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Complete and ready simulation semantics are not finitely based over BCCSP, even with a singleton alphabet$
 

Summary: Complete and ready simulation semantics are not finitely based over
BCCSP, even with a singleton alphabet$
Luca Acetoa,, David de Frutos Escrigb, Carlos Gregorio-RodrŽiguezb, Anna Ingolfsdottira
aICE-TCS, School of Computer Science, Reykjavik University, Menntavegur 1, IS 101 Reykjavik, Iceland
bDepartamento de Sistemas InformŽaticos y ComputaciŽon, Universidad Complutense de Madrid, Spain
Abstract
This note shows that the complete and the ready simulation preorders do not have a finite inequational ba-
sis over the language BCCSP when the set of actions is a singleton. Moreover, the equivalences induced by
those preorders do not have a finite (in)equational axiomatization either. These results are in contrast with
a claim of finite axiomatizability for those semantics in the literature, which was based on the erroneous
assumption that they coincide with complete trace semantics in the presence of a singleton set of actions.
Keywords: Concurrency, process algebra, complete simulation, ready simulation, equational logic,
non-finitely based algebras
1. Introduction
Since the seminal work by Hennessy and Mil-
ner, eventually published in [12], the search for
(in)equational axiomatizations of notions of be-
havioural semantics for fragments of process al-
gebras has been one of the classic topics of inves-
tigation within concurrency theory. A complete

  

Source: Aceto, Luca - School of Computer Science, Reykjavík University

 

Collections: Mathematics; Computer Technologies and Information Sciences