  We give some connections between various functions defined on finitely
presented groups (isoperimetric, isodiametric, Todd-Coxeter radius, filling
length functions, etc.), and we study the relation between those functions and
the computational complexity of the word problem (deterministic time,
nondeterministic time, symmetric space). We show that the isoperimetric
function can always be linearly decreased (unless it is the identity map). We
present a new proof of the Double Exponential Inequality, based on context-free
languages.
