In this article, we introduce a new dispersion order weaker than the classic dispersion order discussed by Lewis and Thompson (1981). We study the equivalence of this order with the majorization order under the assumption of unimodality. Finally, we use this equivalence to characterize the IFR aging notion for unimodal distributions by means of the notion of decreasing in randomness.

This article is concerned with the problem of controlling a simple immigration process, which represents a pest population, by the introduction of a predator. It is assumed that the cost rate caused by the pests is an increasing function of their population size and that the cost rate of the controlling action is constant. The existence of a control-limit policy that minimizes the expected long-run average cost per unit time is established. The proof is based on the variation of a fictitious parameter over the entire real line.

The above-mentioned article by James Lynch was published in Probability in the Engineering and Informational Sciences (1999), 13: 33–36.

It has recently been brought to the author's attention that the results in that paper were preceded and superseded by the results in Thomas H. Savits' paper, “A multivariate IFR class,” which appeared in the Journal of Applied Probability (1985), 22: 197–204. This acknowledgment is to correct this contretemps.

We consider a stochastic input–output system with additional total clearings at certain random times determined by its own evolution (and specified by a controller). Between two clearings, the stock level process is a superposition of a Brownian motion with drift and a compound Poisson process with positive jumps, reflected at zero. We introduce meaningful cost functionals for this system and determine them explicitly under several (classical and new) clearing policies.

This article presents Monte Carlo techniques for estimating network reliability. For highly reliable networks, techniques based on graph evolution models provide very good performance. However, they are known to have significant simulation cost. An existing hybrid scheme (based on partitioning the time space) is available to speed up the simulations; however, there are difficulties with optimizing the important parameter associated with this scheme. To overcome these difficulties, a new hybrid scheme (based on partitioning the edge set) is proposed in this article. The proposed scheme shows orders of magnitude improvement of performance over the existing techniques in certain classes of network. It also provides reliability bounds with little overhead.

We relate two variants of the inspection paradox by showing that both represent the length of a renewal interval that contains a chosen point, the difference being in the way that point is chosen. We show, in both cases, that the length of the interval is likelihood ratio larger than that of an ordinary renewal interval.

The multiarmed-bandit problem is often taken as a basic model for the trade-off between the exploration and utilization required for efficient optimization under uncertainty. In this article, we study the situation in which the unknown performance of a new bandit is to be evaluated and compared with that of a known one over a finite horizon. We assume that the bandits represent random variables with distributions from the one-parameter exponential family. When the objective is to maximize the Bayes expected sum of outcomes over a finite horizon, it is shown that optimal policies tend to simple limits when the length of the horizon is large.

Let τk|n denote the lifetime of a k-out-of-n system, where the n components have independent lifetimes Ti with completely arbitrary distribution Fi, i = 1,..., n. It is shown that τk+1|n ≤hr τk|n, τk|n ≤hr τk−1|n−1, and τk|n−1 ≤hr τk|n if Ti ≤hr Tn, i = 1,..., n − 1; τk+1|n ≤rh τk|n, τk−1|n ≤rh τk|n, and τk|n ≤rh τk−1|n−1 if Tn ≤rh Ti, i = 1,..., n − 1. These results are available in the literature for the special case of Fi's being absolutely continuous. Also, even in this case, the proofs are often tedious and use the concept of “totally positive of order infinity in differences of k.” In contrast, the proofs given here are simple and elegant and do not use the above concept.

Very few stochastic systems are known to have closed-form transient solutions. In this article we consider an immigration birth and death population process with total catastrophes and study its transient as well as equilibrium behavior. We obtain closed-form solutions for the equilibrium distribution as well as the closed-form transient probability distribution at any time t ≥ 0. Our approach involves solving ordinary and partial differential equations, and the method of characteristics is used in solving partial differential equations.

External and internal monotonicity properties for Jackson networks have been established in the literature with the use of coupling constructions. Recently, Lopez et al. derived necessary and sufficient conditions for the (strong) stochastic comparison of two-station Jackson networks with increasing service rates, by constructing a certain Markovian coupling. In this article, we state necessary and sufficient conditions for the stochastic comparison of L-station Jackson networks in the general case. The proof is based on a certain characterization of the stochastic order for continuous-time Markov chains, written in terms of their associated intensity matrices.

