Show that the following definition is equivalent to the definition of strong bisimulation (see Definition 8.6): R is a strong bisimulation if pRq implies a) for all n and for all a1,...,an ∈ Act, p...

Show that the following definition is equivalent to the definition of strong

bisimulation (see Definition 8.6):

R is a strong bisimulation if pRq implies

a) for all n and for all a1,...,an ∈ Act,

p −→a1,...,an p

′ ⇒ ∃q

′

| q −→a1,...,an q

′ and p′Rq′

b) for all n and for all a1,...,an ∈ Act,

q −→a1,...,an q

′ ⇒ ∃p

′

| p −→a1,...,an p

′ and p′Rq′

where p −→a1,...,an p

′ denotes a sequence of transitions from p to p

′

labelled

by the actions a1,...,an.