We previously proposed an unsupervised model using the inclusion-exclusion principle to compute sentence information content. Though it can achieve desirable experimental results in sentence semantic similarity, the computational complexity is more than O(2n). In this paper, we propose an efficient method to calculate sentence information content, which employs the thinking of the difference set in hierarchical network. Impressively, experimental results show that the computational complexity decreases to O(n). We prove the algorithm in the form of theorems. Performance analysis and experiments are also provided.

Sentence similarity computation is an increasingly important task in applications of natural language processing such as information retrieval, machine translation, text summarization and so on. From the viewpoint of information theory, the essential attribute of natural language is that the carrier of information and the capacity of information can be measured by information content which is already successfully used for word similarity computation in simple ways. Existing sentence similarity methods don't emphasize the information contained by the sentence, and the complicated models they employ often need using empirical parameters or training parameters. This paper presents a fully unsupervised computational model of sentence semantic similarity. It is also a simply and straightforward model that neither needs any empirical parameter nor rely on other NLP tools. The method can obtain state-of-the-art experimental results which show that sentence similarity evaluated by the model is closer to human judgment than multiple competing baselines. The paper also tests the proposed model on the influence of external corpus, the performance of various sizes of the semantic net, and the relationship between efficiency and accuracy.

The number of satisfying assignments of k-CNF formulas is computed using the inclusion-exclusion formula for sets of clauses. Recently, it was shown that the information on the sets of clauses of size log k + 2 already uniquely determines the number of satisfying assignments of k-CNF formulas. The proof was, however, only existential and no explicit procedure was presented. In this paper, we show that such a procedure exists.

In this paper, we consider two types of promises for (k-)CNF formulas which can help to find a satisfying assignment of a given formula. The first promise is the Hamming distance between truth assignments. Namely, we know in advance that a k-CNF formula with n variables, if satisfiable, has a satisfying assignment with at most pn variables set to 1. Then we ask whether or not the formula is satisfiable. It is shown that for k 3 and (i) when p=nc (-1 < c 0), the problem is NP-hard; and (ii) when p=log n/n, there exists a polynomial-time deterministic algorithm. The algorithm is based on the exponential-time algorithm recently presented by Schoning. It is also applied for coloring k-uniform hypergraphs. The other promise is the number of satisfying assignments. For a CNF formula having 2n/2nε (0 ε < 1) satisfying assignments, we present a subexponential-time deterministic algorithm based on the inclusion-exclusion formula.