We introduce a general stochastic process operator f d:D p(d) which behaves as the process p(d) where the value d is chosen from a data domain D with a probability density determined by f . We require that f is a measurable function from D to R such that R d∈D f(d)dμD = 1. For finite or countable D the function f represents the probability distribution directly. For bigger domains f represents ...

The standard engineering approach to modelling of complex systems is highly compositional. In order to be able to understand (or to control) the behavior of a complex dynamical systems, it is often desirable, if not necessary, to view this system as an interconnection of smaller interacting subsystems, each of these subsystems having its own functionalities. In this paper, we propose a composit...

ion In concurrency theory it is often useful to distinguish between internal actions, that do not admit interactions with the outside world, and external ones. As normally there is no need to distinguish the internal actions from each other, they all have the same name, namely τ . If A is the set of external actions a certain class of systems may perform, then Aτ := A . ∪ {τ}. Systems in that c...

We improve an existing bisimulation minimisation algorithm for tree automata by introducing backward and forward bisimulations and developing minimisation algorithms for them. Minimisation via forward bisimulation is also effective for deterministic automata and faster than the previous algorithm. Minimisation via backward bisimulation generalises the previous algorithm and is thus more effecti...

In this work, a process algebra is designed around an ACUID equational theory extended with prefixes symbolizing actions, and by making parallel synchronous composition distributive over non-deterministic choice; such a synchronous composition is commutative and non-associative. Bisimulation between processes is then interpretable as congruence over such an equational theory. It is shown that i...

This paper addresses the design of approximately bisimilar finite abstractions of systems that are composed of the interconnection of smaller subsystems. First, it is shown that the ordinary notion of approximate bisimulation does not preserve the interconnection structure of the concrete model. Next, a new definition of approximate bisimulation that is compatible with interconnection is propos...