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108
Probabilistic PolynomialTime Process Calculus and Security Protocol Analysis
 Theoretical Computer Science
, 2006
"... Abstract. We prove properties of a process calculus that is designed for analysing security protocols. Our longterm goal is to develop a form of protocol analysis, consistent with standard cryptographic assumptions, that provides a language for expressing probabilistic polynomialtime protocol step ..."
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Cited by 36 (3 self)
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Abstract. We prove properties of a process calculus that is designed for analysing security protocols. Our longterm goal is to develop a form of protocol analysis, consistent with standard cryptographic assumptions, that provides a language for expressing probabilistic polynomialtime protocol steps, a specification method based on a compositional form of equivalence, and a logical basis for reasoning about equivalence. The process calculus is a variant of CCS, with bounded replication and probabilistic polynomialtime expressions allowed in messages and boolean tests. To avoid inconsistency between security and nondeterminism, messages are scheduled probabilistically instead of nondeterministically. We prove that evaluation of any process expression halts in probabilistic polynomial time and define a form of asymptotic protocol equivalence that allows security properties to be expressed using observational equivalence, a standard relation from programming language theory that involves quantifying over all possible environments that might interact with the protocol. We develop a form of probabilistic bisimulation and use it to establish the soundness of an equational proof system based on observational equivalences. The proof system is illustrated by a formation derivation of the assertion, wellknown in cryptography, that El Gamal encryptionâ€™s semantic security is equivalent to the (computational) Decision DiffieHellman assumption. This example demonstrates the power of probabilistic bisimulation and equational reasoning for protocol security.
A Logical Characterization of Bisimulation for Labeled Markov Processes
, 1998
"... This paper gives a logical characterization of probabilistic bisimulation for Markov processes introduced in [BDEP97]. The thrust of that work was an extension of the notion of bisimulation to systems with continuous state spaces; for example for systems where the state space is the real numbers. In ..."
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Cited by 34 (11 self)
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This paper gives a logical characterization of probabilistic bisimulation for Markov processes introduced in [BDEP97]. The thrust of that work was an extension of the notion of bisimulation to systems with continuous state spaces; for example for systems where the state space is the real numbers. In the present paper we study the logical characterization of probabilistic bisimulation for such general systems. This study revealed some unexpected results even for discrete probabilistic systems. ffl Bisimulation can be characterized by a very weak modal logic. The most striking feature is that one has no negation or any kind of negative proposition. ffl Bisimulation can be characterized by several inequivalent logics; we report five in this paper. ffl We do not need any finite branching assumption yet there is no need of infinitary conjunction. ffl The proofs that we give are of an entirely different character than the typical proofs of these results. They use quite subtle facts abou...
Verifying quantitative properties of continuous probabilistic timed automata
, 2000
"... Abstract. We consider the problem of automatically verifying realtime systems with continuously distributed random delays. We generalise probabilistic timed automata introduced in [19], an extension of the timed automata model of [4], with clock resets made according to continuous probability distri ..."
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Cited by 33 (9 self)
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Abstract. We consider the problem of automatically verifying realtime systems with continuously distributed random delays. We generalise probabilistic timed automata introduced in [19], an extension of the timed automata model of [4], with clock resets made according to continuous probability distributions. Thus, our model exhibits nondeterministic and probabilistic choice, the latter being made according to both discrete and continuous probability distributions. To facilitate algorithmic verification, we modify the standard region graph construction by subdividing the unit intervals in order to approximate the probability to within an interval. We then develop a model checking method for continuous probabilistic timed automata, taking as our specification language Probabilistic Timed Computation Tree Logic (PTCTL). Our method improves on the previously known techniques in that it allows the verification of quantitative probability bounds, as opposed to qualitative properties which can only refer to bounds of probability 0 or 1. 1
Comparative branchingtime semantics for Markov chains
 Information and Computation
, 2003
"... This paper presents various semantics in the branchingtime spectrum of discretetime and continuoustime Markov chains (DTMCs and CTMCs). Strong and weak bisimulation equivalence and simulation preorders are covered and are logically characterised in terms of the temporal logics PCTL (Probabilisti ..."
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Cited by 32 (12 self)
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This paper presents various semantics in the branchingtime spectrum of discretetime and continuoustime Markov chains (DTMCs and CTMCs). Strong and weak bisimulation equivalence and simulation preorders are covered and are logically characterised in terms of the temporal logics PCTL (Probabilistic Computation Tree Logic) and CSL (Continuous Stochastic Logic). Apart from presenting various existing branchingtime relations in a uniform manner, this paper presents the following new results: (i) strong simulation for CTMCs, (ii) weak simulation for CTMCs and DTMCs, (iii) logical characterizations thereof (including weak bisimulation for DTMCs), (iv) a relation between weak bisimulation and weak simulation equivalence, and (v) various connections between equivalences and preorders in the continuous and discretetime setting. The results are summarized in a branchingtime spectrum for DTMCs and CTMCs elucidating their semantics as well as their relationship. Key Words: comparative semantics, Markov chain, (weak) simulation, (weak) bisimulation, temporal logic
Gamebased abstraction for markov decision processes
 In Proc. of QEST: Quantitative Evaluation of Systems
, 2006
"... In this paper we present a novel abstraction technique for Markov decision processes (MDPs), which are widely used for modelling systems that exhibit both probabilistic and nondeterministic behaviour. In the field of model checking, abstraction has proved an extremely successful tool to combat the s ..."
