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

2004
*
Lecture Notes in Computer Science
*

In Sec. 3 we use

doi:10.1007/978-3-540-30482-1_17
fatcat:lgji5mnlz5b35f7wwzuedx2xqy
*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 ...##
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Quantum Weakest Preconditions
[article]

2006
*
arXiv
*
pre-print

We show that there is a Stone-type duality between

arXiv:quant-ph/0501157v2
fatcat:42qlhptlivhx3ap2rrqr3p6dfe
*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. ...##
###
Relatively complete verification of probabilistic programs: an expressive language for expectation-based reasoning

2021
*
Proceedings of the ACM on Programming Languages (PACMPL)
*

value of f evaluated in

doi:10.1145/3434320
fatcat:p4z6fw6ytjf67l64a4ayvt2q4i
*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? ...##
###
Reasoning about probabilistic sequential programs

2007
*
Theoretical Computer Science
*

Our

doi:10.1016/j.tcs.2007.02.040
fatcat:tzpnm45kuzar7irg2y3vy4zanq
*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. ...##
###
Quantum weakest preconditions

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.). ...

##
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Reasoning About States of Probabilistic Sequential Programs
[chapter]

2006
*
Lecture Notes in Computer Science
*

In order to achieve

doi:10.1007/11874683_16
fatcat:ri4vxmijhvhalh4rggozysthc4
*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. ...##
###
Verification Logics for Quantum Programs
[article]

2019
*
arXiv
*
pre-print

We compare

arXiv:1904.04304v1
fatcat:ntt44iavbjhinlbldmuoyvcecy
*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. ...##
###
Relatively Complete Verification of Probabilistic Programs
[article]

2022
*
arXiv
*
pre-print

value of f evaluated in

arXiv:2010.14548v2
fatcat:w2yolfpg4fc4zk4mieomwfznoe
*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? ...##
###
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]

2014
*
Lecture Notes in Computer Science
*

We devise a generic framework where a

doi:10.1007/978-3-662-44124-4_2
fatcat:qxbgfruw5vgztmmqe4vrdtcakq
*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 ). ...##
###
Verifying Probabilistic Correctness in Isabelle with pGCL

2012
*
Electronic Proceedings in Theoretical Computer Science
*

We motivate

doi:10.4204/eptcs.102.15
fatcat:56qu3xr5onctxemgw2svlpq7zq
*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. ...##
###
Weighted Programming
[article]

2022
*
arXiv
*
pre-print

By means of

arXiv:2202.07577v2
fatcat:zpwhajrejbajhlogjn6arh65wq
*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*...##
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Weighted programming : a programming paradigm for specifying mathematical models

2022
*
ACM SIGPLAN International Conference on Object-Oriented Programming Systems
*

By means of

doi:10.18154/rwth-2022-04445
fatcat:axpfhudn35azvemwdq53y37hsm
*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*...##
###
Weighted programming: a programming paradigm for specifying mathematical models

2022
*
Proceedings of the ACM on Programming Languages (PACMPL)
*

By means of

doi:10.1145/3527310
fatcat:43vxsumlmjgyhctekgjqrj6q4a
*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*...##
###
From Operational Models to Information Theory; Side Channels in pGCL with Isabelle
[chapter]

2014
*
Lecture Notes in Computer Science
*

In this paper, we formally

doi:10.1007/978-3-319-08970-6_12
fatcat:yl23myo25fhkzjlzvf2edr5hf4
*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] . ...
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