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11
Nevanlinna theory and holomorphic mappings between albebraic varieties
 Acta Math
, 1973
"... (a) Divisors and line bundles......................... 151 (b) The canonical bundle and volume forms................... 154 ..."
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Cited by 17 (0 self)
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(a) Divisors and line bundles......................... 151 (b) The canonical bundle and volume forms................... 154
Weak Bisimulation for Probabilistic Timed Automata
 PROC. OF SEFM’03, IEEE CS
, 2003
"... We are interested in describing timed systems that exhibit probabilistic behaviour. To this purpose, we consider a model of Probabilistic Timed Automata and introduce a concept of weak bisimulation for these automata, together with an algorithm to decide it. The weak bisimulation relation is shown t ..."
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Cited by 16 (6 self)
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We are interested in describing timed systems that exhibit probabilistic behaviour. To this purpose, we consider a model of Probabilistic Timed Automata and introduce a concept of weak bisimulation for these automata, together with an algorithm to decide it. The weak bisimulation relation is shown to be preserved when either time, or probability are abstracted away. As an application, we use weak bisimulation for Probabilistic Timed Automata to model and analyze a timing attack on the dining cryptographers protocol.
Information Flow Analysis for Probabilistic Timed Automata
 PROC. OF FAST’04, SPRINGER IFIP 173
, 2004
"... In multilevel systems it is important to avoid unwanted indirect information flow from higher levels to lower levels, namely the so called covert channels. Initial studies of information flow analysis were performed by abstracting away from time and probability. Recently, work has been done in order ..."
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Cited by 7 (3 self)
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In multilevel systems it is important to avoid unwanted indirect information flow from higher levels to lower levels, namely the so called covert channels. Initial studies of information flow analysis were performed by abstracting away from time and probability. Recently, work has been done in order to consider also aspects either of time or of probability, but not both. In this paper we propose a general framework, based on Probabilistic Timed Automata, where both probabilistic and timing covert channels can be studied. As an application, we study a system with covert channels that we are able to discover by our techniques.
Automatic Analysis of a NonRepudiation Protocol
 In Proc. of QAPL’03, Elsevier ENTCS
, 2004
"... We define a probabilistic model for the analysis of a NonRepudiation protocol that guarantees fairness, without resorting to a trusted third party, by means of a probabilistic algorithm. By using the PRISM model checker, we estimate the probability for a malicious user to break the nonrepudiation ..."
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Cited by 6 (2 self)
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We define a probabilistic model for the analysis of a NonRepudiation protocol that guarantees fairness, without resorting to a trusted third party, by means of a probabilistic algorithm. By using the PRISM model checker, we estimate the probability for a malicious user to break the nonrepudiation property, depending on various parameters of the protocol.
Decidability Results for Parametric Probabilistic Transition Systems with an Application to Security
 In Proc. of SEFM’04, IEEE
, 2004
"... We develop a model of Parametric Probabilistic Transition Systems. In this model probabilities associated with transitions may be parameters, and we show how to find instances of parameters that satisfy a given property and instances that either maximize or minimize the probability of reaching a giv ..."
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Cited by 5 (3 self)
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We develop a model of Parametric Probabilistic Transition Systems. In this model probabilities associated with transitions may be parameters, and we show how to find instances of parameters that satisfy a given property and instances that either maximize or minimize the probability of reaching a given state. We show, as an application, the model of a probabilistic non repudiation protocol. The theory we develop, allows us to find instances that maximize the probability that the protocol ends in a fair state (no participant has an advantage over the others).
Localization of Events in SpaceTime
, 1997
"... The present paper deals with the quantum coordinates of an event in spacetime, individuated by a quantum object. It is known that these observables cannot be described by selfadjoint operators or by the corresponding spectral projectionvalued measure. We describe them by means of a positiveopera ..."
