  For insight into the parallel composition for true concurrency, we recall the
axiomatization of the parallel composition modulo truly concurrent behavioral
equivalences as the sidelights of truly concurrent process algebra APTC. We
prove that: (1) There is a finite sound and complete axiomatization of the
parallel composition modulo pomset, step and hp-bisimulations, without any
auxiliary operators. (2) There does not exist a finite sound and complete
axiomatization of the parallel composition modulo hhp-bisimulation, without any
auxiliary operator. (3) There is a finite sound and complete axiomatization of
the parallel composition modulo pomset, step, hp-. and hhp-bisimulations, with
the auxiliary left parallel composition and communication merge.
