eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2022-12-14
41:1
41:22
10.4230/LIPIcs.FSTTCS.2022.41
article
New Analytic Techniques for Proving the Inherent Ambiguity of Context-Free Languages
Koechlin, Florent
1
Université de Lorraine, CNRS, Inria, LORIA, F-54000 Nancy, France
This article extends the work of Flajolet [Philippe Flajolet, 1987] on the relation between generating series and inherent ambiguity. We first propose an analytic criterion to prove the infinite inherent ambiguity of some context-free languages, and apply it to give a purely combinatorial proof of the infinite ambiguity of Shamir’s language. Then we show how Ginsburg and Ullian’s criterion on unambiguous bounded languages translates into a useful criterion on generating series, which generalises and simplifies the proof of the recent criterion of Makarov [Vladislav Makarov, 2021]. We then propose a new criterion based on generating series to prove the inherent ambiguity of languages with interlacing patterns, like {a^nb^ma^pb^q | n≠p or m≠q, with n,m,p,q ∈ ℕ^*}. We illustrate the applicability of these two criteria on many examples.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol250-fsttcs2022/LIPIcs.FSTTCS.2022.41/LIPIcs.FSTTCS.2022.41.pdf
Inherent ambiguity
Infinite ambiguity
Ambiguity
Generating series
Context-free languages
Bounded languages