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

Authors:
Luca Aceto;David de Frutos Escrig;Carlos Gregorio-Rodríguez;Anna Ingolfsdottir
Affiliations:
ICE-TCS, School of Computer Science, Reykjavik University, Menntavegur 1, IS 101 Reykjavik, Iceland;Departamento de Sistemas Informáticos y Computación, Universidad Complutense de Madrid, Spain;Departamento de Sistemas Informáticos y Computación, Universidad Complutense de Madrid, Spain;ICE-TCS, School of Computer Science, Reykjavik University, Menntavegur 1, IS 101 Reykjavik, Iceland
Venue:
Information Processing Letters
Year:
2011

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Abstract

This note shows that the complete and the ready simulation preorders do not have a finite inequational basis 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.