TY - GEN

T1 - Computing the Shortest String and the Edit-Distance for Parsing Expression Languages

AU - Cheon, Hyunjoon

AU - Han, Yo Sub

N1 - Publisher Copyright:
© Springer Nature Switzerland AG 2020.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020

Y1 - 2020

N2 - 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).

AB - 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).

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U2 - 10.1007/978-3-030-48516-0_4

DO - 10.1007/978-3-030-48516-0_4

M3 - Conference contribution

AN - SCOPUS:85086181563

SN - 9783030485153

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 43

EP - 54

BT - Developments in Language Theory - 24th International Conference, DLT 2020, Proceedings

A2 - Jonoska, Nataša

A2 - Savchuk, Dmytro

PB - Springer

T2 - 24th International Conference on Developments in Language Theory, DLT 2020

Y2 - 11 May 2020 through 15 May 2020

ER -