Further Closure Properties of Input-Driven Pushdown Automata

  • Alexander Okhotin
  • Kai SalomaaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10952)


The paper investigates the closure of the language family defined by input-driven pushdown automata (IDPDA) under the following operations: insertion \(ins(L, K)=\{xyz \mid xz \in L, \, y \in K\}\), deletion \(del(L, K)=\{xz \mid xyz \in L, \, y \in K\}\), square root \(\sqrt{L}=\{w \mid ww \in L\}\), and the first half \(\frac{1}{2}L=\{u \mid \exists v: |u|=|v|, \, uv \in L\}\). 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.


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© IFIP International Federation for Information Processing 2018

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySaint PetersburgRussia
  2. 2.School of ComputingQueen’s UniversityKingstonCanada

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