P. Sewell, Nonaxiomatisability of equivalences over finite state processes, Annals of Pure and Applied Logic, 90 (1997), pp. 163--191. Home/Search Document Not in Database Summary Related Articles Check |
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2-Nested Simulation is not Finitely Equationally.. - Aceto, Fokkink.. (2000) (Correct)
.... BCCS for most of the other behavioural equivalences in the linear time branching time spectrum that are reviewed by van Glabbeek in [8] Only in the case of additional, more complex operators, such as iteration, are these equivalences known to lack a finite equational axiomatization; see, e.g. [3, 6, 7, 20, 21]. Of special relevance for concurrency theory are Moller s results to the e#ect that the process algebras ACP and CCS (without the auxiliary left merge operator from [5] do not have a finite equational axiomatization modulo bisimulation equivalence [17, 18] Aceto, Esik and Ingolfsdottir [2] ....
P. Sewell, Nonaxiomatisability of equivalences over finite state processes, Annals of Pure and Applied Logic, 90 (1997), pp. 163--191.
Process Algebra with Explicit Termination - Baeten (2000) (Correct)
....= a # x (y z) Note that here we see an advantage of just having prefix iteration. If we add iteration as a binary operator on SPA, where process x # y can iterate the behaviour of x until exiting by doing y, then a complete finite axiomatization cannot be found. This was shown by Sewell [20]. On the other hand, there are extensions of action prefix iteration that still have finite axiomatizations, see e.g. 1, 15] We can look at the combination of prefix iteration and renaming. Here, the axioms we have are definitely not complete, we need the following extra axiom: # f (a # x) ....
P. Sewell. Nonaxiomatisability of equivalences over finite state processes. Annals of Pure and Applied Logic, 90:163--191, 1997.
Process Algebra with Recursive Operations - Bergstra, Fokkink, Ponse (1 citation) (Correct)
....came up with a complete equational axiomatisation including Troeger s axiom. Aceto, Fokkink, and Ing olfsd ottir [4] proved that a whole range of process semantics coarser than strong bisimulation do not allow a finite equational characterisation of the binary Kleene star. Furthermore, Sewell [72] showed that there 5 does not exist a finite equational characterisation of the binary Kleene star modulo strong bisimulation equivalence in the presence of the deadlock ffi, due to the fact that (a k ) ffi is strongly bisimilar to a ffi for positive integers k. Several variations of ....
....3.5 Extensions of BPA (A) The signature of BPA ffi (A) is obtained by extending BPA ffi (A) with BKS. Its axioms are those of BPA (A) and of BPA ffi (A) i.e. A1) A7) in Table 1 for BPA ffi (A) 28 4 AXIOMATISATIONS OF OTHER ITERATIVE OPERATIONS and (BKS1) BKS3) for BKS. Sewell [72] showed that there does not exist a complete equational axiomatisation for BPA ffi (A) modulo strong bisimulation equivalence. This motivates the introduction of the implicational axiom (RSP ) x = yx z x = y z It remains an open question, dating back to Milner [61] whether (A1) A7) ....
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P.M. Sewell. Nonaxiomatisability of equivalences over finite state processes. Annals of Pure and Applied Logic, 90(1/3):163--191, 1997.
Partial-Order Process Algebra (and its Relation to Petri Nets) - Baeten, Basten (2000) (Correct)
....every equality that is valid in the model is also derivable from the axioms of the theory. To the best of our knowledge, it is still an open problem whether the equational theory (ACP # RN RSP # SC) AC, # ) is complete for model M(AC, # ) Note, however, that it follows from the results of [58] that the theory (ACP # RN SC) AC, # ) which is obtained by removing the recursion principle RSP # , is not complete for M(AC, # ) Interleaving process algebra In the previous subsection, it has been defined when an equational theory can be characterized as an interleaving theory. As ....
P. Sewell. Nonaxiomatisability of Equivalences over Finite State Processes. Annals of Pure and Applied Logic, 90(1--3):163--191, 1997.
Some of My Favourite Results in Classic Process Algebra - Aceto (2003) (Correct)
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P. Sewell, Nonaxiomatisability of equivalences over finite state processes, Annals of Pure and Applied Logic, 90 (1997), pp. 163--191.
Nested Semantics over Finite Trees are Equationally Hard - Aceto, Fokkink, van.. (2003) (Correct)
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P. SEWELL, Nonaxiomatisability of equivalences over finite state processes, Annals of Pure and Applied Logic, 90 (1997), pp. 163--191.
2-Nested Simulation is not Finitely Equationally Axiomatizable - Aceto, al. (2000) (Correct)
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P. Sewell, Nonaxiomatisability of equivalences over finite state processes, Annals of Pure and Applied Logic, 90 (1997), pp. 163--191.
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