We show that the size of a Las Vegas automatonand the size of a complete, minimal deterministicautomaton accepting a regularlanguage are polynomially related. More precisely, we showthat if a regular language L is accepted by aLas Vegas automaton having r states such thatthe probability for a definite answer to occur is at least p,then r ≥ np , where n is the number of the statesof the minimal deterministic automaton accepting L.Earlier this result has been obtainedin [2] by using a reduction to one-way Las Vegas communicationprotocols, but here we give a direct proof based on information theory.

Branching programs are a well-established computation model for boolean functions,especially read-once branching programs (BP1s) have been studied intensively. Recently two restricted nondeterministic (parity)BP1 models, called nondeterministic (parity) graph-driven BP1s and well-structured nondeterministic (parity) graph-driven BP1s, have been investigated. The consistency test for a BP-model M is the test whether a given BP is really a BP of model M. Here it is proved that the consistency test is co-NP-complete for nondeterministic (parity) graph-driven BP1s.Moreover, a lower bound technique for nondeterministic graph-driven BP1sis presented. The method generalizes a technique for the well-structured modeland is applied in order to answer in the affirmative the open question whether the model of nondeterministic graph-driven BP1s is a proper restriction of nondeterministic BP1s (with respect to polynomial size).

Drawing on an analogy with temporal fixpoint logic, we relate the arithmetic fixpoint definable sets to the winning positions of certain games, namely games whose winning conditions lie in the difference hierarchy over $\Sigma^0_2$ . This both provides a simple characterization of the fixpoint hierarchy, and refines existing results on the power of the game quantifier in descriptive set theory. We raise the problem oftransfinite fixpoint hierarchies.

Episturmian morphisms generalize Sturmian morphisms. They are definedas compositions of exchange morphisms and two particular morphismsL, and R. Epistandard morphisms are the morphisms obtained withoutconsidering R. In [14], a general study of these morphimsand of conjugacy of morphisms is given. Here, given a decomposition of an Episturmian morphism f over exchange morphisms and {L,R},we consider two problems: how to computea decomposition of one conjugate of f;how to compute a list of decompositions of all the conjugates of f when f is epistandard.For each problem, we give several algorithms.Although the proposed methods are fundamently different, we show thatsome of these lead to the same result. We also give other algorithms, using the same input, to compute for instance the length of the morphism, or its number of conjugates.

Processes in Place/Transition (P/T) nets are definedinductively by a peculiar numbering of place occurrences. Alongwith an associative sequential composition called catenation and a neutralprocess, a monoid of processes is obtained. The power algebra of this monoidcontains all process languages with appropriate operations on them. Hencethe problems of analysis and synthesis, analogous to those in the formallanguages and automata theory, arise. Here, the analysis problem is: for agiven P/T net with an initial marking find the set of all processes the netmay evoke. The synthesis problem is: given a process language Ldecide if there exists a marked net whose evolutions (represented byprocesses) are collected in L and, in the positive case, find suchnet and its initial marking. The problems are posed and given a generalsolution.

We describe Wadge degrees of ω-languages recognizable bydeterministic Turing machines. In particular, it is shown that theordinal corresponding to these degrees is ξω whereξ = ω1 CK is the first non-recursive ordinal known as theChurch–Kleene ordinal. This answers a question raised in [2].

This paper describes the [Lscr][Dscr][Lscr]++ system and the research advances that have enabled its design and development. We begin by discussing the new nonmonotonic and nondeterministic constructs that extend the functionality of the [Lscr][Dscr][Lscr]++ language, while preserving its model-theoretic and fixpoint semantics. Then, we describe the execution model and the open architecture designed to support these new constructs and to facilitate the integration with existing DBMSs and applications. Finally, we describe the lessons learned by using [Lscr][Dscr][Lscr]++ on various tested applications, such as middleware and datamining.

Raymond Reiter, Professor of computer science at the University of Toronto, a Fellow of the Royal Society of Canada, and winner of the 1993 – IJCAI Outstanding Research Scientist Award, died September 16, 2002, after a year-long struggle with cancer. Reiter, known throughout the world as “Ray,” made foundational contributions to artificial intelligence, knowledge representation and databases, and theorem proving.