features: (1) nondeterministic…
Conditioning is a key feature in probabilistic programming to enable modeling the influence of data (also known as observations) to the probability distribution described by such programs. Determining the posterior distribution is also…
In this work, we propose a hyperparameter optimization method named \emph{HyperTime} to find hyperparameters robust to potential temporal distribution shifts in the unseen test data. Our work is motivated by an important observation that it…
Probabilistic Hoare logic (PHL) is an extension of Hoare logic and is specifically useful in verifying randomized programs. It allows researchers to formally reason about the behavior of programs with stochastic elements, ensuring the…
We present a new algorithm for probabilistic planning with no observability. Our algorithm, called Probabilistic-FF, extends the heuristic forward-search machinery of Conformant-FF to problems with probabilistic uncertainty about both the…