R. Segala. Modelling and verification of randomized distributed real-time systems. Ph.D. Thesis, Department of Mathematics, Massachusetts Institute of Technology, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....to include non deterministic decisions whose outcome is left completely unspecified, in cases where it is unrealistic or impossible to associate the possible outcomes with concrete probabilities. This leads to models such as Markov decision processes [1] also called concurrent Markov chains [2,3]. During the analysis of non deterministic models, special techniques must be applied in order to derive maximal or minimal probabilities with which certain requirements are satisfied, conditioned on the strategy by which non deterministic decisions are made. It is also possible to transform a ....

.... the delay until the race finishes follows a continuous distribution with a parameter cumulated from the contributing continuous distributions ( 0 00 in this case) Concurrent probabilistic systems are known to be conveniently captured in the simple probabilistic automata model of Segala [3], the sub model of SPTS considered here. An SPTS S = S; s; Act ; AP;L) is a concurrent probabilistic system (CPS) if ffl for each (s; a; f) 2 , f is of type (i) In this case, only discrete, but not continuous, distributions are allowed to occur. As opposed to DTMCs, non determinism is ....

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R. Segala, Modelling and verification of randomized distributed real time systems, Ph.D. thesis, Massachusetts Institute of Technology (1995).

....techniques, and in particular probabilistic logics, have proved successful in the specification and verification of systems that exhibit uncertainty, for example, fault tolerant systems, randomized algorithms, distributed systems, and communication protocols. However, as already observed in [45,52,56], concurrent probabilistic systems, for example randomized distributed algorithms, are notoriously difficult to verify: the proofs of their correctness are complex, and therefore argued informally, and thus appropriate # Supported in part by EPSRC grant GR K42028. formal methods for their ....

....or not a linear time formula holds with probability 1 for all fair computations. Our method is more general, as it allows to verify properties which hold with probability # p for some p # [0, 1] Verification methods for proving quantitative properties of probabilistic systems can be found in [4, 6, 14, 20, 21, 31, 34, 37, 45, 52, 56]. 21] investigates the complexity of model checking for (sequential and concurrent) probabilistic systems and presents an algorithm which tests whether a sequential Markov chain satisfies a linear time formula with probability 1. This algorithm computes the exact probabilities, and hence can also ....

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Segala R: Modelling and Verification of Randomized Distributed RealTime Systems, Ph.D. Thesis. Massachusetts Institute of Technology, 1995

....of a (pre)categorial theory of compositional specification and verification of probabilistic systems. 1 Introduction Probabilistic automata [Rab63, Paz66] are central in the field of probabilistic methods in verification, namely for providing the appropriate semantic domain (see for instance [Seg95, BCHG 97] Herein, we tackle the problem of aggregating, interconnecting and constraining probabilistic automata, having in mind future work in compositional verification of probabilistic systems. We adopt the viewpoint of category theory, following the so called categorial imperative of ....

R. Segala. Modelling and Verification of Randomized Distributed Real-Time Systems. PhD thesis, Massachusetts Institute of Technology, 1995.

....also [5] for a symbolic algorithm) DTMCs can exhibit probabilistic choice, but not nondeterministic choice, and thus are not suitable for modelling distributed or concurrent systems. For this application, a model called Concurrent Markov Chains in [32] or simply Concurrent Probabilistic Systems [31, 11, 8, 18, 20], has been introduced, together with a logic, again based on CTL, called PBTL (pCTL in [11] These are similar to Markov Decision Processes (MDPs) 10] in that they admit nondeterministic choice between discrete probability distributions on the successor states. The presence of nondeterminism ....

....to the logic CTL, which has a much more expressive counter part called CTL , 2 one can formulate PBTL (pCTL ) see e.g. 11, 8] The model checking algorithms, however, are expensive. For a comprehensive overview of issues in probabilistic verification the interested reader should consult [31, 18, 4] and [6, 26] ....

