Computing the shortest string and the edit-distance for parsing expression languages

H Cheon, YS Han - … Conference on Developments in Language Theory, 2020 - Springer
H Cheon, YS Han
International Conference on Developments in Language Theory, 2020Springer
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 …
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  of a PEG G such that L(G) has a string w of length at most .
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