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

From indexed grammars to generating functions

We extend the Chomsky/Sch\"utzenberger method of computing the growth series of an unambiguous context-free language to the larger class of indexed languages. We illustrate the technique with numerous examples.Comment: 23 pages, 3 figure

Relationships Between Bounded Languages, Counter Machines, Finite-Index Grammars, Ambiguity, and Commutative Equivalence

It is shown that for every language family that is a trio containing only semilinear languages, all bounded languages in it can be accepted by one-way deterministic reversal-bounded multicounter machines (DCM). This implies that for every semilinear trio (where these properties are effective), it is possible to decide containment, equivalence, and disjointness concerning its bounded languages. A condition is also provided for when the bounded languages in a semilinear trio coincide exactly with those accepted by DCM machines, and it is used to show that many grammar systems of finite index — such as finite-index matrix grammars (Mfin) and finite-index ET0L (ET0Lfin) — have identical bounded languages as DCM. Then connections between ambiguity, counting regularity, and commutative regularity are made, as many machines and grammars that are unambiguous can only generate/accept counting regular or com- mutatively regular languages. Thus, such a system that can generate/accept a non-counting regular or non-commutatively regular language implies the existence of inherently ambiguous languages over that system. In addition, it is shown that every language generated by an unambiguous Mfin has a rational char- acteristic series in commutative variables, and is counting regular. This result plus the connections are used to demonstrate that the grammar systems Mfin and ET0Lfin can generate inherently ambiguous languages (over their grammars), as do several machine models. It is also shown that all bounded languages generated by these two grammar systems (those in any semilinear trio) can be generated unambiguously within the systems. Finally, conditions on Mfin and ET0Lfin languages implying commutative regularity are obtained. In particular, it is shown that every finite-index ED0L language is commutatively regular

External versus internal possessor structures and inalienability in Russian

This study deals with the choice between two external possessor structures in Russian: the possessive dative and the U + genitive PP. Is shows that this choice is primarily related to the thematic role of the possessor adjunct, which can vary with the same verb: the possessive dative presents it as a goal or as an experiencer, while the U-construction views it as a source or a location. Two general conclusions can be drawn from this study: - Russian views the possessive relation through its relationship with space. - Russian external possessor structures reflect two different delimitations of inalienable possession, one restricted to animate referents for the dative and one extended to a wide range of possessive relations including inanimate referents for the U-construction

A microparametric approach on goal of motion constructions : properties of adpositional systems in Romance and Germanic

This paper explores the idea that the properties of adpositional systems can suffice to explain the Talmian distinction between satellite and verb framed languages. Following the insight that morphological simple prepositions in Romance languages are only locative, I propose that the functional domain of the directional/path preposition is defective and, hence, has to be licensed via incorporation to the (motion) verb. Prepositional incorporation, understood as head movement, prevents manner incorporation, as a particular case of Kayne's (1994) condition on adjunction. The paper offers an account for Talmian lexicalization patterns from a non lexicalist perspective, reducing typological differences between languages to specific properties within the functional domain of lexical heads.Aquest article explora la idea que les propietats dels sistemes adpositionals poden ser suficients per a explicar la distinció de Talmy entre llengües de marc satèl·lit i de marc verbal. Seguint la idea que les preposicions morfològicament simples en llengües romàniques només són locatives, pro- poso que el domini funcional de la preposició direccional/de trajecte és defectiu i, doncs, ha de ser legitimat per incorporació al verb (de moviment). La incorporació de la preposició, entesa com a trasllat de nucli, impedeix la incorporació de manera, com a cas particular de la condició d'adjunció de Kayne's (1994). Aquest article ofereix una explicació dels patrons de lexicalització de Talmy des d'una perspectiva no lexicalista, i redueix les diferències tipològiques entre les llengües a propietats específiques dins el domini funcional dels nuclis lèxics