Interactive and reactive systems: States, observations, experiments, input, output, nondeterminism, compositionality and all that

Abstract

In this paper, we discuss, analyse, relate, and investigate the basic notions of state, action, experiment, and observation and their importance for questions of compositionality as they appear in reactive systems. In particular, we discuss the concept and role of input and output as well as that of nondeterminism for the mathematical modelling of system behaviours. We argue that for a given state transition system with composition operators there exists a canonical notion of nondeterminism as well as of input and output and that these notions are helpful in the search for modular semantic models.