Restarting automata for insertion languages

Restarting automaton is a type of regulated rewriting system, introduced as a model for analysis by reduction. It is linguistically motivated method for checking correctness of a sentence. In this paper, we introduce a new definition of normal restarting automaton, called 1-normal DRA in which only one substring can be removed using DEL operation in a cycle. This DEL operation is used to reverse the insertion of an insertion rule in an insertion grammar. We use this 1-normal restarting automaton to solve the membership problem of insertion languages. Also the comparison of the power of 1-normal DRA and clearing restarting automaton is addressed in this paper.