On Dehn Functions of Finitely Presented Bi-Automatic Monoids

For each automatic monoid the word problem can be solved in quadratic time (Campbell et al 1996), and hence, the Dehn function of a nitely presented automatic monoid is recursive. Here we show that this result on the Dehn function cannot be improved in general by presenting nitely presented bi-automatic monoids the Dehn functions of which realize arbitrary complexity classes that are suuciently rich.