Recursive process definitions with the state operator - Baeten, Josephus C. M.; Bergstra, Jan A. 1951- (Centrum voor Wiskunde en Informatica <Amsterdam> / Department of Computer Science: Report CS, 1989)
Abstract: "We investigate the defining power of finite recursive specifications over the theory with + (alternative composition and . (sequential composition and [lambda] (the state operator) over a finite set of states, and find that it is greater than that of the same theory without state operator. Thus, adding the state operator is an essential extension of BPA (the theory of processes over +,.). On the other hand, applying the state operator to a regular process again gives a regular process. As a limiting result in the other direction, we find that not all PA-processes (where also parallel composition is present) can be defined over BPA plus state operator."