We apply the idea of weight pushing (Mohri, 1997) to CKY parsing with fixed context-free grammars. Applied after rule binarization, weight pushing takes the weight from the original grammar rule and pushes it down across its binarized pieces, allowing the parser to make better pruning decisions earlier in the parsing process. This process can be viewed as generalizing weight pushing from transd...

Standard models of language learning are concerned with weak learning: the learner, receiving as input only information about the strings in the language, must learn to generalise and to generate the correct, potentially infinite, set of strings generated by some target grammar. Here we define the corresponding notion of strong learning: the learner, again only receiving strings as input, must ...

LR parsing is a popular parsing strategy for variants of Context-Free Grammar (CFG). It has also been used for mildly context-sensitive formalisms, such as Tree-Adjoining Grammar. In this paper, we present the first LRstyle parsing algorithm for Linear ContextFree Rewriting Systems (LCFRS), a mildly context-sensitive extension of CFG which has received considerable attention in the last years.

Attribute grammars are an elegant formalization of the augmented context-free grammars characteristic of most current natural language systems. This paper presents an extension of Earley's algorithm to Knuth's attribute grammars, considering the case of S-attributed grammars. For this case, we study the conditions on the underlying base grammar under which the extended algorithm may be guarante...

Consider the triangle-free process, which is defined as follows. Start with G(0), an empty graph on n vertices. Given G(i − 1), let G(i) = G(i − 1) ∪ {g(i)}, where g(i) is an edge that is chosen uniformly at random from the set of edges that are not in G(i − 1) and can be added to G(i − 1) without creating a triangle. The process ends once a maximal triangle-free graph has been created. Let H b...

Should probability play a role in linguistics? Whereas Chomsky (1957: 16–17) influentially rejected probability in syntactic theory, “[i]n phonological theory, probability has not so much been rejected as disregarded” (Coleman, 2003: 89). Disregard has, however, given way to a growing literature on the use of probability across the various linguistic sub-disciplines (see, e.g., Bod et al., 2003...

We show the existence of noncommutative random variables with finite free entropy but which do not generate a free group factor. In particular, this gives an example of variables X1, . . . , Xn such that δ(X1, . . . , Xn) = n while W ∗(X1, . . . , Xn) ≇ L(Fn).

We prove that 2-abelian-cubes are avoidable over a binary alphabet and that 3-abelian-squares are avoidable over a ternary alphabet, answering positively to two questions of Karhumäki et al.. We also show the existence of infinite additive-cube-free words on several ternary alphabets. To achieve this, we give sufficient conditions for a morphism to be k-abelian-n-power-free (resp. additive-n-po...

We study the probability that a sample of independent, identically distributed random variables with a geometric distribution is gap-free, that is, that the sizes of the variables in the sample form an interval. We indicate that this problem is closely related to the asymptotic probability that a random composition of an integer n is likewise gap-free.

A celebrated result of Schützenberger says that a language is star-free if and only if it is is recognized by a finite aperiodic monoid. We give a new proof for this theorem using local divisors.