Computing the Shortest String and the Edit-Distance for Parsing Expression Languages

Hyunjoon Cheon, Yo Sub Han

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

A distance between two languages is a useful tool to measure the language similarity, and is closely related to the intersection problem as well as the shortest string problem. A parsing expression grammar (PEG) is an unambiguous grammar such that the choice operator selects the first matching in PEG while it can be ambiguous in a context-free grammar. PEGs are also closely related to top-down parsing languages. We consider two problems on parsing expression languages (PELs). One is the r-shortest string problem that decides whether or not a given PEL contains a string of length shorter than r. The other problem is the edit-distance problem of PELs with respect to other language families such as finite languages or regular languages. We show that the r-shortest string problem and the edit-distance problem with respect to finite languages are NEXPTIME-complete, and the edit-distance problem with respect to regular languages is undecidable. In addition, we prove that it is impossible to compute a length bound B(G) of a PEG G such that L(G) has a string w of length at most B(G).

Original languageEnglish
Title of host publicationDevelopments in Language Theory - 24th International Conference, DLT 2020, Proceedings
EditorsNataša Jonoska, Dmytro Savchuk
PublisherSpringer
Pages43-54
Number of pages12
ISBN (Print)9783030485153
DOIs
Publication statusPublished - 2020
Event24th International Conference on Developments in Language Theory, DLT 2020 - Tampa, United States
Duration: 2020 May 112020 May 15

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12086 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference24th International Conference on Developments in Language Theory, DLT 2020
CountryUnited States
CityTampa
Period20/5/1120/5/15

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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    Cheon, H., & Han, Y. S. (2020). Computing the Shortest String and the Edit-Distance for Parsing Expression Languages. In N. Jonoska, & D. Savchuk (Eds.), Developments in Language Theory - 24th International Conference, DLT 2020, Proceedings (pp. 43-54). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12086 LNCS). Springer. https://doi.org/10.1007/978-3-030-48516-0_4