Reduced Ordered Binary Decision Diagram with Implied Literals: A New knowledge Compilation Approach

Knowledge compilation is an approach to tackle the computational intractability of general reasoning problems. According to this approach, knowledge bases are converted off-line into a target compilation language which is tractable for on-line querying. Reduced ordered binary decision diagram (ROBDD) is one of the most influential target languages. We generalize ROBDD by associating some implied literals in each node and the new language is called reduced ordered binary decision diagram with implied literals (ROBDD-L). Then we discuss a kind of subsets of ROBDD-L called ROBDD-i with precisely i implied literals (0 \leq i \leq \infty). In particular, ROBDD-0 is isomorphic to ROBDD; ROBDD-\infty requires that each node should be associated by the implied literals as many as possible. We show that ROBDD-i has uniqueness over some specific variables order, and ROBDD-\infty is the most succinct subset in ROBDD-L and can meet most of the querying requirements involved in the knowledge compilation map. Finally, we propose an ROBDD-i compilation algorithm for any i and a ROBDD-\infty compilation algorithm. Based on them, we implement a ROBDD-L package called BDDjLu and then get some conclusions from preliminary experimental results: ROBDD-\infty is obviously smaller than ROBDD for all benchmarks; ROBDD-\infty is smaller than the d-DNNF the benchmarks whose compilation results are relatively small; it seems that it is better to transform ROBDDs-\infty into FBDDs and ROBDDs rather than straight compile the benchmarks.Comment: 18 pages, 13 figure

Mining simple and complex patterns efficiently using Binary Decision Diagrams

© 2009 Dr. Elsa LoekitoPattern mining is a knowledge discovery task which is useful for finding interesting data characteristics. Existing mining techniques sometimes suffer from limited performance in challenging situations, such as when finding patterns in high-dimensional datasets. Binary Decision Diagrams and their variants are a compact and efficient graph data structure for representing and manipulating boolean functions and they are potentially attractive for solving many problems in pattern mining. This thesis explores techniques for the use of binary decision diagrams for mining both simple and complex types of patterns. Firstly, we investigate the use of Binary Decision Diagrams for mining the fundamental types of patterns. These include frequent patterns, also known as frequent itemsets. We introduce a structure called the Weighted Zero-suppressed Binary Decision Diagram and evaluate its use on high dimensional data. This type of Decision Diagram is extremely useful for re-using intermediate patterns during computation. Secondly, we study the problem of mining patterns in sequential databases. Here, we introduce a new structure called the Sequence Binary Decision Diagram, which can be used for mining frequent subsequences. We show that our technique is competitive with the state of the art and identify situations where it is superior. Thirdly, we show how Weighted Zero-suppressed Binary Decision Diagrams can be used for discovering new and complex types of patterns. We introduce new types of highly expressive patterns for capturing contrasts, which express disjunctions of attribute values. Moreover, to investigate the usefulness of disjunctive patterns for knowledge discovery, we employ a statistical methodology for testing their significance, and study their use for solving classification problems. Our findings show that classifiers based on significant disjunctive patterns can be more robust than those which are only based on simple patterns. Finally, we introduce patterns for capturing second-order differences between two groups of classes, which can provide useful insights for human experts. Again, we show how binary decision diagrams can be deployed for efficiently discovering this type of knowledge. In summary, we demonstrate that Binary Decision Diagrams, are a powerful and scalable tool in pattern mining. We believe their use is very promising for a range of current and future tasks in the data mining context

Efficient incremental mining of contrast patterns in changing data

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A binary decision diagram based approach for mining frequent subsequences

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Optimization Bounds from Binary Decision Diagrams

dbergman,acire,vanhoeve,jh38andrew.cmu.ed

Identification of point mutations in Glucose-6-Phosphate Dehydrogenase gene in Timor Island people : A preliminary report

<p>Glucose 6 phosphate dehydrogenase (G6PD) deficiency is common in malaria endemic region, however no molecular study has been performed on G6PD deficiency in Timor Island, Indonesia a malarial hyperendemic area which Proto Malay is the majority of the people in that island. To observe the frequency and molecular type of mutations in G6PD deficient Proto Malay people, 118 native people were screened using formazan ring test. Mutation in the G6PD gene were determined by MPTP (Multiple PCR using Multiple Tandem Forward Primers and a common Reserve Pimer) method and confirmed by automatic sequencer. This study shows that three males have lower G6PD activity. Using MPTP method, a point mutation could be indicated in the two cases. Sequencing of the amplified products in 2 G6PD patients disclosed mutations of T383C in exon 5 and C 592 T in exon 6 in respective case. Our result documents point mutations in exon 5 and exon 6 in the G6PD gene of two Proto Malay people in Timor. These mutations are common in Asia region. <em><strong>(Med J Indones 2001; 10: 210-3)</strong></em></p><p><strong>Keywords:</strong><em> mutations, G6PD, Proto Malay.</em></p