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Cited by 32 (6 self)
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In this paper we present a novel abstraction technique for Markov decision processes (MDPs), which are widely used for modelling systems that exhibit both probabilistic and nondeterministic behaviour. In the field of model checking, abstraction has proved an extremely successful tool to combat the statespace explosion problem. In the probabilistic setting, however, little practical progress has been made in this area. We propose an abstraction method for MDPs based on stochastic twoplayer games. The key idea behind this approach is to maintain a separation between nondeterminism present in the original MDP and nondeterminism introduced through abstraction, each type being represented by a different player in the game. Crucially, this allows us to obtain distinct lower and upper bounds for both the best and worstcase performance (minimum or maximum probabilities) of the MDP. We have implemented our techniques and illustrate their practical utility by applying them to a quantitative analysis of the Zeroconf dynamic network configuration protocol. 1
Probabilistic Game Semantics
 Computer Science Society
, 2000
"... A category of HO/Nstyle games and probabilistic strategies is developedwhere the possible choices of a strategy are quantified so as to give a measure of the likelihood of seeing a given play. A 2sided die is shown to be universal in this category, in the sense that any strategy breaks down into a ..."
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Cited by 31 (1 self)
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A category of HO/Nstyle games and probabilistic strategies is developedwhere the possible choices of a strategy are quantified so as to give a measure of the likelihood of seeing a given play. A 2sided die is shown to be universal in this category, in the sense that any strategy breaks down into a composition between some deterministic strategy and that die. The interpretative power of the category is then demonstrated by delineating a Cartesian closed subcategory which provides a fully abstract model of a probabilistic extension of Idealized Algol.
Stochastic processes as concurrent constraint programs
 In Symposium on Principles of Programming Languages
, 1999
"... ) Vineet Gupta Radha Jagadeesan Prakash Panangaden y vgupta@mail.arc.nasa.gov radha@cs.luc.edu prakash@cs.mcgill.ca Caelum Research Corporation Dept. of Math. and Computer Sciences School of Computer Science NASA Ames Research Center Loyola UniversityLake Shore Campus McGill University Moffe ..."
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Cited by 29 (1 self)
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) Vineet Gupta Radha Jagadeesan Prakash Panangaden y vgupta@mail.arc.nasa.gov radha@cs.luc.edu prakash@cs.mcgill.ca Caelum Research Corporation Dept. of Math. and Computer Sciences School of Computer Science NASA Ames Research Center Loyola UniversityLake Shore Campus McGill University Moffett Field CA 94035, USA Chicago IL 60626, USA Montreal, Quebec, Canada Abstract This paper describes a stochastic concurrent constraint language for the description and programming of concurrent probabilistic systems. The language can be viewed both as a calculus for describing and reasoning about stochastic processes and as an executable language for simulating stochastic processes. In this language programs encode probability distributions over (potentially infinite) sets of objects. We illustrate the subtleties that arise from the interaction of constraints, random choice and recursion. We describe operational semantics of these programs (programs are run by sampling random choices), deno...
Probabilistic Bisimulation and Equivalence for Security Analysis of Network Protocols
 In FOSSACS 2004  Foundations of Software Science and Computation Structures
, 2004
"... Using a probabilistic polynomialtime process calculus designed for specifying security properties as observational equivalences, we develop a form of bisimulation that justifies an equational proof system. ..."
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Cited by 24 (9 self)
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Using a probabilistic polynomialtime process calculus designed for specifying security properties as observational equivalences, we develop a form of bisimulation that justifies an equational proof system.
Bisimulation Relations for Dynamical and Control Systems
, 2002
"... In this paper we propose a new equivalence relation for dynamical and control systems called bisimulation. As the name implies this definition is inspired by the fundamental notion of bisimulation introduced by R. Milner for labeled transition systems. It is however, more subtle than its namesake in ..."
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Cited by 18 (8 self)
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In this paper we propose a new equivalence relation for dynamical and control systems called bisimulation. As the name implies this definition is inspired by the fundamental notion of bisimulation introduced by R. Milner for labeled transition systems. It is however, more subtle than its namesake in concurrency theory, mainly due to the fact that here, one deals with relations on manifolds. We further show that the bisimulation relations for dynamical and control systems defined in this paper are captured by the notion of abstract bisimulation of Joyal, Nielsen and Winskel (JNW). This result not only shows that our equivalence notion is on the right track, but also confirms that the abstract bisimulation of JNW is general enough to capture equivalence notions in the domain of continuous systems. We believe that the unification of the bisimulation relation for labeled transition systems and dynamical systems under the umbrella of abstract bisimulation, as achieved in this work, is a first step towards a unified approach to modeling of and reasoning about the dynamics of discrete and continuous structures in computer science and control theory.