Input-Driven Pushdown Automata for Edit Distance Neighborhood.

Edit distance l-neighborhood of a language (sic) is the set of strings that can be obtained by at most l elementary edit operations-deleting or inserting one symbol in the string-from some string in (sic). We show that if (sic) is recognized by a nondeterministic input-driven pushdown automaton (pda) with vertical bar vertical bar Gamma vertical bar pushdown symbols and vertical bar vertical bar Q vertical bar vertical bar states, then its edit distance l-neighborhood can be recognized by a nondeterministic input-driven pda with 2.vertical bar vertical bar Gamma vertical bar vertical bar+1 pushdown symbols and O(vertical bar vertical bar Q vertical bar vertical bar.l vertical bar vertical bar Gamma vertical bar vertical bar(l)) states, which improves the known upper bound. We have obtained also a lower bound, namely, at least (vertical bar vertical bar Q vertical bar vertical bar-1).vertical bar vertical bar Gamma vertical bar vertical bar(l) states are required. If the measure of edit distance includes also the operation of rewriting one symbol with another, the edit distance l-neighborhood can be recognized with 2.vertical bar vertical bar Gamma vertical bar vertical bar+1 pushdown symbols and O(vertical bar vertical bar Q vertical bar vertical bar.l vertical bar vertical bar(Gamma)vertical bar vertical bar(l)) states.