One of computer scientist and Professor Emeritus Vaughan Pratt’s most recent conference papers is on “linear process algebra,” which relates several of his previous interests on linear logic, Chu spaces, concurrent processes, events and states, etc.
The paper opens with a nice overview of computer science research primarily concerned with concurrent processes. Computation itself divides into the aspects of logical and algorithmic, formal methods into the logical and algebraic, concurrent computation into operational and denotational, and then the author gives a brief list of models of processes by a variety of mathematical structures until he comes to his theme of using Chu spaces.
As an example, he presents processes as Chu spaces over the set K, where K = { 0, T, 1, X}, with names and meanings :
- 0: Ready
- T: Transition
- 1: Done
- X: Cancelled
and then details four binary operations as working in Chu spaces over K:
- P ; Q: Sequence
- P + Q: Choice
- P || Q: Concurrence
- P ⊗ Q: Orthocurrence
Further Reading:
Vaughan Pratt / Linear Process Algebra
https://www.researchgate.net/publication/2663060_Chu_Spaces_A_Model_Of_Concurrency
https://www.researchgate.net/publication/222310260_Types_as_Processes_via_Chu_spaces
https://en.wikipedia.org/wiki/Vaughan_Pratt
https://dblp.org/pid/p/VRPratt.html
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