Related papers: Deciding the existence of cut-off in parameterized…
Given a sequence $(\mathfrak{X}_i, \mathscr{K}_i)_{i=1}^\infty$ of Markov chains, the cut-off phenomenon describes a period of transition to stationarity which is asymptotically lower order than the mixing time. We study mixing times and…
We analyze the problem of scheduling in wireless networks to meet end-to-end service guarantees, defined by instantaneous throughput and hard packet deadlines. Using a network slicing model to decouple the queueing dynamics between flows,…
Common experience suggests that many networks might possess community structure - division of vertices into groups, with a higher density of edges within groups than between them. Here we describe a new computer algorithm that detects…
Population protocols are a well-studied model of distributed computation in which a group of anonymous finite-state agents communicates via pairwise interactions. Together they decide whether their initial configuration, that is, the…
Modern networks achieve robustness and scalability by maintaining states on their nodes. These nodes are referred to as middleboxes and are essential for network functionality. However, the presence of middleboxes drastically complicates…
A communicating system is $k$-synchronizable if all of the message sequence charts representing the executions can be divided into slices of $k$ sends followed by $k$ receptions. It was previously shown that, for a fixed given $k$, one…
In this paper we investigate formal verification of extracted rules for Neural Networks under a complexity theoretic point of view. A rule is a global property or a pattern concerning a large portion of the input space of a network. These…
One of the basic properties of a queueing network is stability. Roughly speaking, it is the property that the total number of jobs in the network remains bounded as a function of time. One of the key questions related to the stability issue…
Complex systems often have features that can be modeled by advanced mathematical tools [1]. Of special interests are the features of complex systems that have a network structure as such systems are important for modeling technological and…
A random sequence having two segments being the homogeneous Markov processes is registered. Each segment has his own transition probability law and the length of the segment is unknown and random. The transition probabilities of each…
We study the simple random walk on trees and give estimates on the mixing and relaxation time. Relying on a recent characterization by Basu, Hermon and Peres, we give geometric criteria, which are easy to verify and allow to determine…
We focus on the majority model in a topology consisting of two coupled fully-connected networks, thereby mimicking the existence of communities in social networks. We show that a transition takes place at a value of the inter-connectivity…
The cutoff phenomenon describes the case when an abrupt transition occurs in the convergence of a Markov chain to its equilibrium measure. There are various metrics which can be used to measure the distance to equilibrium, each of which…
The proliferation of networked devices, systems, and applications that we depend on every day makes managing networks more important than ever. The increasing security, availability, and performance demands of these applications suggest…
Offline runtime verification involves the static analysis of executions of a system against a specification. For distributed systems, it is generally not possible to characterize executions in the form of global traces, given the absence of…
Modeling distributed computing in a way enabling the use of formal methods is a challenge that has been approached from different angles, among which two techniques emerged at the turn of the century: protocol complexes, and directed…
The finite intrinsic nature of the most distributed algorithms gives us this ability to use model checking tools for verification of this type of algorithms. In this paper, I attempt to use NuSMV as a model checking tool for verifying…
In this paper we investigate formal verification problems for Neural Network computations. Of central importance will be various robustness and minimization problems such as: Given symbolic specifications of allowed inputs and outputs in…
We consider the problems of computing the average degree and the size of a given network in a distributed fashion under quantized communication. We present two distributed algorithms which rely on quantized operation (i.e., nodes process…
We present different classes of solutions to the Firing Squad Synchronization Problem on networks of different shapes. The nodes are finite state processors that work at unison discrete steps. The networks considered are the line, the ring…