The equivalence of four extensions of context-free grammars

There is currently considerable interest among computational linguists in grammatical formalisms with highly restricted generative power. This paper concerns the relationship between the class of string languages generated by several such formalisms, namely, combinatory categorial grammars, head grammars, linear indexed grammars, and tree adjoining grammars. Each of these formalisms is known to generate a larger class of languages than context-free grammars. The four formalisms under consideration were developed independently and appear superficially to be quite different from one another. The result presented in this paper is that all four of the formalisms under consideration generate exactly the same class of string languages

Graph Interpolation Grammars as Context-Free Automata

A derivation step in a Graph Interpolation Grammar has the effect of scanning an input token. This feature, which aims at emulating the incrementality of the natural parser, restricts the formal power of GIGs. This contrasts with the fact that the derivation mechanism involves a context-sensitive device similar to tree adjunction in TAGs. The combined effect of input-driven derivation and restricted context-sensitiveness would be conceivably unfortunate if it turned out that Graph Interpolation Languages did not subsume Context Free Languages while being partially context-sensitive. This report sets about examining relations between CFGs and GIGs, and shows that GILs are a proper superclass of CFLs. It also brings out a strong equivalence between CFGs and GIGs for the class of CFLs. Thus, it lays the basis for meaningfully investigating the amount of context-sensitiveness supported by GIGs, but leaves this investigation for further research

Efficiency of Top-Down Parsing of Recursive Adjunction for Tree Adjoining Grammar

CKY-type parser and Earley-type parser are two widely-used parsing algorithms for Tree Adjoining Grammar (TAG). In contrast, a standard top-down parser is not efficient since the looping problem occurs during both the left and right recursion of standard TAG derivation. Roark (2001) combines the top-down parser for CFG with a beam search, showing that the probabilistic top-down parser yields a perplexity improvement over previous results. In this paper, we define the stochastic tree adjoining grammar and apply the probabilistic top-down parser for CFG to TAG. Comparing the parsing efficiency of the standard and alternative TAG derivation of the recursive adjunction, we find that the alternative derivation is more efficient since it avoids the looping problem of the right recursion, increasing the parsing efficiency of our top-down parser

Pere Alberch's developmental morphospaces and the evolution of cognition

In this article we argue for an extension of Pere Alberch's notion of developmental morphospace into the realm of cognition and introduce the notion of cognitive phenotype as a new tool for the evolutionary and developmental study of cognitive abilities

On Finite-Index Indexed Grammars and Their Restrictions

The family, L(INDLIN), of languages generated by linear indexed grammars has been studied in the literature. It is known that the Parikh image of every language in L(INDLIN) is semi-linear. However, there are bounded semi-linear languages that are not in L(INDLIN). Here, we look at larger families of (restricted) indexed languages and study their combinatorial and decidability properties, and their relationships