mCRL2: Are there process algebras in our brain?
When Cool Runnings had its one year birthday recently, we took time to reflect on what kind of sites we had come to particularly value. They had to do with neuroscience, of course, and when possible, with consciousness science. But Cool Runnings has seemed to move inexorably into the world of MIND TOOLS – conceptual, visual and mathematical. Furthermore, the tools we have come to cherish most are:
- Simple to use
In the last Cool Runnings we reviewed a basic, interactive set of Java applets to get the novice going with networks, and provide a glance for others with varying degrees of familiarity.
Network analysis has morphed in its short lifetime into studying how networks communicate with one another, a topic in mathematics called higher-dimensional or process algebras. As Ronald Brown and Timothy Porter note in a classic paper:
Higher Dimensional Algebra has already shown its use in models of information management, and in concurrency. Descriptions of systems by graphs are well known, with development described algebraically by paths in graphs. Interacting systems need higher dimensional graphs, and a generalization of the notion of path. Higher Dimensional Algebra is still young, and there are many new possibilities opened up, as a web search shows.[i]
The site developed by the department of Mathematics and Computer Science of the Technische Universiteit Eindhoven, in collaboration with LaQuSo, CWI and the University of Twente has given all webbies mCRL2. Below, you can see some examples of what you can do with this tool.
From the web site:
mCRL2 is a formal specification language with an associated toolset. The toolset can be used for modeling, validation and verification of concurrent systems and protocols. It can be run on Windows, Linux, Apple Mac OS X and FreeBSD.
The toolset supports a collection of tools for linearization, simulation, state-space exploration and generation and tools to optimize and analyze specifications. Moreover, state spaces can be manipulated, visualized and analyzed.
Visualisation of clusters of states as a graph
Visualisation of a directed graph using automatic positioning
In neuroscience, process algebras are being used to develop formal models of decision making, problem solving, object identification, concept establishment, categorization, comparison, qualification, quantification, selection, search and attentional capture.
Make room in your tool kit!
[i] Ronald Brown Timothy Porter 2013 (revised) Category theory and higher dimensional algebra: potential descriptive tools in neuroscience International Conference on Theoretical Neurobiology Delhi 2003