Partial evaluation and &ohgr;-completeness of algebraic specifications
Theoretical Computer Science
Tools for proving inductive equalities, relative completeness, and &ohgr;-completeness
Information and Computation
The linear time-branching time spectrum (extended abstract)
CONCUR '90 Proceedings on Theories of concurrency : unification and extension: unification and extension
PAM: a process algebra manipulator
Formal Methods in System Design
Communication and Concurrency
A New Strategy for Proving omega-Completeness applied to Process Algebra
CONCUR '90 Proceedings of the Theories of Concurrency: Unification and Extension
Nested semantics over finite trees are equationally hard
Information and Computation
Ready to preorder: get your BCCSP axiomatization for free!
CALCO'07 Proceedings of the 2nd international conference on Algebra and coalgebra in computer science
On finite alphabets and infinite bases II: completed and ready simulation
FOSSACS'06 Proceedings of the 9th European joint conference on Foundations of Software Science and Computation Structures
A finite equational base for CCS with left merge and communication merge
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
A finite basis for failure semantics
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
On finite alphabets and infinite bases III: simulation
CONCUR'06 Proceedings of the 17th international conference on Concurrency Theory
Finite equational bases in process algebra: results and open questions
Processes, Terms and Cycles
Ready to preorder: The case of weak process semantics
Information Processing Letters
A Cancellation Theorem for BCCSP
Fundamenta Informaticae
On Finite Bases for Weak Semantics: Failures Versus Impossible Futures
SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science
Information Processing Letters
Axiomatizing weak ready simulation semantics over BCCSP
ICTAC'11 Proceedings of the 8th international conference on Theoretical aspects of computing
The equational theory of weak complete simulation semantics over BCCSP
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
A Cancellation Theorem for BCCSP
Fundamenta Informaticae
Hi-index | 0.00 |
Van Glabbeek presented the linear time-branching time spectrum of behavioral semantics. He studied these semantics in the setting of the basic process algebra BCCSP, and gave finite, sound and ground-complete, axiomatizations for most of these semantics. Groote proved for some of van Glabbeek's axiomatizations that they are @w-complete, meaning that an equation can be derived if (and only if) all of its closed instantiations can be derived. In this paper, we settle the remaining open questions for all the semantics in the linear time-branching time spectrum, either positively by giving a finite sound and ground-complete axiomatization that is @w-complete, or negatively by proving that such a finite basis for the equational theory does not exist. We prove that in case of a finite alphabet with at least two actions, failure semantics affords a finite basis, while for ready simulation, completed simulation, simulation, possible worlds, ready trace, failure trace and ready semantics, such a finite basis does not exist. Completed simulation semantics also lacks a finite basis in case of an infinite alphabet of actions.