Further closure properties of input-driven pushdown automata

Alexander Okhotin, Kai Salomaa

Research output


The paper investigates the closure of the language family defined by input-driven pushdown automata (IDPDA) under the following operations: insertion ins(L,K)={xyz|xz∈L,y∈K}, deletion del(L,K)={xz|xyz∈L,y∈K}, square root L={w|ww∈L}, the first half [Formula presented] and cyclic shift (Figure presented.). For K and L recognized by nondeterministic IDPDA, with m and with n states, respectively, insertion requires exactly mn+2m states, as long as K is well-nested; deletion requires exactly 2n states, for well-nested K; square root requires n3−O(n2) states, for well-nested L; the well-nested subset of the first half is representable with 2O(n2) states; the well-nested subset of the cyclic shift requires exactly 2n2 states. Without the well-nestedness constraints, non-closure is established in each case.

Original languageEnglish
Pages (from-to)65-77
JournalTheoretical Computer Science
Early online date20 May 2019
Publication statusPublished - 17 Dec 2019

Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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