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Probabilistic Simulations for Probabilistic Processes
, 1994
"... Several probabilistic simulation relations for probabilistic systems are defined and evaluated according to two criteria: compositionality and preservation of "interesting" properties. Here, the interesting properties of a system are identified with those that are expressible in an untimed ..."
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Cited by 370 (22 self)
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Several probabilistic simulation relations for probabilistic systems are defined and evaluated according to two criteria: compositionality and preservation of "interesting" properties. Here, the interesting properties of a system are identified with those that are expressible in an untimed version of the Timed Probabilistic concurrent Computation Tree Logic (TPCTL) of Hansson. The definitions are made, and the evaluations carried out, in terms of a general labeled transition system model for concurrent probabilistic computation. The results cover weak simulations, which abstract from internal computation, as well as strong simulations, which do not.
Sharedmemory mutual exclusion: Major research trends since
 Distributed Computing
, 1986
"... * Exclusion: At most one process executes its critical section at any time. ..."
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Cited by 68 (6 self)
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* Exclusion: At most one process executes its critical section at any time.
Proving Time Bounds for Randomized Distributed Algorithms
 In Proceedings of the 13th Annual ACM Symposium on the Principles of Distributed Computing
, 1994
"... A method of analyzing time bounds for randomized distributed algorithms is presented, in the context of a new and general framework for describing and reasoning about randomized algorithms. The method consists of proving auxiliary statements of the form U , which means that whenever the algor ..."
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Cited by 37 (10 self)
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A method of analyzing time bounds for randomized distributed algorithms is presented, in the context of a new and general framework for describing and reasoning about randomized algorithms. The method consists of proving auxiliary statements of the form U , which means that whenever the algorithm begins in a state in set U , with probability p, it will reach a state in set U within time t.
TimingBased Mutual Exclusion
 Proceedings of the Thirteenth IEEE RealTime Systems Symposium
, 1992
"... Known asynchronous nprocess deadlockfree mutual exclusion algorithms require O(n) read/write registers and O(n) operations to access the critical region, rendering them impractical for large scale applications. Burns and Lynch have shown that n registers are necessary for solving this problem, in ..."
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Cited by 24 (2 self)
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Known asynchronous nprocess deadlockfree mutual exclusion algorithms require O(n) read/write registers and O(n) operations to access the critical region, rendering them impractical for large scale applications. Burns and Lynch have shown that n registers are necessary for solving this problem, in the asynchronous setting. This paper examines the benefits...
Analysing randomized distributed algorithms
 Validation of Stochastic Systems
, 2004
"... Abstract. Randomization is of paramount importance in practical applications and randomized algorithms are used widely, for example in coordinating distributed computer networks, message routing and cache management. The appeal of randomized algorithms is their simplicity and elegance. However, thi ..."
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Cited by 14 (2 self)
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Abstract. Randomization is of paramount importance in practical applications and randomized algorithms are used widely, for example in coordinating distributed computer networks, message routing and cache management. The appeal of randomized algorithms is their simplicity and elegance. However, this comes at a cost: the analysis of such systems become very complex, particularly in the context of distributed computation. This arises through the interplay between probability and nondeterminism. To prove a randomized distributed algorithm correct one usually involves two levels: classical, assertionbased reasoning, and a probabilistic analysis based on a suitable probability space on computations. In this paper we describe a number of approaches which allows us to verify the correctness of randomized distributed algorithms. 1
Verifying Randomized Distributed Algorithms with PRISM
 In Proc. of the Workshop on Advances in Verification (WAVe
, 2000
"... In this paper we describe our experience with model checking randomized distributed algorithms using PRISM, a symbolic model checker for concurrent probabilistic systems currently being developed. PRISM uses MultiTerminal Binary Decision Diagrams (MTBDDs) as supplied by the CUDD package of Fabio So ..."
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Cited by 10 (0 self)
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In this paper we describe our experience with model checking randomized distributed algorithms using PRISM, a symbolic model checker for concurrent probabilistic systems currently being developed. PRISM uses MultiTerminal Binary Decision Diagrams (MTBDDs) as supplied by the CUDD package of Fabio Somenzi. Implemented in Java, PRISM has a system description language similar to Reactive Modules and supports model checking of probabilistic temporal logic PCTL (also under fairness constraints). Our experiments indicate that using the BDD variable ordering induced from the Kronecker representation yields very ecient MTBDD representations of randomized distributed algorithms. In particular, we are able to construct models of up to 10 30 states in seconds. Model checking of `with probability 1' PCTL properties is also fast. The eciency of numerical computation with MTBDDs, however, and hence also model checking of quantitative probabilistic temporal logic properties, is still considerably poorer than e.g. for sparse matrices. Descriptions and statistics obtained for several case studies can be found at http://www.cs.bham.ac.uk/~dxp/prism/.
Using probabilistic kleene algebra for protocol verification
 In Relmics/AKA 2006, volume 4136 of LNCS
"... Abstract. We describe pKA, a probabilistic Kleenestyle algebra, based on a well known model of probabilistic/demonic computation [3, 16, 10]. Our technical aim is to express probabilistic versions of Cohen’s separation theorems[1]. Separation theorems simplify reasoning about distributed systems, w ..."
