Further Closure Properties of Input-Driven Pushdown Automata

Abstract

The paper investigates the closure of the language family defined by input-driven pushdown automata (IDPDA) under the following operations: insertion ins(L, K)For K and L recognized by nondeterministic IDPDA, with m and with n states, respectively, insertion requires mn + 2m states, as long as K is well-nested; deletion is representable with 2n states, for well-nested K; square root requires n 3 −O(n 2 ) states, for well-nested L; the well-nested subset of the first half is representable with 2 O(n 2 ) states. Without the well-nestedness constraints, non-closure is established in each case.