  The study of word hyperbolic groups is a prominent topic in geometric group
theory; however word hyperbolic groups are defined by a geometric condition
which does not extend naturally to semigroups. We propose a linguistic
definition. Roughly speaking a semigroup is word hyperbolic if its
multiplication table is a context free language. For groups this definition is
equivalent to the original geometric one. We also briefly consider word
problems of semigroups.
