A weakly connected dominating set (WCDS) of graph is a subset of so that the vertex set of the given subset and all vertices with at least one endpoint in the subset induce a connected sub‐graph of . Finding the WCDS is a new promising approach for clustering the wireless networks. The minimum WCDS (MWCDS) problem is known to be NP‐hard, and several approximation algo...

Probabilistic Automata⋆ Benôıt Delahaye, Joost-Pieter Katoen, Kim G. Larsen, Axel Legay, Mikkel L. Pedersen, Falak Sher, and Andrzej Wąsowski 1 INRIA/IRISA, Rennes, France 2 RWTH Aachen University, Software Modeling and Verification Group, Germany 3 Aalborg University, Denmark 4 IT University of Copenhagen, Denmark Abstract. Probabilistic Automata (PAs) are a widely-recognized mathematical fram...

This paper discusses a notion of approximate abstraction for linear stochastic hybrid automata (LSHA). The idea is based on the construction of the so called stochastic bisimulation function. Such function can be used to quantify the distance between a system and its approximate abstraction. The work in this paper generalizes our earlier work for jump linear stochastic systems (JLSS). In this p...

This chapter surveys some basic algorithms for analyzing Markov chains (MCs) and Markov decision processes (MDPs), and discusses their computational complexity. We focus on discrete-time processes, and we consider both finite-state models as well as countably infinite-state models that are finitely-presented. The analyses we will primarily focus on are hitting (reachability) probabilities and ω...

We describe a simple, fast and easy to implement recursive algorithm with four alternate intuitive heuristics for inferring Probabilistic Finite State Automata. The algorithm is an extension for stochastic machines of the k-tails method introduced in 1972 by Biermann and Feldman for non-stochastic machines. Experiments comparing the two are done and benchmark results are also presented. It is a...

This paper can be thought of as a companion paper to Van Loan’s The Ubiquitous Kronecker Product paper [23]. We collect and catalog the most useful properties of the Kronecker product and present them in one place. We prove several new properties that we discovered in our search for a Stochastic Automata Network preconditioner. We conclude by describing one application of the Kronecker product,...

In this paper we present a compositional semantics for the channel-based coordination language Reo which enables the analysis of quality of service (QoS) properties of service compositions. For this purpose, we annotate Reo channels with stochastic delay rates and explicitly model data-arrival rates at the boundary of a connector, to capture its interaction with the services that comprise its e...

in this paper, intelligent algorithm of ALATO based on Learning Automata using Adaptive Stochastic Petri Net presented to optimize the time in Economical Grid. Adaptive Stochastic Petri nets based on learning automata predicts the following optimized state through getting information from former system states and dynamic environmental reactions, makes the system current states appeared based on...

A stochastic automaton can perform a finite number of actions in a random environment. When a specific action is performed, the environment responds by producing an environment output that is stochastically related to the action. The aim is to design an automaton, using a reinforcement scheme based on the computational model of wasp behaviour that can determine the best action guided by past ac...

This paper presents a process algebra for specifying soft real-time constraints in a compositional way. For these soft constraints we take a stochastic point of view and allow arbitrary probability distributions to express delays of activities. The semantics of this process algebra is given in terms of stochastic automata, a variant of timed automata where clocks are initialised randomly and ru...