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Deriving Probabilistic Semantics Via the 'Weakest Completion' [chapter]

He Jifeng, Carroll Morgan, Annabelle McIver
2004 Lecture Notes in Computer Science  
In Sec. 3 we use the weakest completion to derive a semantic definition of a probabilistic programming language from the relational semantics [12, 13] of the "standard", that is non-probabilistic, guarded  ...  Relational Semantics Our first example uses weakest completion to extend a relational semantics for the standard language (Sec. 2 without r ⊕) to a semantics for the probabilistic language (Sec. 2 with  ... 
doi:10.1007/978-3-540-30482-1_17 fatcat:lgji5mnlz5b35f7wwzuedx2xqy

Quantum Weakest Preconditions [article]

Ellie D'Hondt, Prakash Panangaden
2006 arXiv   pre-print
We show that there is a Stone-type duality between the usual state-transformer semantics and the weakest precondition semantics.  ...  The proof that weakest preconditions exist for completely positive maps follows immediately from the Kraus representation theorem.  ...  Comments by the referees were very helpful.  ... 
arXiv:quant-ph/0501157v2 fatcat:42qlhptlivhx3ap2rrqr3p6dfe

Relatively complete verification of probabilistic programs: an expressive language for expectation-based reasoning

Kevin Batz, Benjamin Lucien Kaminski, Joost-Pieter Katoen, Christoph Matheja
2021 Proceedings of the ACM on Programming Languages (PACMPL)  
value of f evaluated in the final states reached after termination of C on σ (also called the weakest preexpectation wp C (f )) is also expressible in our syntax.  ...  We prove that our syntax is expressive in the following sense: Given any probabilistic program C, if a function f is expressible in our syntax, then the function mapping each initial state σ to the expected  ...  (2) Completeness: Can every true assertion be derived and is it expressible in the assertion language?  ... 
doi:10.1145/3434320 fatcat:p4z6fw6ytjf67l64a4ayvt2q4i

Reasoning about probabilistic sequential programs

R. Chadha, L. Cruz-Filipe, P. Mateus, A. Sernadas
2007 Theoretical Computer Science  
Our probabilistic state assertion logic, henceforth referred to as Exogenous Probabilistic Propositional Logic (EPPL), is essentially the logic of [11] , designed by taking the exogenous semantics approach  ...  This paper addresses the gap between [31] and [10, 8] , providing a complete and decidable Hoare logic for iterationfree probabilistic programs using a complete and decidable truth-functional probabilistic  ...  The first author was supported by FCT and FEDER grant SFRH/BPD/26137/2005. The second author was supported by FCT and FEDER grant SFRH/BPD/16372/2004.  ... 
doi:10.1016/j.tcs.2007.02.040 fatcat:tzpnm45kuzar7irg2y3vy4zanq

Quantum weakest preconditions

ELLIE D'HONDT, PRAKASH PANANGADEN
2006 Mathematical Structures in Computer Science  
The proof that weakest preconditions exist for completely positive maps follows from the Kraus representation theorem.  ...  We show that there is a Stone-type duality between the usual state-transformer semantics and the weakest precondition semantics.  ...  This research was funded by the FWO (Flanders) for the first author; for the second author in part by a grant from NSERC (Canada) and in part by a visiting fellowship from EPSRC (U.K.).  ... 
doi:10.1017/s0960129506005251 fatcat:lmspzaalerar3ab44voq5gaolm

Reasoning About States of Probabilistic Sequential Programs [chapter]

R. Chadha, P. Mateus, A. Sernadas
2006 Lecture Notes in Computer Science  
In order to achieve complete and recursive axiomatization of the state logic, the probabilities are taken in arbitrary real closed fields. Supported by FCT and FEDER through POCI via CLC QuantLog  ...  The Hoare calculus presented herein is the first probabilistic Hoare calculus with a complete and decidable state logic that has truth-functional propositional (not arithmetical) connectives.  ...  We will also like to thank the anonymous referees whose useful comments have greatly benefited the presentation.  ... 
doi:10.1007/11874683_16 fatcat:ri4vxmijhvhalh4rggozysthc4

Verification Logics for Quantum Programs [article]

Robert Rand
2019 arXiv   pre-print
We compare the mathematical foundations of the logics, their underlying languages, and the expressivity of their assertions.  ...  We also use the languages to verify the Deutsch-Jozsa Algorithm, and discuss their relative usability in practice.  ...  Soundness and Completeness The Hoare logic of Figure 3 is shown to be sound via the Exogenous Probabilistic Propositional Logic (EPPL) introduced in the paper.  ... 
arXiv:1904.04304v1 fatcat:ntt44iavbjhinlbldmuoyvcecy

Relatively Complete Verification of Probabilistic Programs [article]

Kevin Batz, Benjamin Lucien Kaminski, Joost-Pieter Katoen, Christoph Matheja
2022 arXiv   pre-print
value of f evaluated in the final states reached after termination of C on σ (also called the weakest preexpectation wp [C](f)) is also expressible in our syntax.  ...  We prove that our syntax is expressive in the following sense: Given any probabilistic program C, if a function f is expressible in our syntax, then the function mapping each initial state σ to the expected  ...  (2) Completeness: Can every true assertion be derived and is it expressible in the assertion language?  ... 
arXiv:2010.14548v2 fatcat:w2yolfpg4fc4zk4mieomwfznoe

Page 7115 of Mathematical Reviews Vol. , Issue 97K [page]

1997 Mathematical Reviews  
The main results yield a general algorithm for verifying the timing properties of real-time (reactive) systems via the mentioned semantics.  ...  Here we introduce nondetermin- istic expressions into the refinement calculus by constructing a weakest precondition semantics for imperative specifications and programs that holds good even when expressions  ... 

