Abstract
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.