Concurrent Processes and Their Syntax

George Milne, Robin Milner

Research output: Contribution to journalArticlepeer-review


A mathematical model of concurrent computation is presented Starting from synchronized communication as the only primitive notion, a process is defined as a set of communication capabilities. The domain of processes is built using the weak powerdomain construction of Smyth, which evolved from that of Plotkin. A minimal set of operations for composing processes is defined These operations suggest a corresponding minimal syntax -the language of flowgraphs- in which to specify these compositions. The concept of flow algebra is defined, processes and flowgraphs are examples of flow algebras. Elsewhere it will be shown that flowgraphs are free (over a set of generators) in the category of flow algebras, here it is shown that processes are a flow algebra, and therefore constitute a suitable semantics for flowgraphs. However, we emphasize that the notion of flowgraph evolved from the notion of process and not the reverse.
Original languageEnglish
Pages (from-to)302-321
Number of pages20
JournalJournal of the ACM
Issue number2
Publication statusPublished - 1 Apr 1979


  • concurrency
  • parallelism
  • process
  • semantics
  • algebraic semantics
  • communicating processes
  • flow diagrams
  • nondeterminism
  • semantic domains
  • continuous functions


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