19 research outputs found
On Languages Generated by Signed Grammars
We consider languages defined by signed grammars which are similar to
context-free grammars except productions with signs associated to them are
allowed. As a consequence, the words generated also have signs. We use the
structure of the formal series of yields of all derivation trees over such a
grammar as a method of specifying a formal language and study properties of the
resulting family of languages.Comment: In Proceedings NCMA 2023, arXiv:2309.0733
New Analytic Techniques for Proving the Inherent Ambiguity of Context-Free Languages
International audienceThis 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