R. Segala. Modelling and Verification of Randomized Distributed Real-Time Systems. PhD thesis, MIT, 1995.

....system. 1 Introduction In recent years, the need for reasoning about probabilistic behavior, as exhibited for instance in randomized, distributed and fault tolerant systems, has triggered much interest in the area of formal methods for the specification and analysis of probabilistic systems [6, 11, 13 15, 27, 28, 30]. The general approach taken has been to extend existing models and techniques which have proved successful in the nonprobabilistic setting with probability. Thus, much work in the area of formal models for probabilistic systems has been based on labeled transition systems [23] In order to ....

.... On one end of the spectrum, several approaches have replaced nondeterministic branching in labeled transition systems with probabilistic branching [13] by assigning probabilities to each transition, while others explored the possibility of integrating nondeterministic and probabilistic behavior [30, 21, 13, 14, 28]. For example, in the reactive model of [13] as well as in the simple probabilistic automata of [28] probability distributions are dependent on the occurrence of actions, whereas in the stratified model, levelwise probabilistic branching is also possible [13] A more general model for ....

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R. Segala. Modelling and Verification of Randomized Distributed Real-Time Systems. PhD thesis, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, 1995.

....states of a labelled concurrent probabilistic system. Note that since sequential systems admit only one adversary, for such systems these intervals collapse to single values. Clearly, this interval semantics is preserved by maximal trace equivalence , defined in an appropriate way in the style of [21], where a probabilistic counterpart to (finite) trace inclusion is given. 6 5 Defining lower and upper bounds on probability for the truth value of LTL formulas We now propose the maps lb and ub from LTL formulas and states to the [0,1] interval which respectively define a lower and upper bound ....

R. Segala. Modelling and verification of randomized distributed real-time systems. Ph.D. Thesis, Department of Mathematics, Massachusetts Institute of Technology, 1995.

....states of a labelled concurrent probabilistic system. Note that since sequential systems admit only one adversary, for such systems these intervals collapse to single values. Clearly, this interval semantics is preserved by maximal trace equivalence , defined in an appropriate way in the style of [21], where a probabilistic counterpart to (finite) trace inclusion is given. Baier, Kwiatkowska and Norman 5 Defining lower and upper bounds on probability for the truth value of LTL formulas We now propose the maps lb and ub from LTL formulas and states to the [0,1] interval which respectively ....

R. Segala. Modelling and verification of randomized distributed real-time systems. Ph.D. Thesis, Department of Mathematics, Massachusetts Institute of Technology, 1995.

....equations of the form X = maxfX 1 ; X n g, we introduce, the set of inequations X X i . Consequently, our aim is to minimize the function P s2S X s Phi . Using algorithms based on the ellipsoid method, this problem can be solved in time polynomial to the number of variables (see, e.g. [13]) 5 A Telecommunications Application In this section we present an application of PACSR for the specification and analysis of a probabilistic system. The example was inspired by the specification of a switching system presented in [1] The system is comprised of a number of interacting ....

R. Segala. Modelling and Verification of Randomized Distributed Real-Time Systems. PhD thesis, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, 1995.

....including [12, 21, 2, 10, 16, 20] The approach of [12] is particularly relevant as it also adds probability to a real time process algebra. It does not, however, consider the notions of resource and resource probability, nor use priorities to control communication and resource access. In [18], an automata based formalism that combines the notions of real time and probabilities is presented. It employs a different notion of time in that transitions can have variable durations. Also, probabilities are associated with instantaneous events. Since a PACSR specification typically consists ....

....behavior, which cannot be resolved through probabilities. To provide for both probabilistic and non deterministic behavior, the semantics of PACSR processes are given via labeled concurrent Markov chains [22] This model has also been employed in [12] and variations of it appeared in [18, 6]. Regarding previous work on model checking for probabilistic systems, a closely related approach involves associating a probability threshold with the until operator of the temporal logic CTL [7] For example, see [13, 4, 6, 14] We find that this approach can become problematic when expressing ....

R. Segala. Modelling and Verification of Randomized Distributed Real-Time Systems. PhD thesis, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, 1995.

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R. Segala. Modelling and Verification of Randomized Distributed Real-Time Systems. PhD thesis, MIT, 1995.

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R. Segala. Modelling and Verification of Randomized Distributed Real-Time Systems. PhD thesis, MIT, 1995.

