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42
Compositional design methodology with constraint Markov chains
 in: International Conference on Quantitative Evaluation of Systems, QEST, IEEE Computer Society
"... Notions of specification, implementation, satisfaction, and refinement, together with operators supporting stepwise design, constitute a specification theory. We construct such a theory for Markov Chains (MCs) employing a new abstraction of a Constraint MC. Constraint MCs permit rich constraints on ..."
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Cited by 13 (7 self)
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Notions of specification, implementation, satisfaction, and refinement, together with operators supporting stepwise design, constitute a specification theory. We construct such a theory for Markov Chains (MCs) employing a new abstraction of a Constraint MC. Constraint MCs permit rich constraints on probability distributions and thus generalize prior abstractions such as Interval MCs. Linear (polynomial) constraints suffice for closure under conjunction (respectively parallel composition). This is the first specification theory for MCs with such closure properties. We discuss its relation to simpler operators for known languages such as probabilistic process algebra. Despite the generality, all operators and relations are computable. I.
On Automated Verification of Probabilistic Programs
"... Abstract. We introduce a simple procedural probabilistic programming language which is suitable for coding a wide variety of randomised algorithms and protocols. This language is interpreted over finite datatypes and has a decidable equivalence problem. We have implemented an automated equivalence c ..."
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Abstract. We introduce a simple procedural probabilistic programming language which is suitable for coding a wide variety of randomised algorithms and protocols. This language is interpreted over finite datatypes and has a decidable equivalence problem. We have implemented an automated equivalence checker, which we call apex, for this language, based on game semantics. We illustrate our approach with three nontrivial case studies: (i) Herman’s selfstabilisation algorithm; (ii) an analysis of the average shape of binary search trees obtained by certain sequences of random insertions and deletions; and (iii) the problem of anonymity in the Dining Cryptographers protocol. In particular, we record an exponential speedup in the latter over stateoftheart competing approaches. 1
Game relations and metrics
 In LICS’07
, 2007
"... We consider twoplayer games played over finite state spaces for an infinite number of rounds. At each state, the players simultaneously choose moves; the moves determine a successor state. It is often advantageous for players to choose probability distributions over moves, rather than single moves. ..."
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Cited by 12 (3 self)
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We consider twoplayer games played over finite state spaces for an infinite number of rounds. At each state, the players simultaneously choose moves; the moves determine a successor state. It is often advantageous for players to choose probability distributions over moves, rather than single moves. Given a goal (e.g., “reach a target state”), the question of winning is thus a probabilistic one: “what is the maximal probability of winning from a given state?”. On these game structures, two fundamental notions are those of equivalences and metrics. Given a set of winning conditions, two states are equivalent if the players can win the same games with the same probability from both states. Metrics provide a bound on the difference in the probabilities of winning across states, capturing a quantitative notion of state “similarity”. We introduce equivalences and metrics for twoplayer game structures, and we show that they characterize the difference in probability of winning games whose goals are expressed in the quantitative µcalculus. The quantitative µcalculus can express a large set of goals, including reachability, safety, and ωregular properties. Thus, we claim that our relations and metrics provide the canonical extensions to games, of the classical notion of bisimulation for transition systems. We develop our results both for equivalences and metrics, which generalize bisimulation, and for asymmetrical versions, which generalize simulation.
PROBMELA: a modeling language for communicating probabilistic processes
, 2004
"... Building automated tools to address the analysis of reactive probabilistic systems requires a simple, but expressive input language with a formal semantics based on a probabilistic operational model that can serve as starting point for verification algorithms. We introduce a higher level description ..."
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Cited by 11 (4 self)
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Building automated tools to address the analysis of reactive probabilistic systems requires a simple, but expressive input language with a formal semantics based on a probabilistic operational model that can serve as starting point for verification algorithms. We introduce a higher level description language for probabilistic parallel programs with shared variables, message passing via synchronous and (perfect or lossy) fifo channels and atomic regions and provide a structured operational semantics. Applied to finitestate systems, the semantics can serve as basis for the algorithmic generation of a Markov decision process that models the stepwise behavior of the given system.
Testing Semantics for Probabilistic LOTOS
, 1995
"... In this paper we present a probabilistic extension of LOTOS which is upward compatible with LOTOS. We present testing semantics for the reactive and generative models described in [vGSST90]. While there is a certain lose of the meaning of probabilities in the reactive model, testing with probabilist ..."
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Cited by 11 (7 self)
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In this paper we present a probabilistic extension of LOTOS which is upward compatible with LOTOS. We present testing semantics for the reactive and generative models described in [vGSST90]. While there is a certain lose of the meaning of probabilities in the reactive model, testing with probabilistic tests proves to be too strong, because it does not relate behavior expressions which we expect to be equivalent. This is why we introduce the limited generative model, where tests are not allowed to have explicit probabilities. We give a fully abstract characterization for the reactive model, while we give alternative characterizations (based on a set of essential tests) for the generative and limited generative models. We also present some algebraic laws for each of the models, including some laws which establish the difference between the three models.
