Cpo's of measures for nondeterminism

Saheb-Djahromi, Nasser

doi:10.1016/0304-3975(80)90003-1

Cited by 99 publications

(44 citation statements)

References 2 publications

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“…Commutative C*-algebras provide relatively standard semantics for labelled Markov processes, albeit not often phrased that way, and bisimulations can be expressed algebraically [6], [7], [8], [9], [10]. But also noncommutative approximately finite-dimensional C*-algebras have been used as operational semantics of probabilistic languages [11], [12].…”

Section: B Related Workmentioning

confidence: 99%

Domains of Commutative C*-Subalgebras

Heunen

Lindenhovius

2015

2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science

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Abstract-Operator algebras provide uniform semantics for deterministic, reversible, probabilistic, and quantum computing, where intermediate results of partial computations are given by commutative subalgebras. We study this setting using domain theory, and show that a given operator algebra is scattered if and only if its associated partial order is, equivalently: continuous (a domain), algebraic, atomistic, quasi-continuous, or quasialgebraic. In that case, conversely, we prove that the Lawson topology, modelling information approximation, allows one to associate an operator algebra to the domain.

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Section: B Related Workmentioning

confidence: 99%

Domains of Commutative C*-Subalgebras

Heunen

Lindenhovius

2015

2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science

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“…First, the domain-theoretic approach has led to a probabilistic powerdomain [19,29] which is a sibling of the nondeterministic power domain [27]. This approach follows the computational monad method [25]: programs are interpreted as functions from the input domain to the powerdomain of the output domain.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic coherence spaces are fully abstract for probabilistic PCF

Ehrhard

Tasson

Pagani

2014

Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

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Probabilistic coherence spaces (PCoh) yield a semantics of higherorder probabilistic computation, interpreting types as convex sets and programs as power series. We prove that the equality of interpretations in PCoh characterizes the operational indistinguishability of programs in PCF with a random primitive. This is the first result of full abstraction for a semantics of probabilistic PCF. The key ingredient relies on the regularity of power series.Along the way to the theorem, we design a weighted intersection type assignment system giving a logical presentation of PCoh.

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“…We will now discuss how to define the set D(Y ) of such probability distributions, which turns out to be a CPO. Our approach follows [25].…”

Section: Foundations: Domain Theory and Probabilistic Processesmentioning

confidence: 99%

An equational approach to secure multi-party computation

Micciancio

Tessaro

2013

Proceedings of the 4th Conference on Innovations in Theoretical Computer Science

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We present a novel framework for the description and analysis of secure computation protocols that is at the same time mathematically rigorous and notationally lightweight and concise. The distinguishing feature of the framework is that it allows to specify (and analyze) protocols in a manner that is largely independent of time, greatly simplifying the study of cryptographic protocols. At the notational level, protocols are described by systems of mathematical equations (over domains), and can be studied through simple algebraic manipulations like substitutions and variable elimination. We exemplify our framework by analyzing in detail two classic protocols: a protocol for secure broadcast, and a verifiable secret sharing protocol, the second of which illustrates the ability of our framework to deal with probabilistic systems, still in a purely equational way.

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Cpo's of measures for nondeterminism

Cited by 99 publications

References 2 publications

Domains of Commutative C*-Subalgebras

Domains of Commutative C*-Subalgebras

Probabilistic coherence spaces are fully abstract for probabilistic PCF

An equational approach to secure multi-party computation

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