Prime Implicate Generation in Equational Logic

Journal of Artificial Intelligence Research ◽

10.1613/jair.5481 ◽

2017 ◽

Vol 60 ◽

pp. 827-880 ◽

Cited By ~ 1

Author(s):

Mnacho Echenim ◽

Nicolas Peltier ◽

Sophie Tourret

Keyword(s):

Data Structure ◽

Experimental Evaluation ◽

State Of The Art ◽

Equational Logic ◽

First Order ◽

Correctness Proofs ◽

Tree Data ◽

Tree Data Structure

We present an algorithm for the generation of prime implicates in equational logic, that is, of the most general consequences of formulæ containing equations and disequations between first-order terms. This algorithm is defined by a calculus that is proved to be correct and complete. We then focus on the case where the considered clause set is ground, i.e., contains no variables, and devise a specialized tree data structure that is designed to efficiently detect and delete redundant implicates. The corresponding algorithms are presented along with their termination and correctness proofs. Finally, an experimental evaluation of this prime implicate generation method is conducted in the ground case, including a comparison with state-of-the-art propositional and first-order prime implicate generation tools.

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Cache-efficient sweeping-based interval joins for extended Allen relation predicates

The VLDB Journal ◽

10.1007/s00778-020-00650-5 ◽

2021 ◽

Author(s):

Danila Piatov ◽

Sven Helmer ◽

Anton Dignös ◽

Fabio Persia

Keyword(s):

Data Structure ◽

Experimental Evaluation ◽

State Of The Art ◽

Temporal Databases ◽

Access Method ◽

Wide Range ◽

Interval Relation ◽

Cache Efficient ◽

Join Algorithms ◽

Better Than

AbstractWe develop a family of efficient plane-sweeping interval join algorithms for evaluating a wide range of interval predicates such as Allen’s relationships and parameterized relationships. Our technique is based on a framework, components of which can be flexibly combined in different manners to support the required interval relation. In temporal databases, our algorithms can exploit a well-known and flexible access method, the Timeline Index, thus expanding the set of operations it supports even further. Additionally, employing a compact data structure, the gapless hash map, we utilize the CPU cache efficiently. In an experimental evaluation, we show that our approach is several times faster and scales better than state-of-the-art techniques, while being much better suited for real-time event processing.

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A Scalable Algorithm for Constructing Frequent Pattern Tree

International Journal of Intelligent Information Technologies ◽

10.4018/ijiit.2014010103 ◽

2014 ◽

Vol 10 (1) ◽

pp. 42-56 ◽

Cited By ~ 3

Author(s):

Zailani Abdullah ◽

Tutut Herawan ◽

A. Noraziah ◽

Mustafa Mat Deris

Keyword(s):

Data Structure ◽

Frequent Pattern ◽

Frequent Patterns ◽

Scalable Algorithm ◽

Tree Construction ◽

Frequent Pattern Tree ◽

Support Threshold ◽

Benchmark Datasets ◽

Tree Data ◽

Tree Data Structure

Frequent Pattern Tree (FP-Tree) is a compact data structure of representing frequent itemsets. The construction of FP-Tree is very important prior to frequent patterns mining. However, there have been too limited efforts specifically focused on constructing FP-Tree data structure beyond from its original database. In typical FP-Tree construction, besides the prior knowledge on support threshold, it also requires two database scans; first to build and sort the frequent patterns and second to build its prefix paths. Thus, twice database scanning is a key and major limitation in completing the construction of FP-Tree. Therefore, this paper suggests scalable Trie Transformation Technique Algorithm (T3A) to convert our predefined tree data structure, Disorder Support Trie Itemset (DOSTrieIT) into FP-Tree. Experiment results through two UCI benchmark datasets show that the proposed T3A generates FP-Tree up to 3 magnitudes faster than that the benchmarked FP-Growth.

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