Groote and Luttik (1998a) proved that the extension of the theory pCRL with the axioms for branching bisimulation of Van Glabbeek and Weijland (1996) yields a ground complete axiomatisation of branching bisimulation algebras with data, and conditionals and alternative quantification over these, provided that the data part has built-in equality and built-in Skolem functions. In this paper we shall use this result to obtain ground complete axiomatisations of $eta$-bisimulation algebras, delay bisimulation algebras and weak bisimulation algebras with data, conditionals and alternative quantification over data, under the same proviso as before. Groote and Luttik (1998a) proved that the extension of the theory pCRL with the axioms for branching bisimulation of Van Glabbeek and Weijland (1996) yields a ground complete axiomatisation of branching bisimulation algebras with data, and conditionals and alternative quantification over these, provided that the data part has built-in equality and built-in Skolem functions. In this paper we shall use this result to obtain ground complete axiomatisations of $eta$-bisimulation algebras, delay bisimulation algebras and weak bisimulation algebras with data, conditionals and alternative quantification over data, under the same proviso as before.

Concurrent Programming (acm D.1.3), Models of Computation (acm F.1.1), Mathematical Logic (acm F.4.1)
Other algebras related to logic (msc 03G25), Applications of universal algebra in computer science (msc 08A70), Abstract data types; algebraic specification (msc 68Q65), Algebraic theory of languages and automata (msc 68Q70)
CWI
Software Engineering [SEN]

Luttik, S.P. (1999). Complete axiomatisations of weak-, delay- and $ eta $ -bisimulation for process algebras with alternative quantification over data. Software Engineering [SEN]. CWI.