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Cited by 7 (2 self)
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Abstract. We describe pKA, a probabilistic Kleenestyle algebra, based on a well known model of probabilistic/demonic computation [3, 16, 10]. Our technical aim is to express probabilistic versions of Cohen’s separation theorems[1]. Separation theorems simplify reasoning about distributed systems, where with purely algebraic reasoning they can reduce complicated interleaving behaviour to “separated ” behaviours each of which can be analysed on its own. Until now that has not been possible for probabilistic distributed systems. Algebraic reasoning in general is very robust, and easy to check: thus an algebraic approach to probabilistic distributed systems is attractive because in that “doubly hostile ” environment (probability and interleaving) the opportunities for subtle error abound. Especially tricky is the interaction of probability and the demonic or “adversarial ” scheduling implied by concurrency. Our case study — based on Rabin’s Mutual exclusion with bounded waiting [6] — is one where just such problems have already occurred: the original presentation was later shown to have subtle flaws [15]. It motivates our interest in algebras, where assumptions relating probability and secrecy are clearly exposed and, in some cases, can be given simple characterisations in spite of their intricacy.
Lower Bounds for Randomized Mutual Exclusion
 SIAM Journal on Computing
, 1993
"... We establish, for the first time, lower bounds for randomized mutualexclusion algorithms (with a readmodifywrite operation). Our main result is that a constant size sharedvariable cannot guarantee strong fairness, even if randomization is allowed. In fact, we prove a lower bound of\Omega\Gamma/4 ..."
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Cited by 5 (1 self)
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We establish, for the first time, lower bounds for randomized mutualexclusion algorithms (with a readmodifywrite operation). Our main result is that a constant size sharedvariable cannot guarantee strong fairness, even if randomization is allowed. In fact, we prove a lower bound of\Omega\Gamma/46 log n) bits on the size of the sharedvariable, which is also tight. We investigate weaker fairness conditions and derive tight (upper and lower) bounds for them as well. Surprisingly, it turns out that slightly weakening the fairness condition results in an exponential reduction in the size of the required sharedvariable. Our lower bounds rely on an analysis of Markovchains, that may be of interest on its own and may have applications elsewhere. Keywords: Mutual Exclusion, Randomized Distributed Algorithms, MarkovChains, LowerBounds. 1 Introduction Randomization has played an important role in the design and understanding of distributed algorithms. It is a natural tool which is usual...
On Lotteries with Unique Winners
, 1995
"... Lotteries with the unique maximum property and the unique winner property are considered. Tight lower bounds are proven on the domain size of such lotteries. 1 Introduction A lottery is a collection of discrete, independent random variables \Pi 1 ; : : : ; \Pi N defined over a set f1; : : : ; Bg. ..."
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Cited by 1 (0 self)
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Lotteries with the unique maximum property and the unique winner property are considered. Tight lower bounds are proven on the domain size of such lotteries. 1 Introduction A lottery is a collection of discrete, independent random variables \Pi 1 ; : : : ; \Pi N defined over a set f1; : : : ; Bg. We associate with the random variable \Pi i a player P i . A lottery has the unique maximum property if for every subset of \Pi 1 ; : : : ; \Pi N , with constant probability (say 2=3), the maximum value of the random variables is chosen by exactly one random variable. (Formally, for every nonempty subset S ` f1; : : : ; Ng, define the random variable M S = max fi2Sg \Pi i . Let p S be the probability that jfi 2 S : \Pi i = M S gj = 1. The unique maximum property states that p S 2=3 for every S.) A lottery has the unique winner property if for every subset of random variables, with constant probability, there exists a value that is chosen by exactly one random variable. (Formally, let q...
Layered Reasoning for Randomized Distributed Algorithms
 UNDER CONSIDERATION FOR PUBLICATION IN FORMAL ASPECTS OF COMPUTING
, 2012
"... This paper adopts the communication closed layer (CCL) concept of Elrad and Francez to the formal reasoning of randomized distributed algorithms. We do so by enriching probabilistic automata (PA) with a layered composition operator, an intermediate between parallel and sequential composition. Layer ..."
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This paper adopts the communication closed layer (CCL) concept of Elrad and Francez to the formal reasoning of randomized distributed algorithms. We do so by enriching probabilistic automata (PA) with a layered composition operator, an intermediate between parallel and sequential composition. Layered composition is used to establish probabilistic counterparts of the CCL laws that exploit independence and / or precedence conditions between the constituent PA. The probabilistic CCL laws enable partial order (po) equivalence when layered composition is replaced by sequential composition. Such poequivalence induces a purely syntactic partialorder state space reduction via layered separation in compositions of PA while preserving probabilistic nextfree lineartime properties. The feasibility of such layered separation is demonstrated on a randomized mutual exclusion algorithm by Kushilevitz and Rabin, complementing an algebraic approach (for analyzing this algorithm) by McIver, Gonzalia, Cohen, and Morgan.