= Combing
{synonym}

Choose a finite symmetric generating alphabet $\Sigma$ and one word $\sigma(g)$ representing each group element, with $\sigma(1)$ the empty word. The associated <paths> in the <Cayley graph> start at the identity and traverse one edge per unit time, remaining at their endpoint after completion. A synchronous <combing> has a constant $K$ such that <paths> to adjacent endpoints stay within $K$ at equal times. An asynchronous version permits increasing reparametrizations. The <formal language> need not be a <regular language>; regular synchronous representative languages define <automatic groups>.


 Combing of a group (source code)