Runs and patterns in a sequence of Bernoulli trials and multi-state trials have broadly been used for various purposes and in many areas of statistics and applied probability. Recently, Fu and Koutras (1994) developed a new method based on finite Markov chain imbedding technique to study the exact distributions for the number of specified runs and patterns in a sequence of Bernoulli trials. In ...

The 2015 Text REtrieval Conference (TREC) introduced the concept of ‘Open Runs’ in response to the increasing focus on repeatability of information retrieval experiments. An Open Run is a TREC submission backed by a software repository such that the software in the repository reproduces the system that created that exact run. The ID of the repository was captured during the process of submittin...

The concept of runs, i.e. maximal periodicity or maximal occurrence of repetitions, coined by Iliopoulos et al. [10] when analysing Fibanacci words, has been introduced to represent in a succinct manner all occurrences of repetitions in a word. It is known that there are only O(n) many of them in a word of length n from Kolpakov and Kucherov [11] who proved it in a non-constructive manner. The ...

In this paper, we present recent results about the verification of counter machines by using decision procedures for Presburger arithmetic. We recall several known classes of counter machines for which the reachability sets are Presburger-definable as well as temporal logics with arithmetical constraints. We discuss issues related to flat counter machines, path schema enumeration, and the use o...

Given a cryptographic protocol, and some assumptions, can we present everything that can happen, subject to these assumptions? The assumptions may include: (i) some behavior assumed to have occurred, (ii) some keys assumed to be uncompromised, and (iii) some values assumed to have been freshly chosen. An object representing these types of information is called a skeleton. The shapes for a skele...

In a version of the Diamond and Dybvig [3] model with aggregate uncertainty, we show that there exist an equilibrium with the following properties: all consumers deposit at the bank, all patient consumers wait for the last period to withdraw and the bank fails with strictly positive probability. Furthermore, we show that the probability of a bank failure remains bounded away from zero as the nu...

Given a word w and a Parikh vector P , an abelian run of period P in w is a maximal occurrence of a substring of w having abelian period P . Our main result is an online algorithm that, given a word w of length n over an alphabet of cardinality σ and a Parikh vector P , returns all the abelian runs of period P in w in time O(n) and space O(σ + p), where p is the norm of P , i.e., the sum of its...

Given a word w and a Parikh vector P, an abelian run of period P in w is a maximal occurrence of a substring of w having abelian period P. We give an algorithm that finds all the abelian runs of period P in a word of length n in time O(n× |P|) and space O(σ + |P|).