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Cited by 5 (2 self)
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The present paper deals with the quantum coordinates of an event in spacetime, individuated by a quantum object. It is known that these observables cannot be described by selfadjoint operators or by the corresponding spectral projectionvalued measure. We describe them by means of a positiveoperatorvalued (POV) measure in the Minkowski spacetime, satisfying a suitable covariance condition with respect to the Poincaré group. This POV measure determines the probability that a measurement of the coordinates of the event gives results belonging to a given set in spacetime. We show that this measure must vanish on the vacuum and the oneparticle states, which cannot define any event. We give a general expression for the Poincaré covariant POV measures. We define the baricentric events, which lie on the worldline of the centreofmass, and we find a simple expression for the average values of their coordinates. Finally, we discuss the
Events in a NonCommutative SpaceTime.
, 2008
"... We treat the events determined by a quantum physical state in a noncommutative spacetime, generalizing the analogous treatment in the usual Minkowski spacetime based on positiveoperatorvalued measures (POVMs). We consider in detail the model proposed by Snyder in 1947 and we calculate the POVMs ..."
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We treat the events determined by a quantum physical state in a noncommutative spacetime, generalizing the analogous treatment in the usual Minkowski spacetime based on positiveoperatorvalued measures (POVMs). We consider in detail the model proposed by Snyder in 1947 and we calculate the POVMs defined on the real line that describe the measurement of a single coordinate. The approximate joint measurement of all the four spacetime coordinates is described in terms of a generalized Wigner function (GWF). We derive lower bounds for the dispersion of the coordinate observables and we discuss the covariance of the model under the Poincaré group. The unusual transformation law of the coordinates under spacetime translations is interpreted as a failure of the absolute character of the concept of spacetime coincidence. The model shows that a minimal length is compatible with Lorents covariance.
Topological Groups Part III, Spring 2003
, 2003
"... This document is written in L A T E X2e and available in tex, dvi, ps and pdf form from my home page http://www.dpmms.cam.ac.uk/~twk/. My email address is twk@dpmms.cam.ac.uk ..."
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This document is written in L A T E X2e and available in tex, dvi, ps and pdf form from my home page http://www.dpmms.cam.ac.uk/~twk/. My email address is twk@dpmms.cam.ac.uk
A Classification of Time and/or Probability . . .
 IN WORKSHOP ON QUANTITATIVE ASPECTS OF PROGRAMMING LANGUAGES (QAPL05
, 2005
"... In multilevel systems it is important to avoid unwanted indirect information flow from higher levels to lower levels, namely the so called covert channels. Initial studies of information flow analysis were performed by abstracting away from time and probability. It is already known that systems that ..."
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In multilevel systems it is important to avoid unwanted indirect information flow from higher levels to lower levels, namely the so called covert channels. Initial studies of information flow analysis were performed by abstracting away from time and probability. It is already known that systems that are considered to be secure may turn out to be insecure when time or probability are considered. Recently, work has been done in order to consider also aspects either of time or of probability, but not both. In this paper we propose a general framework, based on Probabilistic Timed Automata, where both probabilistic and timing covert channels can be studied. We define a NonInterference security property that allows one to express information flow in a timed and probabilistic setting, and we compare the property with analogous properties defined in settings where either time or probability or none of them are taken into account. This allows to classify properties depending on their discerning power.
Time and Probability based Information Flow Analysis
"... Abstract—In multilevel systems it is important to avoid unwanted indirect information flow from higher levels to lower levels, namely the so called covert channels. Initial studies of information flow analysis were performed by abstracting away from time and probability. It is already known that sys ..."
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Abstract—In multilevel systems it is important to avoid unwanted indirect information flow from higher levels to lower levels, namely the so called covert channels. Initial studies of information flow analysis were performed by abstracting away from time and probability. It is already known that systems that are proved to be secure in a possibilistic framework may turn out to be insecure when time or probability are considered. Recently, work has been done in order to consider also aspects either of time or of probability, but not both. In this paper we propose a general framework, based on Probabilistic Timed Automata, where both probabilistic and timing covert channels can be studied. We define a NonInterference security property and a Non Deducibility on Composition security property, which allow expressing information flow in a timed and probabilistic setting. We then compare these properties with analogous ones defined in contexts where either time or probability or neither of them are taken into account. This permits a classification of the properties depending on their discerning power. As an application, we study a system with covert channels that we are able to discover by applying our techniques.