The synthesis of stochastic finite-state automata is possible using two kinds of components-deterministic finite-state automata and ergodic signal generators. The starting point in such a synthesis methods is a decomposition of stochastic matrix, its representation as a linear form of simple matrices which belong to the class of transition matrices of deterministic automata. New heuristic crite...

The goal of the present paper is to provide a systematic and comprehensive study of rational stochastic languages over a semiring K ∈ {Q,Q,R,R}. A rational stochastic language is a probability distribution over a free monoid Σ which is rational over K, that is which can be generated by a multiplicity automata with parameters in K. We study the relations between the classes of rational stochasti...

We present spectral methods of moments for learning sequential models from a single trajectory, in stark contrast with the classical literature that assumes the availability of multiple i.i.d. trajectories. Our approach leverages an efficient SVD-based learning algorithm for weighted automata and provides the first rigorous analysis for learning many important models using dependent data. We st...

A new class of non-Markovian models is introduced that results from the combination of stochastic automata networks and a very general class of stochastic processes namely rational arrival processes which are derived from matrix exponential distributions. It is shown that the modeling formalism allows a compact representation of complex models with large state spaces. The resulting stochastic p...

This article describes the use of Stochastic Automata Networks (SAN) as a modelling tool. A SAN model consists of some individual stochastic automata that act more or less independently of each other. An automata is represented by a number of states and probabilistic rules that govern the manner in which it moves from one state to the next. The state of a SAN is given by the state of each of it...

This article describes the use of Stochastic Automata Networks (SAN) as a modelling tool. A SAN model consists of some individual stochastic automata that act more or less independently of each other. An automata is represented by a number of states and probabilistic rules that govern the manner in which it moves from one state to the next. The state of a SAN is given by the state of each of it...

The general theory of randomly timed automata is developed: starting with the practical motivation and presentation of the envisaged notion, the categorical theory of minimization, aggregation, encapsulation, interconnection and realization of such automata is worked out. All these constructions are presented universally: minimization and realization as adjunctions, aggregation as product, inte...

Probabilistic finite automata (PFA) model stochastic languages, i.e. probability distributions over strings. Inferring PFA from stochastic data is an open field of research. We show that PFA are identifiable in the limit with probability one. Multiplicity automata (MA) is another device to represent stochastic languages. We show that a MA may generate a stochastic language that cannot be genera...

Automata expressiveness is an essential feature in understanding which of the formalisms available should be chosen for modelling a particular problem. Probabilistic and stochastic automata are suitable for modelling systems exhibiting probabilistic behaviour and their expressiveness has been studied relative to non-probabilistic transition systems and Markov chains. In this paper, we consider ...

We present a new performance evaluation tool based on the analysis of large Markov chains and Stochastic Automata Networks. Using some graph theoretical arguments, we show how to systematically perform state reduction. The graph properties can be checked easily because we take advantage of the tensorial construction of the Markov chain from the Stochastic Automata Network.