While symbolic parsers can be viewed as deduction systems, this view is less natural for probabilistic parsers. We present a view of parsing as directed hypergraph analysis which naturally covers both symbolic and probabilistic parsing. We illustrate the approach by showing how a dynamic extension of Dijkstra’s algorithm can be used to construct a probabilistic chart parser with an Ç Ò time bound for arbitrary PCFGs, while preserving as much of the flexibility of symbolic chart parsers as allowed by the inherent ordering of probabilistic dependencies. 1

We introduce a notion of hyperconnection (formally denoted L-hyperpath) between nodes in a directed hypergraph and relate this notion to existing notions of hyperpaths in directed hypergraphs. We show that some interesting questions in problem domains such as secret transfer protocols and routing in packet filtered networks are basically questions about the existence of L-hyperpaths in directed hypergraphs. We study the computational complexity of problems related to L-hyperpaths and the L-cyclomatic number of directed hypergraphs (the minimum number of hyperedges that need to be deleted to make a directed hypergraph free of L-hypercycles). We prove that the L-hyperpath existence problem, the L-cyclomatic number problem, the minimum L-cyclomatic set problem, and the minimal L-cyclomatic, Πp, and DP, respectively. set problem are each complete for the complexity class NP, Σ p 2 1

In this note we show that a commonly used definition of a hyperpath in a directed hypergraph is not correct. This is done by presenting a counter-example which fulfils the definition but is not a hyperpath. Keywords: Directed hypergraphs, hyperpaths, B-paths. 1