Parikh's Theorem: A simple and direct automaton construction

Parikh's theorem states that the Parikh image of a context-free language is semilinear or, equivalently, that every context-free language has the same Parikh image as some regular language. We present a very simple construction that, given a context-free grammar, produces a finite automaton recognizing such a regular language.Comment: 12 pages, 3 figure

Towards Robustness in Parsing - Fuzzifying Context-Free Language Recognition

We discuss the concept of robustness with respect to parsing a context-free language. Our approach is based on the notions of fuzzy language, (generalized) fuzzy context-free grammar and parser / recognizer for fuzzy languages. As concrete examples we consider a robust version of Cocke-Younger-Kasami's algorithm and a robust kind of recursive descent recognizer

Multiple Context-Free Tree Grammars: Lexicalization and Characterization

Multiple (simple) context-free tree grammars are investigated, where "simple" means "linear and nondeleting". Every multiple context-free tree grammar that is finitely ambiguous can be lexicalized; i.e., it can be transformed into an equivalent one (generating the same tree language) in which each rule of the grammar contains a lexical symbol. Due to this transformation, the rank of the nonterminals increases at most by 1, and the multiplicity (or fan-out) of the grammar increases at most by the maximal rank of the lexical symbols; in particular, the multiplicity does not increase when all lexical symbols have rank 0. Multiple context-free tree grammars have the same tree generating power as multi-component tree adjoining grammars (provided the latter can use a root-marker). Moreover, every multi-component tree adjoining grammar that is finitely ambiguous can be lexicalized. Multiple context-free tree grammars have the same string generating power as multiple context-free (string) grammars and polynomial time parsing algorithms. A tree language can be generated by a multiple context-free tree grammar if and only if it is the image of a regular tree language under a deterministic finite-copying macro tree transducer. Multiple context-free tree grammars can be used as a synchronous translation device.Comment: 78 pages, 13 figure

Controlled Rewriting Using Productions and Reductions

We investigate context-free grammars the rules of which can be used in a productive and in a reductive fashion, while the application of these rules is controlled by a regular language. We distinguish several modes of derivation for this kind of grammar. The resulting language families (properly) extend the family of context-free languages. We establish some closure properties of these language families and some grammatical transformations which yield a few normal forms for this type of grammar. Finally, we consider some special cases (viz. the context-free grammar is linear or left-linear), and generalizations, in particular, the use of arbitrary rather than regular control languages