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).
|Title of host publication||Developments in Language Theory - 24th International Conference, DLT 2020, Proceedings|
|Editors||Nataša Jonoska, Dmytro Savchuk|
|Number of pages||12|
|Publication status||Published - 2020|
|Event||24th International Conference on Developments in Language Theory, DLT 2020 - Tampa, United States|
Duration: 2020 May 11 → 2020 May 15
|Name||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Conference||24th International Conference on Developments in Language Theory, DLT 2020|
|Period||20/5/11 → 20/5/15|
Bibliographical notePublisher Copyright:
© Springer Nature Switzerland AG 2020.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Computer Science(all)