Edit distance neighbourhoods of input-driven pushdown automata

Alexander Okhotin, Kai Salomaa

Research output

2 Citations (Scopus)

Abstract

Edit distance ℓ-neighbourhood of a formal language is the set of all strings that can be transformed to one of the strings in this language by at most ℓ insertions and deletions. Both the regular and the context-free languages are known to be closed under this operation, whereas the family recognized by deterministic pushdown automata is not. This paper establishes the closure of the family recognized by input-driven pushdown automata (IDPDA), also known as visibly pushdown automata, under the edit distance neighbourhood operation. For an n-state nondeterministic IDPDA with n stack symbols, an automaton for its edit distance ℓ-neighbourhood using O(nℓ+1) states is constructed, and an asymptotically matching lower bound is established. For an n-state deterministic IDPDA, its 1-neighbourhood in the worst case requires a deterministic IDPDA with at least 2Ω(n2) states.

Original languageEnglish
Pages (from-to)417-430
Number of pages14
JournalTheoretical Computer Science
Volume777
DOIs
Publication statusPublished - 19 Jul 2019

Fingerprint

Context free languages
Pushdown Automata
Edit Distance
Formal languages
Strings
Context-free Languages
Formal Languages
Deletion
Insertion
Automata
Closure
Lower bound
Closed

Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

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Edit distance neighbourhoods of input-driven pushdown automata. / Okhotin, Alexander; Salomaa, Kai.

In: Theoretical Computer Science, Vol. 777, 19.07.2019, p. 417-430.

Research output

TY - JOUR

T1 - Edit distance neighbourhoods of input-driven pushdown automata

AU - Okhotin, Alexander

AU - Salomaa, Kai

PY - 2019/7/19

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N2 - Edit distance ℓ-neighbourhood of a formal language is the set of all strings that can be transformed to one of the strings in this language by at most ℓ insertions and deletions. Both the regular and the context-free languages are known to be closed under this operation, whereas the family recognized by deterministic pushdown automata is not. This paper establishes the closure of the family recognized by input-driven pushdown automata (IDPDA), also known as visibly pushdown automata, under the edit distance neighbourhood operation. For an n-state nondeterministic IDPDA with n stack symbols, an automaton for its edit distance ℓ-neighbourhood using O(nℓ+1) states is constructed, and an asymptotically matching lower bound is established. For an n-state deterministic IDPDA, its 1-neighbourhood in the worst case requires a deterministic IDPDA with at least 2Ω(n2) states.

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