It is shown how weighted context-free grammars can be used to recognize languages beyond their weak generative capacity by a one-step constant time extension of standard recognition algorithms.

We study a transformation of pseudo-Boolean functions which, when applicable, amounts to constructing from a graph G = (V, E) a new graph G’ = (V’, E’) with the same stability number and such that 1 V’1 = 1 VI 1. This transformation provides a polynomial time algorithm for the computation of the stability number of graphs which contain neither an induced chordless cycle with four vertices, nor ...

The Minimalist Grammars (MGs) proposed by Stabler(1997) have tree-shaped derivations (Harkema, 2001b; Michaelis, 2001a). As in categorial grammars, each lexical item is an association between a vocabulary element and complex of features, and so the “yields” or “fringes” of the derivation trees are sequences of these lexical items, and the string parts of these lexical items are reordered in the...

A space-efficient linear-time approximation algorithm for the grammar-based compression problem, which requests for a given string to find a smallest context-free grammar deriving the string, is presented. The algorithm consumes only O(g∗ log g∗) space and achieves the worstcase approximation ratio O(log g∗ log n), with the size n of an input and the optimum grammar size g∗. Experimental result...

We present two structural results concerning longest common prefixes of non-empty languages. First, we show that the longest common prefix of the language generated by a context-free grammar of size N equals the longest common prefix of the same grammar where the heights of the derivation trees are bounded by 4N . Second, we show that each non-empty language L has a representative subset of at ...

We compare the asymptotic time complexity of left-to-right and bidirectional parsing techniques for bilexical context-free grammars, a grammar formalism that is an abstraction of language models used in several state-of-the-art real-world parsers. We provide evidence that left-to-right parsing cannot be realised within acceptable time-bounds if the so called correct-prefix property is to be ens...

We give efficient ranking and unranking algorithms for left Szilard languages of context-free grammars. If O(n2) time and space preprocessing is allowed then each ranking operation is possible in linear time. Unranking takes time O(n log n). These algorithms imply similar algorithms for context-free languages generated by arbitrary unambiguous context-free grammars.

In the continuation of [DF], we study reversible reaction-diffusion equations via entropy methods (based on the free energy functional) for a 1D system of four species. We improve the existing theory by getting 1) almost exponential convergence in L1 to the steady state via a precise entropy-entropy dissipation estimate, 2) an explicit global L ∞ bound via interpolation of a polynomially growin...

We prove a uniform Poincaré-like estimate of the relative free energy by the dissipation rate for implicit Euler, finite volume discretized reaction-diffusion systems. This result is proven indirectly and ensures the exponential decay of the relative free energy with a unified decay rate for admissible finite volume meshes.

We present the first polynomial-time algorithm to solve the maximum weight independent set problem for apple-free graphs, which is a common generalization of several important classes where the problem can be solved efficiently, such as claw-free graphs, chordal graphs, and cographs. Our solution is based on a combination of two algorithmic techniques (modular decomposition and decomposition by...