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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].

Planar automaton accepting Le-diagram, alternative tableaux