A CKY parser for picture grammars

We study the complexity of the membership or parsing problem for pictures generated by a family of picture grammars: Siromoney's Context-Free Kolam Array grammars (coincident with Matz's context-free picture grammars). We describe a new parsing algorithm, which extends the Cocke, Kasami and Younger's classical parsing technique for string languages and preserves the polynomial time complexity.     

Abstract families of context-free grammars

An abstract family of grammars (AFG) may be defined as a class of grammars for which the corresponding class of languages forms an abstract family of languages (AFL) as defined by Ginsburg and Greibach. The derivation bounded grammars of Ginsburg and Spanier is an example of an AFG which is properly included in the class of all context-free grammars (also AFG). The main result is that there exist two distinct infinite hierarchies of AFG which exhaust the derivation bounded AFG such that the AFL associated with the kth member of one of these AFG hierarchies is properly included in the AFL associated with the k-lst member of that same hierarchy. Each hierarchy is shown to be strongly incomparable to the other; that is, the first member of each generates some language not generated by a fixed but arbitrary member of the other. We designate these hierarchies as the hierarchies of left and right dominant grammars (languages)     

Attribute grammars in constraint-based graphics systems

A constraint-based graphics system provides a flexible, intuitive framework for describing relationships among graphical objects in applications such as document preparation, fount design and solid modelling. This paper describes two constraint-based graphics systems, micro-COSM and the IDEAL Synthesizer, and their implementation in terms of attribute grammars. Our experiences with attribute grammars suggest that they provide a powerful framework for representing constraints and extracting important semantic information such as the equations to be solved by the constraint solver. We discuss the advantages of using attribute grammars in constraint-based graphics and from our experiences make several observations about the way attribute grammars should be used.     

COCOVILA – Compiler-Compiler for Visual Languages

A compiler-compiler for visual languages is presented. It has been designed as a framework for building visual programming environments that translate schemas into textual representation as well as into programs representing the deep meaning of schemas. The deep semantics is implemented by applying attribute grammars to schema languages; attribute dependencies are implemented as methods of Java classes. Unlike compiler-compilers of textual languages, a large part of the framework is needed for support of interactive usage of a visual language.     

Stochastic Inference of Regular Tree Languages

We generalize a former algorithm for regular language identification from stochastic samples to the case of tree languages. It can also be used to identify context-free languages when structural information about the strings is available. The procedure identifies equivalent subtrees in the sample and outputs the hypothesis in linear time with the number of examples. The results are evaluated with a method that computes efficiently the relative entropy between the target grammar and the inferred one.     

Lower bounds for context-free grammars

Ellul, Krawetz, Shallit and Wang prove an exponential lower bound on the size of any context-free grammar generating the language of all permutations over some alphabet. We generalize their method and obtain exponential lower bounds for many other languages, among them the set of all squares of given length, and the set of all words containing each symbol at most twice.     

Highly Constrained Unification Grammars

Unification grammars are widely accepted as an expressive means for describing the structure of natural languages. In general, the recognition problem is undecidable for unification grammars. Even with restricted variants of the formalism, off-line parsable grammars, the problem is computationally hard. We present two natural constraints on unification grammars which limit their expressivity and allow for efficient processing. We first show that non-reentrant unification grammars generate exactly the class of context-free languages. We then relax the constraint and show that one-reentrant unification grammars generate exactly the class of mildly context-sensitive languages. We thus relate the commonly used and linguistically motivated formalism of unification grammars to more restricted, computationally tractable classes of languages.     

The complexity of the membership problem for some extensions of context-free languagest†

The time and tape complexity of some families of languages defined in the literature by altering methods of generation by context-free grammars is considered. Specifically; it is shown that the following families of languages can be recognized by deterministic multitape Turing machines either in polynomial time or within (log n)² tape:

1) the context independent developmental (EOL) languages;

2) the simple matrix languages;

3) the languages generated by derivation restricted state grammars.:

4) the languages generated by linear context-free grammars with certain non-regular control sets;

5) the languages generated by certain classes of vector grammars.

In fact, these languages are of the same tape complexity as context-free languages. Other results indicate the complexity of EDOL languages and the effects on complexity of applying the homomorphic replication operator to regular and context-free languages.