Coinduction in Concurrent Timed Systems

An important class of timed transition systems can be modeled by deterministic weighted automata, which are essentially partial Mealy automata, and their extensions using synchronous compositions defined over extended alphabets. From a coalgebraic viewpoint, behaviours of deterministic partial Mealy automata are causal and length preserving partial functions between finite and infinite sequences of inputs and outputs, called stream functionals. After a study of fundamental properties of functional stream calculus an application to the definition by coinduction of the synchronous product of stream functionals is proposed.