We establish that several classical context-free languages are inherently ambiguous by proving that their counting generating functions, when considered as analytic functions, exhibit some characteristic form of transcendental behaviour. To that purpose, we survey some general results on elementary analytic properties and enumerative uses of algebraic functions in relation to formal languages. ...

The problem of inferring an agent’s intentions from her spatio-temporal behavior is called mobile intention recognition problem. Using formal grammars we can state these problems as parsing problems. We argue that context-free formalisms are not sufficient for important use cases. We introduce Spatially Constrained Tree-Adjoining Grammars which enrich TAGs with knowledge about the structure of ...

We consider the question “How much strong generative power can be squeezed out of a formal system without increasing its weak generative power?” and propose some theoretical and practical constraints on this problem. We then introduce a formalism which, under these constraints, maximally squeezes strong generative power out of context-free grammar. Finally, we generalize this result to formalis...

We present an algorithm for learning context free grammars from positive structural examples (unlabeled parse trees). The algorithm receives a parameter in the form of a finite set of structures and the class of languages learnable by the algorithm depends on this parameter. Every context free language belongs to many such learnable classes. A second part of the algorithm is then used to determ...

The theorem stating that the family of frontiers of recognizable tree languages is exactly the family of context-free languages (see J. Mezei and J. B. Wright, 1967, Inform. and Comput. 11, 3 29), is a basic result in the theory of formal languages. In this article, we prove a similar result: the family of frontiers of recognizable picture languages is exactly the family of context-sensitive la...

The purposes of this paper is to give simple new proofs of some interesting recent results about the relative succinctness of different representations of regular, deterministic and unambiguous context-free languages and to derive some new results about how the relative succinctness of representations change when the representations contain a formal proof that the languages generated are in the...

We consider several novel aspects of unique factorization in formal languages. We reprove the familiar fact that the set uf(L) of words having unique factorization into elements of L is regular if L is regular, and from this deduce an quadratic upper and lower bound on the length of the shortest word not in uf(L). We observe that uf(L) need not be context-free if L is context-free. Next, we con...

The aim of this paper is to elaborate the power of cooperation in generating and analysing (handwritten) characters by array grammars. We present various non-context-free sets of arrays that can be generated in a simple way by cooperating distributed array grammar systems with prescribed teams working in diierent modes and show the power of the mechanism of cooperation for picture description a...

We investigate Global Index Grammars (GIGs), a grammar formalism that uses a stack of indices associated with productions and has restricted context-sensitive power. We discuss some of the structural descriptions that GIGs can generate compared with those generated by LIGs. We show also how GIGs can represent structural descriptions corresponding to HPSGs (Pollard and Sag, 1994) schemas.

By introducing a new operation, the exponentiation of formal languages, we can define Heyting algebras of formal languages. It turns out that some well known families of languages are closed under this exponentiation, e. g., the families of regular and of context-sensitive languages.