In this paper, two types of cellular automata are studied in order to describe the 2-dimensional free growth of an avascular tumor under the effect of a limited nutrient source. On one hand a deterministic cellular automata approach is used. On the other hand a stochastic one is presented. An existing reaction-diffusion model including cell proliferation, motility and death is used. Finally, a ...

A new weak bisimulation semantics is defined for Markov automata that, in addition to abstracting from internal actions, sums up the expected values of consecutive exponentially distributed delays possibly intertwined with internal actions. The resulting equivalence is shown to be a congruence with respect to parallel composition for Markov automata. Moreover, it turns out to be comparable with...

We prove the following facts about the language recognition power of Kondacs-Watrous quantum finite automata in the unbounded error setting: One-way automata of this kind recognize all and only the stochastic languages. When the tape head is allowed two-way (or even " 1.5-way ") movement, more languages become recognizable. This leads to the conclusion that quantum Turing machines are more powe...

We prove that the class of languages recognized by generalized quantum finite automata (GQFA's) with unbounded error equals the class of stochastic languages. The capability of performing additional intermediate projective measurements does not increase the recognition power of GQFA's over Kondacs-Watrous quantum finite automata in this setting. Unlike their probabilistic counterparts, allowing...

Stochastic deterministic finite automata have been introduced and are used in a variety of settings. We use them to model musical styles: a same automaton can be used to classify new melodies but also to generate them. Through grammatical inference these automata are learned and new pieces of music can be parsed. We show that this works by proposing promising classification results and discuss ...

We investigate some graph properties which may simplify the computation of the steady-state distribution of Markov chain. We consider the directed graph associated to a Markov chain derived from Stochastic Automata Network and we give an algorithm to solve the Kolmogorov equations for the steady-state distribution. Then, we present an extension of this algorithm which allows the parametric anal...

Stochastic switched systems are a relevant class of stochastic hybrid systems with probabilistic evolution over a continuous domain and control-dependent discrete dynamics over a finite set of modes. In the past few years several different techniques have been developed to assist in the stability analysis of stochastic switched systems. However, more complex and challenging objectives related t...

A stochastic hybrid system contains a collection of interacting discrete and continuous components, subject to random behaviour. The formal verification of a stochastic hybrid system often comprises a method for the generation of a finite-state probabilistic system which either represents exactly the behaviour of the stochastic hybrid system, or which approximates conservatively its behaviour. ...

The analysis of models specified with formalisms like Markovian process algebras or stochastic automata can be based on equivalence relations among the states. In this paper we introduce a relation called exact equivalence that, differently from most aggegation approaches, induces an exact lumping on the underlying Markov chain instead of a strong lumping. We prove that this relation is a congr...