previous up next
Go backward to Reachability
Go up to Top
Go forward to Composition of Relations
RISC-Linz logo

Composition of Relations

Let R and S be binary relations on Nn for some n in N.

The composition of R and S is

R o S = {<a, c>: a in Nn /\  c in Nn /\ 
   (exists b: <a, b> in R /\  <b, c> in S)}.

For the corresponding adjacency matrix, we thus have

forall i in Nn, j in Nn:
   adjacency(<Nn, R o S>)i, j = true <=>
      exists k in Nn: Ai, k = true /\  Bk, j = true
      where A = adjacency(<Nn, R>), B = adjacency(<Nn, S>).

Author: Wolfgang Schreiner
Last Modification: January 26, 2000

previous up next