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We discuss weighted deductive parsing and consider the problem of finding the derivation with the lowest weight. We show that Knuth's generalization of Dijkstra's algorithm for the shortest-path problem offers a general method to solve this problem. Our approach is modular in the sense that Knuth's algorithm is formulated independently from the weighted deduction system.

Several methods are discussed that construct a finite automaton given a context-free grammar, including both methods that lead to subsets and those that lead to supersets of the original context-free language. Some of these methods of regular approximation are new, and some others are presented here in a more refined form with respect to existing literature. Practical experiments with the different methods of regular approximation are performed for spoken-language input: hypotheses from a speech recognizer are filtered through a finite automaton. * DFKI,

We present a modular proof of strong normalization for the Calculus of Constructions of Coquand and Huet (1985, 1988). This result was first proved by Coquand (1986), but our proof is more perspicious. The method consists of a little juggling with some systems in the cube of Barendregt (1989), which provides a fine structure of the calculus of constructions. It is proved that the strong normalization of the calculus of constructions is equivalent with the strong normalization of Fω.In order to give the proof, we first establish some properties of various type systems. Therefore, we present a general framework of typed lambda calculi, including many well-known ones.