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On probabilistic model checking
, 1996
"... Abstract. This tutorial presents an overview of model checking for both discrete and continuoustime Markov chains (DTMCs and CTMCs). Model checking algorithms are given for verifying DTMCs and CTMCs against specifications written in probabilistic extensions of temporal logic, including quantitative ..."
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Cited by 104 (25 self)
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Abstract. This tutorial presents an overview of model checking for both discrete and continuoustime Markov chains (DTMCs and CTMCs). Model checking algorithms are given for verifying DTMCs and CTMCs against specifications written in probabilistic extensions of temporal logic, including quantitative properties with rewards. Example properties include the probability that a fault occurs and the expected number of faults in a given time period. We also describe the practical application of stochastic model checking with the probabilistic model checker PRISM by outlining the main features supported by PRISM and three realworld case studies: a probabilistic security protocol, dynamic power management and a biological pathway. 1
Comparing functional paradigms for exact realnumber computation
 in Proceedings ICALP 2002, Springer LNCS 2380
, 2002
"... Abstract. We compare the definability of total functionals over the reals in two functionalprogramming approaches to exact realnumber datatype of real numbers; and the intensional approach, in which one encodes real numbers using ordinary datatypes. We show that the type hierarchies coincide up to ..."
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Cited by 20 (4 self)
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Abstract. We compare the definability of total functionals over the reals in two functionalprogramming approaches to exact realnumber datatype of real numbers; and the intensional approach, in which one encodes real numbers using ordinary datatypes. We show that the type hierarchies coincide up to secondorder types, and we relate this fact to an analogous comparison of type hierarchies over the external and internal real numbers in Dana Scott’s category of equilogical spaces. We do not know whether similar coincidences hold at thirdorder types. However, we relate this question to a purely topological conjecture about the KleeneKreisel continuous functionals over the natural numbers. Finally, although it is known that, in the extensional approach, parallel primitives are necessary for programming total firstorder functions, we demonstrate that, in the intensional approach, such primitives are not needed for secondorder types and below. 1
Algebraic Information Theory For Binary Channels
"... We study the algebraic structure of the monoid of binary channels and show that it is dually isomorphic to the interval domain over the unit interval with the operation from [3]. We show that the capacity of a binary channel is Scott continuous as a map on the interval domain and that its restrictio ..."
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Cited by 6 (4 self)
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We study the algebraic structure of the monoid of binary channels and show that it is dually isomorphic to the interval domain over the unit interval with the operation from [3]. We show that the capacity of a binary channel is Scott continuous as a map on the interval domain and that its restriction to any maximally commutative submonoid of binary channels is an order isomorphism onto the unit interval. These results allows us to solve an important open problem in the analysis of covert channels: a provably correct method for injecting noise into a covert channel which will reduce its capacity to any level desired in such a way that the practitioner is free to insert the noise at any point in the system.
This document in subdirectory RS/03/23 / Recent Advances in Σdefinability over Continuous Data Types ∗
, 2003
"... Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRICS ..."
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Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRICS
The Interval Domain as a Semantic Foundation for Reasoning About Uncertainty Or Vagueness
"... . We reinterpret the category of relations according to views, pairs of dcpos hP; T i such that T embeds as a set into the set of maximal elements of P . A qualitative view hM; 2i renders the modal transition systems of K. Larsen and B. Thomsen as a partial view, R : X \Theta Y ! P , of relations, ..."
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. We reinterpret the category of relations according to views, pairs of dcpos hP; T i such that T embeds as a set into the set of maximal elements of P . A qualitative view hM; 2i renders the modal transition systems of K. Larsen and B. Thomsen as a partial view, R : X \Theta Y ! P , of relations, R : X \Theta Y ! 2. A quantitative view represents relations as fuzzy (T is the unit interval UI) or intervalvalued (P is the interval domain I) relations. We specify functors mediating between these categories to provide soundness of these interpretations. As for probability theory, we propose the view hI; UIi to embed the set of probability measures into the set of maximal elements of a space of partial probability measures. It is hoped that this provides a foundation for reasoning probabilistically about systems with inherent uncertainty, or vagueness, such as the probabilistic specifications of B. Jonsson and K. Larsen. 1 Motivation and outline 1.1 Motivation The work presented here ...
Real PCF extended with ∃ is universal (Extended Abstract ∗)
, 1996
"... Real PCF is an extension of the programming language PCF with a data type for the real line, introduced elsewhere. We show that Real PCF extended with ∃ is universal, in the sense that all computable elements of all types of its universe of discourse are definable. We also show that ∃ is not necessa ..."
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Real PCF is an extension of the programming language PCF with a data type for the real line, introduced elsewhere. We show that Real PCF extended with ∃ is universal, in the sense that all computable elements of all types of its universe of discourse are definable. We also show that ∃ is not necessary to define first order computable functions in Real PCF. In order to obtain our definability results, we consider a domainequationlike structure on the real numbers data type.
Abstract Datatypes for Real Numbers in Type Theory
"... Abstract. We propose an abstract datatype for a closed interval of real numbers to type theory, providing a representationindependent approach to programming with real numbers. The abstract datatype requires only function types and a natural numbers type for its formulation, and so can be added to ..."
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Abstract. We propose an abstract datatype for a closed interval of real numbers to type theory, providing a representationindependent approach to programming with real numbers. The abstract datatype requires only function types and a natural numbers type for its formulation, and so can be added to any type theory that extends Gödel’s System datatype is equivalent in power to programming intensionally with representations of real numbers. We also consider representing arbitrary real numbers using a mantissaexponent representation in which the mantissa is taken from the abstract interval. 1