Normal-order reduction grammars

Normal-order reduction grammars

We present an algorithm which, for given n, generates an unambiguous regular tree grammar defining the set of combinatory logic terms, over the set {S,K} of primitive combinators, requiring exactly n normal-order reduction steps to normalize. As a consequence of Curry and Feys’s standardization theorem, our reduction grammars form a complete syntactic characterization of normalizing combinatory...

Second-Order Simple Grammars

Second-Order Abstract Categorial Grammars as Hyperedge Replacement Grammars

Second-order abstract categorial grammars (de Groote 2001) and hyperedge replacement grammars (see Engelfriet 1997) are two natural ways of generalizing “context-free” grammar formalisms for string and tree languages. It is known that the string generating power of both formalisms is equivalent to (non-erasing) multiple context-free grammars (Seki et al. 1991) or linear context-free rewriting s...

Marciani Normal Form of context-free grammars

In this paper, we prove the semidecidability of the problem of saying whether or not a context-free grammar generates a regular language. We introduce the notion of contextfree grammar in Marciani Normal Form. We prove that a context-free grammar in Marciani Normal Form always generates a regular language. CCS Concepts •Theory of computation → Grammars and contextfree languages;

Order and Optionality: Minimalist Grammars with Adjunction

Adjuncts are characteristically optional, but many, such as adverbs and adjectives, are strictly ordered. In Minimalist Grammars (MGs), it is straightforward to account for optionality or ordering, but not both. I present an extension of MGs, MGs with Adjunction, which accounts for optionality and ordering simply by keeping track of two pieces of information at once: the original category of th...