Showing papers on "Disjunctive normal form published in 1989"
TL;DR: The emphasis is on the development and analysis of a much more efficient ϵ, δ approximation algorithm for the DNF counting problem, which is substantially faster than the fastest known deterministic solution for the problem.
351 citations
Proceedings Article•
20 Aug 1989
TL;DR: This work proposes a representation of the propositional calculus which is straightforward, yet compact and sufficiently flexible to circumvent the combinatorial difficulties posed by many problems, and relies on a non-canonical representation in disjunctive normal form.
Abstract: Despite the long history and descriptive simplicity of the propositional calculus, practical aspects of its implementation on the computer remain an active area of study. We propose a representation of the propositional calculus which is straightforward, yet compact and sufficiently flexible to circumvent the combinatorial difficulties posed by many problems. The methodology does not involve term-rewriting, production systems, or similar, symbol-oriented approaches, but, rather, relies on a non-canonical representation in disjunctive normal form. It has been implemented in PASCAL, and efficiently solves what are described in the literature as "difficult" problems. The approach, which is simple and highly structured, and perhaps more procedural than many others, may be recommended for its ease of interpretation and for incorporation as a tool in larger systems.
12 citations
TL;DR: The method reduces to solving problems of integervalued linear programming of a special kind of special kind by constructing efficient lower bounds for the complexity of disjunctive normal forms of Boolean functions with a fixed number of zeros.
Abstract: A method is given for constructing efficient lower bounds for the complexity of disjunctive normal forms of Boolean functions with a fixed number of zeros. The method reduces to solving problems of integervalued linear programming of a special kind. Examples are given.
2 citations
09 Apr 1989
TL;DR: A prototype topological information retrieval system (TIRS) has been created and subjected to preliminary testing and analysis indicates that the TIRS prototype performs significantly better than the Boolean control at >or=0.999 level of confidence.
Abstract: A prototype topological information retrieval system (TIRS) has been created and subjected to preliminary testing. Two standard test suites, the CACM collection and the MED collection, were used in the test. The queries in each test suite were converted into disjunctive normal form and one document-retrieval pass was performed for each converted query. Precision and recall were measured for each query. The average value for precision was 0.763, while the average value for recall was 0.188. These values correspond to values of 0.529 and 0.114 for a slightly modified Boolean retrieval run as a control case. An analysis of the results indicates that the TIRS prototype performs significantly better than the Boolean control at >or=0.999 level of confidence. >
21 Aug 1989
TL;DR: The requirements of known algorithms (upper and lower bounds) under uniform distribution are analyzed and a new combinatorial measure is proposed in order to characterize the complexity of boolean formulae.
Abstract: We study the learnability from examples of boolean formulae assuming that the examples satisfy a uniform distribution assumption. We analyze the requirements of known algorithms (upper and lower bounds) under uniform distribution and we propose a new combinatorial measure in order to characterize the complexity of boolean formulae.