### Master Project Assignments

Title: mCRL2 with shared variables Description: The process specification language mCRL2 does not have a notion of global variable; parallel components can only communicate by message passing. For many applications, especially when mCRL2 specifications are obtained through translation from another formalism that does have global variables, their absence in mCRL2 is inconvenient. It would therefore be interesting to investigate how a notion of global variable can be added to mCRL2, and what would be the theoretical and practical implications of such an addition.

The assignment would consist of addressing some of the following questions: What are the implications for the process-algebraic semantics of mCRL2 specifications? What are the appropriate notions of behavioural equivalence? How should global variables be used in modal logics for specifying properties of mCRL2 specifications? How would adding a notion of global variable to mCRL2 affect the tools in the mCRL2 toolset.

Title: Process Algebra with Signals Description: There are various proposals in the process-algebraic literature for extending process algebra with a notion of signal [1,2]. In those proposals processes can emit information about their state to other processes without resorting to the message passing paradigm. There are several theoretical open questions pertaining these proposals. For instance, to what extent do the addition of signals increase the expressiveness of the process algebra, and is the equational theory presented in [1] sound and ground-complete for rooted branching bisimilarity. Furthermore, it would be interesting to develop the theory of a process algebra with data and signals. This could serve as a stepping stone towards and extension of mCRL2 with a notion of shared variable.

[1] Jan A. Bergstra and Jos C. M. Baeten. Process Algebra with Propositional Signals. Theoretical Computer Science 177(2):381-405, 1997. [2] Victor Dyseryn, Rob van Glabbeek and Peter Höfner. Analysing Mutual Exclusion using Process Algebra with Signals. In K. Peters and S. Tini (editors): Proceedings of EXPRESS/SOS 2017, pp. 18-34, 2017.