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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)

Abstract

The paper investigates the closure of the language family defined by input-driven pushdown automata (IDPDA) under the following operations: insertion \(ins(L, K)=\{xyz \mid xz \in L, \, y \in K\}\), 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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Copyright information

© 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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