8 research outputs found
CCS with Hennessy's merge has no finite-equational axiomatization
Abstract
This paper confirms a conjecture of Bergstra and Klop驴s from 1984 by establishing that the process algebra obtained by adding an auxiliary operator proposed by Hennessy in 1981 to the recursion free fragment of Milner驴s Calculus of Communicationg Systems is not finitely based modulo bisimulation equivalence. Thus Hennessy驴s merge cannot replace the left merge and communication merge operators proposed by Bergstra and Klop, at least if a finite axiomatization of parallel composition is desired.
2000 MATHEMATICS SUBJECT CLASSIFICATION: 08A70, 03B45, 03C05, 68Q10, 68Q45, 68Q55, 68Q70.
CR SUBJECT CLASSIFICATION (1991): D.3.1, F.1.1, F.1.2, F.3.2, F.3.4, F.4.1.
KEYWORDS AND PHRASES: Concurrency, process algebra, CCS, bisimulation, Hennessy驴s merge, left merge, communication merge, parallel composition, equational logic, complete axiomatizations, non-finitely based algebras
CCS with Hennessy's merge has no finite-equational axiomatization
This paper confirms a conjecture of Bergstra and Klop鈥檚 from 1984 by establishing that the process algebra obtained by adding an auxiliary operator proposed by Hennessy in 1981 to the recursion free fragment of Milner鈥檚 Calculus of Communicationg Systems is not finitely based modulo bisimulation equivalence. Thus Hennessy鈥檚 merge cannot replace the left merge and communication merge operators proposed by Bergstra and Klop, at least if a finite axiomatization of parallel composition is desired