Group multiplier automaton
= Group multiplier automaton
{title2=$M_x$}
A <group multiplier automaton> accepts exactly the <padded convolutions of words> $u\otimes v$ with $u,v\in L$ and $\overline u x=\overline v$. The case $x=\varepsilon$ recognizes equality in the <group>, rather than equality of literal <words over an alphabet>.