Completed Research Projects

This page describes the status of my research projects in mathematics and computer science completed by 1996.

Branching bisimulation

The concept of branching (bisimulation) equivalence was invented by Peter Weijland and myself as an alternative to Milner's notion of weak (bisimulation) equivalence, also known as observation equivalence. Our findings are reported in the paper(s)
Branching time and abstraction in bisimulation semantics, of which the following versions appeared:
  1. April 1989: an extended abstract (proceedings 1989 IFIP World Computer Congress),
  2. May 1990: Chapter III of my Ph.D. Thesis,
  3. December 1990: A technical report of the TU München (1990) and CWI (1991),
  4. 1996 (written end 1993): Chapter III of the second edition of my Ph.D. Thesis,
  5. 1996: the final version in the JACM.
The first is most suitable as historical reference; the last as standard reference. The full list of inclusions is 1 in 2 in 3 in 4. The introduction, basic definitions, conclusion and references of 5 are also available as hypertext document. The main new results in 4 are listed here, items 16 to 34.

I'm not able to give a complete list of all papers on branching bisimulation here; some of the more fundamental ones are discussed in 5. Besides the above, my own contributions in this area are (included in):

Probabilistic processes

we introduce three models of probabilistic processes, and show how they form a hierarchy. The former paper is properly included in the latter.

Modular specification

The following two papers by Frits Vaandrager and myself propose and apply a modular approach to the algebraic specification of process algebras:
Although the second is a substantial revision of the first, it does not include all its results. The first paper also appears as Chapter II in my Ph.D. Thesis; its main new results are listed here, items 6 to 15.


An interpolation theorem in equational logic Piet Rodenburg and I show that in a natural formulation, Craig's interpolation theorem holds for equational logic. We also discuss the prevalent claims that equational logic does not have the interpolation property.

Differential topology

My contribution to this area is my
master thesis.