Probability and Nondeterminism
 Aim: The goal of this project is to build a theory of processes that faithfully integrates probabilities and nondeterminism.

Context:
A satisfactory semantic theory for processes which encompass both nondeterministic and
probabilistic behaviour has been a longstanding research problem.
Such a theory is indispensable for the successful modelling, analysis and verification of systems
where the interplay of probability and nondeterminism plays an essential role.
In 1992 Wang & Larsen posed the problems of finding complete axiomatisations and alternative characterisations for a natural generalisation of the standard testing preorders to such processes. Recently, we solved both for finite processes, by providing a detailed account of both may and must testing preorders for a finite version of the process calculus CSP extended with probabilistic choice. Further work deals with infinite processes, and generalisations to other testing disciplines, such as reward testing.  Approach: We bring together techniques from process algebra, Markov decision processes and Euclidean geometry (e.g. separating hyperplane lemmas).
 Collaboration: Shanghai Jiao Tong University, Trinity College Dublin.
People
Past

Publications
2019
Rob van Glabbeek, Jan Friso Groote and Erik de Vink A complete axiomatization of branching bisimilarity for a simple process language with probabilistic choice The Art of Modelling Computational Systems: A Journey from Logic and Concurrency to Security and Privacy — Essays Dedicated to Catuscia Palamidessi on the Occasion of Her 60th Birthday, pp. 139162, Paris, November, 2019  
Carroll Morgan, Annabelle McIver and Tahiry Rabehaja Abstract hidden markov models: A monadic account of quantitative information flow Mathematical Structures in Computer Science, Volume 15, Issue 1, pp. 36:136:50, March, 2019  
Nick Fischer and Rob van Glabbeek Axiomatising infinitary probabilistic weak bisimilarity of finitestate behaviours Journal of Logical and Algebraic Methods in Programming, Volume 102, pp. 64102, January, 2019 
2018
Annabelle McIver, Carroll Morgan, Benjamin Kaminski and JoostPieter Katoen A new proof rule for almostsure termination ACM SIGPLANSIGACT Symposium on Principles of Programming Languages, Los Angeles, January, 2018 
2014
Yuxin Deng, Rob van Glabbeek, Matthew Hennessy and Carroll Morgan Real reward testing for probabilistic processes Theoretical Computer Science, Volume 538, pp. 16–36, July, 2014 
2011
Yuxin Deng, Rob van Glabbeek, Matthew Hennessy and Carroll Morgan Real reward testing for probabilistic processes (extended abstract) Ninth Workshop on Quantitative Aspects of Programming Languages (QAPL 2011), pp. 61–73, Saarbrücken, Germany, July, 2011 
2010
2009
Yuxin Deng, Rob van Glabbeek, Matthew Hennessy and Carroll Morgan Testing finitary probabilistic processes (extended abstract) Proceedings of the 20th International Conference on Concurrency Theory (CONCUR), pp. 274–288, Bologna, Italy, August, 2009 
2008
Yuxin Deng, Rob van Glabbeek, Matthew Hennessy and Carroll Morgan Characterising testing preorders for finite probabilistic processes Logical Methods in Computer Science, Volume 4, Number 4, pp. 1–33, October, 2008 
2007
Yuxin Deng, Rob van Glabbeek, Matthew Hennessy, Carroll Morgan and Cuicui Zhang Characterising testing preorders for finite probabilistic processes Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science, pp. 313–322, Wroclaw, Poland, July, 2007  
Yuxin Deng, Rob van Glabbeek, Matthew Hennessy, Carroll Morgan and Cuicui Zhang Remarks on testing probabilistic processes Electronic Notes in Theoretical Computer Science, Volume 172, Number , pp. 359–397, April, 2007  
Yuxin Deng, Rob van Glabbeek, Carroll Morgan and Chenyi Zhang Scalar outcomes suffice for finitary probabilistic testing Proceedings of the 16thEuropean Symposium on Programming, pp. 363–378, Braga, Portugal, March, 2007 