Sequential value passing yields a Kleene theorem for processes

Communication with value passing has received ample attention in process theory. Value passing through a sequential composition has received much less attention. In recent work, we found that sequential value passing is the essen- tial ingredient to prove the analogue of the classical theorem of the equivalence of pushdown automata and context-free grammars in a setting of interactive pro- cesses and bisimulation. Subsequently, we found that the treatment of sequential value passing in the process setting can be simplified considerably. We report on this simplification here, and find another application of sequential value passing, viz. a Kleene theorem for processes.