Planar automaton accepting Le-diagram, alternative tableaux

Abstract

Here we focus on the construction of the planar automatons accepting two types of tableaux, namely, Le-diagrams
and alternative tableaux. Then we associate a quadratic algebra Q with the constructed planar automaton and
then by redefining the transition function by giving distinct labeling for distinct terms of the rewriting rule we get
Q-tableaux. Finally, we give the proof of the equivalence between the tableaux accepting a planar automaton
and Q-tableaux obtained, where the equivalence is given by Xavier Viennot in [8].