by Theo Verelst (of course feel free to comment / correct, pref. with id)
The Process Algebra page gives an idea of that concept, but lacking in it was some indication of the algebraic manipulation that is of interest, and that, of course, is a major reason for the algebraic angle.
Distributiveness, associativeness, substitution of the parallel and serial composition and the restriction operator.
Let's see (sort of like typing while my memory and imagination are working, I should do my library work first, in fact), starting with parallel composition of agents capable of communication with a certain message set and a certain set of state progression orders:
(A | B) | C ^= A | (B | C) ^= A | B | C A | B ^= B ^| A
TV, nope, I tjink I must have or should have typed :
A | B ^= B | A
Parallel composition simply doesn't depend on the algebraic ordering of the defining composition. A | B means the same as B | A: processes A and B are put together in a composition and may communicate with eachother. The ^= I made stand for is defined as
Serial composition:
A ; B != B ; A ( A ; B ) ; C ==> ( A ; C ) && ( B ; C )
Combined:
( A | B ) ; C ==>
Oh boy, still thinking, don't take this for granted, it's been years....