....concurrent probabilistic systems in [2] without implementation) The algorithm for checking PCTL until properties reduces to solving a system of linear equations . In this paper we consider models for concurrent probabilistic systems based on Markov Decision Processes [9] similar to those of [50, 22, 43, 10, 6, 24]. These are state labelled systems which admit nondeterministic choice between discrete probability distributions on the successor states, and are particularly appropriate for the representation of randomized distributed algorithms, fault tolerant and self stabilising systems. The presence of ....

....In this section, we briefly summarise our underlying model for concurrent probabilistic systems; the reader is referred to [6, 2] for more details. Our model is based on Markov decision processes , and is similar to Concurrent Markov Chains of [50, 22] and simple deterministic automata of [43]. Some familiarity with Markov chains and probability theory is assumed, see e.g. 48] We begin by recalling the standard definition of (discrete time) Markov chains and the associated probability measure. A Markov chain is a pair M = S; P) where S is a finite set of states and P : S Theta S ....

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R. Segala. Modelling and Verification of Randomized Distributed Real-Time Systems. PhD thesis, MIT, 1995.

.... 7, 40127 Bologna, Italy segala cs.unibo.it January 22, 1999 Abstract Symbolic model checking for purely probabilistic processes using MTBDDs [12] was introduced in [4] and further developed in [20, 3] In this paper we consider models for concurrent probabilistic systems similar to those of [28, 7, 5] and the concurrent Markov chains of [35, 13] which extend the purely probabilistic processes through the addition of nondeterministic choice. As a specification formalism we use probabilistic branchingtime temporal logic PBTL of [5, 7] which allows to express properties such as under any ....

....parallel randomized programs. The research concerning Probabilistic Verus focuses on semantics and case studies, featuring timing and performance analysis, but does not include support for nondeterminism. In this paper we consider models for concurrent probabilistic systems similar to those of [28, 7, 5] and slightly more general than the concurrent Markov chains of [35, 13] These admit nondeterministic choice between discrete probability distributions on the successor states, and are particularly appropriate for the representation of randomized distributed algorithms, fault tolerant and ....

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R. Segala. Modelling and Verification of Randomized Distributed Real-Time Systems. PhD thesis, MIT, 1995.

....successor states (node and clock assignment pairs) paired up with a real time value. Thus each adversary A and state hs 0 ; 0 i give rise to a probabilistic computation (a cycle free Markov chain) where each state of the computation corresponds to a finite path of G starting at hs 0 ; 0 i, cf [16]. We denote such a probabilistic computation by H and its start state by h 0 . Single step probability space We need to define the probability space ( Omega h0 ; F h0 ; P h0 ) that identifies the next state reachable from h 0 in H . Let h 0 = hs 0 ; 0 i. By definition of the probabilistic ....

....do not have h as a prefix and by replacing each remaining state h 0 by h 0 . h. Strictly speaking H . h is not a probabilistic computation since its start state is not a start state of the original probabilistic automaton. This is usually referred to as a probabilistic computation fragment [16]. We now define the basic measurable sets for any probabilistic computation fragment. Definition 10 (Basic measurable sets) A basic measurable set with respect to H of dimension 0 is either the set Omega 0 H or the empty set. Define the probability measure P 0 H as follows: P 0 H ( def ....

R. Segala. Modelling and Verification of Randomized Distributed Real-Time Systems. PhD thesis, MIT, 1995.

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R. Segala. Modelling and verification of randomized distributed real-time systems. Ph.D. Thesis, Department of Mathematics, Massachusetts Institute of Technology, 1995.

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R. Segala. Modelling and Verification of Randomized Distributed Real Time Systems. PhD thesis, Massachusetts Institute of Technology, 1995.

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R. Segala, Modelling and verification of randomized distributed real time systems, Ph.D. thesis, Massachusetts Institute of Technology (1995). 54

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R. Segala. Modelling and Verification of Randomized Distributed Real-Time Systems. PhD thesis, Massachusetts Institute of Technology, 1995.

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R. Segala. Modelling and verification of randomized distributed real-time systems, PhD Thesis, Massachusetts Institute of Technology, 1995.

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R. Segala. Modelling and verification of randomized distributed real-time systems, PhD Thesis, Massachusetts Institute of Technology, 1995.

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