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Communication Dans Un Congrès Année : 2022

New Analytic Techniques for Proving the Inherent Ambiguity of Context-Free Languages

Résumé

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.
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Dates et versions

hal-03944635 , version 1 (18-01-2023)

Identifiants

Citer

Florent Koechlin. New Analytic Techniques for Proving the Inherent Ambiguity of Context-Free Languages. Foundations of Software Technology and Theoretical Computer Science (FSTTCS), Dec 2022, Chennai, India. pp.10.4230/LIPIcs.FSTTCS.2022, ⟨10.4230/LIPIcs.FSTTCS.2022.41⟩. ⟨hal-03944635⟩
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