Communicating sequential processes
Communicating sequential processes
A complete axiomatisation for observational congruence of finite-state behaviours
Information and Computation
Journal of the ACM (JACM)
The linear time-branching time spectrum (extended abstract)
CONCUR '90 Proceedings on Theories of concurrency : unification and extension: unification and extension
Iteration theories: the equational logic of iterative processes
Iteration theories: the equational logic of iterative processes
A completeness theorem for Kleene algebras and the algebra of regular events
Papers presented at the IEEE symposium on Logic in computer science
A complete equational axiomatization for prefix iteration
Information Processing Letters
A complete axiomatization of timed bisimulation for a class of timed regular behaviours
Theoretical Computer Science
Communication and Concurrency
Process Algebra with Timing
An Asynchronous Algebra with Multiple Clocks
ESOP '94 Proceedings of the 5th European Symposium on Programming: Programming Languages and Systems
A Complete Axiomatization for Branching Bisimulation Congruence of Finite-State Behaviours
MFCS '93 Proceedings of the 18th International Symposium on Mathematical Foundations of Computer Science
Iteration Algebras Are Not Finitely Axiomatizable. Extended Abstract
LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
An Algebraic Theory of Multiple Clocks
CONCUR '97 Proceedings of the 8th International Conference on Concurrency Theory
The Equational Theory of Fixed Points with Applications to Generalized Language Theory
DLT '01 Revised Papers from the 5th International Conference on Developments in Language Theory
On the axiomatizability of priority
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
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
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It is well known that bisimulation on µ-expressions cannot be finitely axiomatised in equational logic. Complete axiomatisations such as those of Milner and Bloom/Ésik necessarily involve implicational rules. However, both systems rely on features which go beyond pure equational Horn logic: either the rules are impure by involving nonequational side-conditions, or they are schematically infinitary like the congruence rule which is not Horn. It is an open question whether these complications cannot be avoided in the proof-theoretically and computationally clean and powerful setting of second-order equational Horn logic. This paper presents a positive and a negative result regarding axiomatisability of observational congruence in equational Horn logic. Firstly, we show how Milner's impure rule system can be reworked into a pure Horn axiomatisation that is complete for guarded processes. Secondly, we prove that for unguarded processes, both Milner's and Bloom/Ésik's axiomatisations are incomplete without the congruence rule, and neither system has a complete extension in rank 1 equational axioms. It remains open whether there are higher-rank equational axioms or Horn rules which would render Milner's or Bloom/Ésik's axiomatisations complete for unguarded processes.