Generic Weakest Precondition Semantics from Monads Enriched with Order [chapter]

Ichiro Hasuo
2014 Lecture Notes in Computer Science  
We devise a generic framework where a weakest precondition semantics, in the form of indexed posets, is derived from a monad whose Kleisli category is enriched by posets.  ...  "must") are captured by Eilenberg-Moore algebras; 2) nested alternating branching-like in games and in probabilistic systems with nondeterministic environments-is modularly modeled by a monad on the Eilenberg-Moore  ...  The claim follows from the monotonicity of (postulated in Def. 2.1). We shall derive a weakest precondition semantics from a given PT situation (T, Ω, τ ).  ... 
doi:10.1007/978-3-662-44124-4_2 fatcat:qxbgfruw5vgztmmqe4vrdtcakq

Verifying Probabilistic Correctness in Isabelle with pGCL

David Cock
2012 Electronic Proceedings in Theoretical Computer Science  
We motivate the applicability of the formalism to the mechanical verification of probabilistic security properties, including the effectiveness of side-channel countermeasures in real systems.  ...  We demonstrate the facility with which the model can be extended to incorporate existing results, including those of the L4.verified project.  ...  The Expectation-Transformer Model The intuitive interpretation of a program, its operational semantics, is as a probabilistic automaton.  ... 
doi:10.4204/eptcs.102.15 fatcat:56qu3xr5onctxemgw2svlpq7zq

Weighted Programming [article]

Kevin Batz, Adrian Gallus, Benjamin Lucien Kaminski, Joost-Pieter Katoen, Tobias Winkler
2022 arXiv   pre-print
By means of weakest-precondition-style reasoning, we can determine the competitive ratio of the online algorithm on source code level.  ...  We argue that weighted programming as a paradigm can be used to specify mathematical models beyond probability distributions (as is done in probabilistic programming).  ...  ACKNOWLEDGMENTS This work was supported by the ERC AdG Frappant (787914) (https://cordis.europa.eu/project/id/787914) and RTG 2236 UnRAVeL (https://gepris.dfg.de/gepris/projekt/282652900) funded by the  ... 
arXiv:2202.07577v2 fatcat:zpwhajrejbajhlogjn6arh65wq

Weighted programming : a programming paradigm for specifying mathematical models

Kevin Batz, Adrian Gallus, Benjamin Lucien Kaminski, Joost-Pieter Katoen, Tobias Winkler
2022 ACM SIGPLAN International Conference on Object-Oriented Programming Systems  
By means of weakest-precondition-style reasoning, we can determine the competitive ratio of the online algorithm on source code level.  ...  We argue that weighted programming as a paradigm can be used to specify mathematical models beyond probability distributions (as is done in probabilistic programming).  ...  ACKNOWLEDGMENTS This work was supported by the ERC AdG Frappant (787914) (https://cordis.europa.eu/project/id/ 787914) and RTG 2236 UnRAVeL (https://gepris.dfg.de/gepris/projekt/282652900) funded by the  ... 
doi:10.18154/rwth-2022-04445 fatcat:axpfhudn35azvemwdq53y37hsm

Weighted programming: a programming paradigm for specifying mathematical models

Kevin Batz, Adrian Gallus, Benjamin Lucien Kaminski, Joost-Pieter Katoen, Tobias Winkler
2022 Proceedings of the ACM on Programming Languages (PACMPL)  
By means of weakest-precondition-style reasoning, we can determine the competitive ratio of the online algorithm on source code level.  ...  We argue that weighted programming as a paradigm can be used to specify mathematical models beyond probability distributions (as is done in probabilistic programming).  ...  ACKNOWLEDGMENTS This work was supported by the ERC AdG Frappant (787914) (https://cordis.europa.eu/project/id/ 787914) and RTG 2236 UnRAVeL (https://gepris.dfg.de/gepris/projekt/282652900) funded by the  ... 
doi:10.1145/3527310 fatcat:43vxsumlmjgyhctekgjqrj6q4a

From Operational Models to Information Theory; Side Channels in pGCL with Isabelle [chapter]

David Cock
2014 Lecture Notes in Computer Science  
In this paper, we formally derive the probabilistic security predicate (expectation) for a guessing attack against a system with sidechannel leakage, modelled in pGCL.  ...  Our practical contribution is to illustrate the selection of probabilistic loop invariants to verify such security properties, and the demonstration of a mechanical proof linking traditionally distinct  ...  We thus link the renement order on our operational models, with a (dual) order on this complete lattice of bounds. For the full derivation see Cock [2014] .  ... 
doi:10.1007/978-3-319-08970-6_12 fatcat:yl23myo25fhkzjlzvf2edr5hf4
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