Bounded stacks, bags and queues
We prove that a bounded stack can be specified in process algebra with just the operators alternative and sequential composition and iteration. The bounded bag cannot be specified with these operators, but can be specified if we add the parallel composition operator without communication (free merge). The bounded queue cannot even be specified in this signature; we need a form of variable binding such as given by general communication and encapsulation, the state operator, or abstraction.
KeywordsOperational Semantic Sequential Composition Parallel Composition Atomic Action Recursive Equation
Unable to display preview. Download preview PDF.
- 1.J.C.M. Baeten and J.A. Bergstra. Global renaming operators in concrete process algebra. Information and Computation, 78:205–245, 1988.Google Scholar
- 2.J.A. Bergstra, I. Bethke, and A. Ponse. Process algebra with iteration and nesting. The Computer Journal, 37(4):243–258, 1994.Google Scholar
- 3.J.A. Bergstra and J.W. Klop. The algebra of recursively defined processes and the algebra of regular processes. In J. Paredaens, editor, Proceedings 11th ICALP, number 172 in LNCS, pages 82–95. Springer Verlag, 1984.Google Scholar
- 4.J.A. Bergstra and J.W. Klop. Algebra of communicating processes. In J.W. de Bakker, M. Hazewinkel, and J.K. Lenstra, editors, Mathematics and Computer Science I, volume 1 of CWI Monograph, pages 89–138. North-Holland, Amsterdam, 1986.Google Scholar
- 5.J.A. Bergstra and J. Tiuryn. Process algebra semantics for queues. Fundamenta Informaticae, X:213–224, 1987.Google Scholar
- 6.D.M.R. Park. Concurrency and automata on infinite sequences. In P. Deussen, editor, Proceedings 5th GI Conference, number 104 in LNCS, pages 167–183. Springer Verlag, 1981.Google Scholar
- 7.G.D. Plotkin. An operational semantics for CSP. In D. Bjørner, editor, Proceedings Conference on Formal Description of Programming Concepts II, pages 199–225. North-Holland, Amsterdam, 1983.Google Scholar
- 8.F.W. Vaandrager. Process algebra semantics of POOL. In J.C.M. Baeten, editor, Applications of Process Algebra, number 17 in Cambridge Tracts in Theoretical Computer Science, pages 173–236. Cambridge University Press, 1990.Google Scholar