We consider the class of constant depth AND/OR circuits augmented with a layer of modular counting gates at the bottom layer, i.e AC◦MODm circuits. We show that the following holds for several types of gates G: by adding a gate of type G at the output, it is possible to obtain an equivalent probabilistic depth 2 circuit of quasipolynomial size consisting of a gate of type G at the output and a ...

Abstract Modularity is a quantity which has been introduced in the context of complex networks order to quantify how close network an ideal modular nodes form small interconnected communities that are joined together with relatively few edges. In this article, we consider on probabilistic model by Krioukov et al. (2010, Phys. Rev. E, 82, 036106). This views as expression hidden popularity hiera...

In this paper, we give some new coupled common  fixed point theorems for probabilistic $varphi$-contractions  in Menger probabilistic metric spaces.  As applications of the main results, we obtain some coupled common fixed point theorems in usual metric spaces and fuzzy metric spaces. The main results of this paper improvethe corresponding results given by some authors. Finally, we give one exa...

Modular automata are symbolic transition systems halfway between families of automata and their synchronized products. They allow for analysis of liveness properties without incurring the state space explosion problem. A modular automaton is composed of modules and a synchronization graph. We consider the problem whether such specifications may be implemented by a distributed Petri net up to la...

This presentation introduces a process-algebraic framework with data for modelling and generating Markov automata. We show how an existing linearisation procedure for process-algebraic representations of probabilistic automata can be reused to transform systems in our new framework to a special format. This format enables easy state space generation and facilitates the definition of syntactic r...

This paper describes a modular component of the MABEL model agents’ cognitive inference mechanism. The probabilistic and probabilogic representation of the agents’ environment and state space is coupled with a Bayesian belief and decision network functionality, which in fact holds Markovian semiparametric properties. Different approaches to modeling multi-agent systems are described and analyze...