Communicating sequential processes
Communicating sequential processes
Specification-oriented semantics for communicating processes
Acta Informatica
Algebraic theory of processes
Independence of the equational axioms for iteration theories
Journal of Computer and System Sciences
The equational theory of pomsets
Theoretical Computer Science
Axiomatising finite concurrent processes
SIAM Journal on Computing
A complete axiomatisation for observational congruence of finite-state behaviours
Information and Computation
Process algebra
Bisimulation through probabilistic testing
Information and Computation
Complete systems of B -rational identities
Theoretical Computer Science
Theoretical Computer Science - Selected papers of the International Colloquium on Words, Languages and Combinatorics, Kyoto, Japan, August 1990
Structured operational semantics and bisimulation as a congruence
Information and Computation
Models of a K-rational identity system
Journal of Computer and System Sciences
Decidability of bisimulation equivalence for process generating context-free languages
Journal of the ACM (JACM)
On "Axiomatising Finite Concurrent Processes"
SIAM Journal on Computing
A completeness theorem for Kleene algebras and the algebra of regular events
Papers presented at the IEEE symposium on Logic in computer science
Selected papers of the second international colloquium on Words, languages and combinatorics
A complete equational axiomatization for prefix iteration
Information Processing Letters
Journal of the ACM (JACM)
Equational properties of Kleene algebras of relations with conversion
Theoretical Computer Science
Axiomatizing prefix iteration with silent steps
Information and Computation
A complete axiomatization for prefix iteration in branching bisimulation
Fundamenta Informaticae
The algebra of communicating processes with empty process
ACP '95 Proceedings from the international workshop on Algebra of communicating processes
Termination modulo equations by abstract commutation with an application to iteration
ACP '95 Proceedings from the international workshop on Algebra of communicating processes
Realization of Events by Logical Nets
Journal of the ACM (JACM)
Two Complete Axiom Systems for the Algebra of Regular Events
Journal of the ACM (JACM)
Formal verification of parallel programs
Communications of the ACM
Communication and Concurrency
A Calculus of Communicating Systems
A Calculus of Communicating Systems
Automata, Languages, and Machines
Automata, Languages, and Machines
A Completeness Theorem fro Nondeterministic Kleene Algebras
MFCS '94 Proceedings of the 19th International Symposium on Mathematical Foundations of Computer Science 1994
An Equational Axiomatization of Observation Congruence for Prefix Iteration
AMAST '96 Proceedings of the 5th International Conference on Algebraic Methodology and Software Technology
On the Completeness of the Euations for the Kleene Star in Bisimulation
AMAST '96 Proceedings of the 5th International Conference on Algebraic Methodology and Software Technology
Action Logic and Pure Induction
JELIA '90 Proceedings of the European Workshop on Logics in AI
The Linear Time-Branching Time Spectrum (Extended Abstract)
CONCUR '90 Proceedings of the Theories of Concurrency: Unification and Extension
The Linear Time - Branching Time Spectrum II
CONCUR '93 Proceedings of the 4th International Conference on Concurrency Theory
Fully Abstract Models for Nondeterministic Regular Expressions
CONCUR '95 Proceedings of the 6th International Conference on Concurrency Theory
Concurrency and Automata on Infinite Sequences
Proceedings of the 5th GI-Conference on Theoretical Computer Science
Full Abstraction in Structural Operational Semantics (Extended Abstract)
AMAST '93 Proceedings of the Third International Conference on Methodology and Software Technology: Algebraic Methodology and Software Technology
Register-machine based processes
Journal of the ACM (JACM)
2-Nested Simulation Is Not Finitely Equationally Axiomatizable
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
Axiomatizing the Least Fixed Point Operation and Binary Supremum
Proceedings of the 14th Annual Conference of the EACSL on Computer Science Logic
The max-plus algebra of the natural numbers has no finite equational basis
Theoretical Computer Science
Precongruence formats for decorated trace semantics
ACM Transactions on Computational Logic (TOCL)
Nested semantics over finite trees are equationally hard
Information and Computation
Bisimilarity is not finitely based over BPA with interrupt
Theoretical Computer Science - Algebra and coalgebra in computer science
A Cancellation Theorem for BCCSP
Fundamenta Informaticae
Ready to preorder: get your BCCSP axiomatization for free!
CALCO'07 Proceedings of the 2nd international conference on Algebra and coalgebra in computer science
A finite basis for failure semantics
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Bisimilarity is not finitely based over BPA with interrupt
CALCO'05 Proceedings of the First international conference on Algebra and Coalgebra in Computer Science
Finite equational bases in process algebra: results and open questions
Processes, Terms and Cycles
A Cancellation Theorem for BCCSP
Fundamenta Informaticae
Hi-index | 0.00 |
Fokkink and Zantema (Fokkink and Zantema 1994) have shown that bisimulation equivalence has a finite equational axiomatization over the language of Basic Process Algebra with the binary Kleene star operation (BPA*). In light of this positive result on the mathematical tractability of bisimulation equivalence over BPA*, a natural question to ask is whether any other (pre)congruence relation in van Glabbeek's linear time/branching time spectrum is finitely (in)equationally axiomatizable over it. In this paper, we prove that, unlike bisimulation equivalence, none of the preorders and equivalences in van Glabbeek's linear time/branching time spectrum, whose discriminating power lies in between that of ready simulation and that of completed traces, has a finite equational axiomatization. This we achieve by exhibiting a family of (in)equivalences that holds in ready simulation semantics (which is the finest semantics that we consider) and whose instances cannot all be proved by means of any finite set of (in)equations that is sound in completed trace semantics (which is the coarsest semantics that is appropriate for the language BPA*). To this end, for every finite collection of (in)equations that are sound in completed trace semantics, we build a model in which some of the (in)equivalences of the family under consideration fail. The construction of the model mimics the one used by Conway (Conway 1971, p. 105) in his proof of a result, originally due to Redko, to the effect that infinitely many equations are needed to axiomatize equality of regular expressions.Our non-finite axiomatizability results apply to the language BPA* over an arbitrary non-empty set of actions. In particular, we show that completed trace equivalence is not finitely based over BPA* even when the set of actions is a singleton. Our proof of this result may be adapted to the standard language of regular expressions to yield a solution to an open problem posed by Salomaa (Salomaa 1969, p. 143).Another semantics that is usually considered in process theory is trace semantics. Trace semantics is, in general, not preserved by sequential composition, and is therefore inappropriate for the language BPA*. We show that, if the set of actions is a singleton, trace equivalence and preorder are preserved by all the operators in the signature of BPA*, and coincide with simulation equivalence and preorder, respectively. In that case, unlike all the other semantics considered in this paper, trace semantics have finite, complete equational axiomatizations over closed terms.