Markovian Processes go Algebra
, 1994
"... We propose a calculus MPA for reasoning about random behaviour through time. In contrast to classical calculi each atomic action is supposed to happen after a delay that is characterized by a certain exponentially distributed random variable. The operational semantics of the calculus defines markovi ..."
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Cited by 8 (4 self)
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We propose a calculus MPA for reasoning about random behaviour through time. In contrast to classical calculi each atomic action is supposed to happen after a delay that is characterized by a certain exponentially distributed random variable. The operational semantics of the calculus defines markovian labelled transition systems as a combination of classical actionoriented transition systems and markovian processes, especially continuous time markov chains. This model allows to calculate performance measures (e.g. response times), as well as purely functional statements (e.g. occurences of deadlocks). In order to reflect different behavioural aspects we define a hierarchy of bisimulation equivalences and show that they are all congruences. Finally we present syntactic laws characterizing markovian bisimulation equivalence, our central notion of equivalence, and show that these laws form a sound and complete axiomatization for finite processes. 1 Introduction In recent years reasoning...
Stochastic PiCalculus With General Distributions
 in Proc. of the 4th Workshop on Process Algebras and Performance Modelling (PAPM '96), CLUT
, 1996
"... In this study we extend stochastic ßcalculus allowing general probabilistic distributions to occur in its prefixes. We show that no additional information is needed in the labels of transitions or in the states of systems to derive an enabling relation between transitions. Enabling is then used to ..."
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Cited by 7 (0 self)
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In this study we extend stochastic ßcalculus allowing general probabilistic distributions to occur in its prefixes. We show that no additional information is needed in the labels of transitions or in the states of systems to derive an enabling relation between transitions. Enabling is then used to compute the residual life times of parallel activities that are not immediately selected when enabled. The policy according to which residual life times are computed is the enabling memory introduced for stochastic Petri nets and also implemented in TIPP through the mechanism of start references. 1 Introduction Many researchers advocate the need of integrating behavioural and performance analysis since the early stages of design of complex systems. This problem is even presented as a challenge for the future of computer science in [11]. The widespread dissemination of distributed systems and the paradigm of mobile computing makes the above integration essential. In fact, a design error whic...
Metric semantics for reactive probabilistic processes
, 1997
"... In this thesis we present three mathematical frameworks for the modelling of reactive probabilistic communicating processes. We first introduce generalised labelled transition systems as a model of such processes and introduce an equivalence, coarser than probabilistic bisimulation, over these syst ..."
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Cited by 6 (1 self)
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In this thesis we present three mathematical frameworks for the modelling of reactive probabilistic communicating processes. We first introduce generalised labelled transition systems as a model of such processes and introduce an equivalence, coarser than probabilistic bisimulation, over these systems. Two processes are identified with respect to this equivalence if, for all experiments, the probabilities of the respective processes passing a given experiment are equal. We next consider a probabilistic process calculus including external choice, internal choice, actionguarded probabilistic choice, synchronous parallel and recursion. We give operational semantics for this calculus be means of our generalised labelled transition systems and show that our equivalence is a congruence for this language. Following the methodology introduced by de Bakker & Zucker, we then give denotational semantics to the calculus by means of a complete metric space of probabilistic processes. The derived metric, although not an ultrametric, satisfies the intuitive property that the distance between two processes tends to 0 if a measure of the dif
Deriving syntax and axioms for quantitative regular behaviours
, 2009
"... We present a systematic way to generate (1) languages of (generalised) regular expressions, and (2) sound and complete axiomatizations thereof, for a wide variety of quantitative systems. Our quantitative systems include weighted versions of automata and transition systems, in which transitions ar ..."
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Cited by 6 (2 self)
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We present a systematic way to generate (1) languages of (generalised) regular expressions, and (2) sound and complete axiomatizations thereof, for a wide variety of quantitative systems. Our quantitative systems include weighted versions of automata and transition systems, in which transitions are assigned a value in a monoid that represents cost, duration, probability, etc. Such systems are represented as coalgebras and (1) and (2) above are derived in a modular fashion from the underlying (functor) type of these coalgebras. In previous work, we applied a similar approach to a class of systems (without weights) that generalizes both the results of Kleene (on rational languages and DFA’s) and Milner (on regular behaviours and finite LTS’s), and includes many other systems such as Mealy and Moore machines. In the present paper, we extend this framework to deal with quantitative systems. As a consequence, our results now include languages and axiomatizations, both existing and new ones, for many different kinds of probabilistic systems.