Automatic structure for a group
= Automatic structure for a group
{title2=$(A,L)$}
An <automatic structure for a group> consists of a finite generating <alphabet> $A$, a surjective representative <regular language> $L\subseteq A^*$, and <finite-state automata> accepting the <padded convolutions of words> $(u,v)$ in $L$ satisfying $\overline u x=\overline v$ for each $x\in A\cup\{\varepsilon\}$. Symmetry of $A$ and uniqueness of representatives are additional conditions, not part of this definition.