▁a ▁padding ▁symbol . ▁ ▁The ▁concept ▁of ▁an ▁automatic ▁sem igr oup ▁was ▁generalized ▁from ▁automatic ▁groups ▁by ▁Campbell ▁et ▁al . ▁( 2 0 0 1 ) ▁ ▁Un like ▁automatic ▁groups ▁( see ▁Ep stein ▁et ▁al . ▁ 1 9 9 2 ), ▁a ▁sem igr oup ▁may ▁have ▁an ▁automatic ▁structure ▁with ▁respect ▁to ▁one ▁generating ▁set , ▁but ▁not ▁with ▁respect ▁to ▁another . ▁However , ▁if ▁an ▁automatic ▁sem igr oup ▁has ▁an ▁identity , ▁then ▁it ▁has ▁an ▁automatic ▁structure ▁with ▁respect ▁to ▁any ▁generating ▁set ▁( D un can ▁et ▁al . ▁ 1 9 9 9 ). ▁ ▁Dec ision ▁problems ▁ ▁Like ▁automatic ▁groups , ▁automatic ▁sem igr oups ▁have ▁word ▁problem ▁sol v able ▁in ▁quadratic ▁time . ▁K amb ites ▁& ▁Otto ▁( 2 0 0 6 ) ▁showed ▁that ▁it ▁is ▁und ec id able ▁whether ▁an ▁element ▁of ▁an ▁automatic ▁mon oid ▁poss esses ▁a ▁right ▁inverse . ▁ ▁C ain ▁( 2 0 0 6 ) ▁proved ▁that ▁both ▁can cell ativity ▁and ▁left - can cell ativity ▁are ▁und ec id able ▁for ▁automatic ▁sem igr oups . ▁On ▁the ▁other ▁hand , ▁right - can cell ativity ▁is ▁decid able ▁for ▁automatic ▁sem igr oups ▁( Sil va ▁& ▁Stein berg ▁ 2 0 0 4 ). ▁ ▁Ge ometric ▁character ization ▁ ▁Autom atic ▁structures ▁for ▁groups ▁have ▁an ▁elegant ▁geometric ▁character ization ▁called ▁the ▁fellow ▁trav eller ▁property ▁( E p stein ▁et