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Calculating Exact Transitive Closure for a Normalized Affine Integer Tuple Relation
Institution:1. Faculty of Computing Science, Technical University of Szczecin, Szczecin, Poland;2. INRIA Saclay and LRI/University of Paris-Sud XI, Orsay, France;1. Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore, Pakistan;2. Sirt University, Art and Science Faculty, Department of Mathematics, 56100 Sirt, Turkey;3. Near East University, Mathematics Research Center, Department of Mathematics, Near East Boulenvard, PC:99138 Nicosia/Mersin 10, Turkey;4. Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand;5. Physics Department, Faculty of Science, University of Jeddah, Jeddah 23218, Saudi Arabia;1. Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China;2. School of Management, Beijing University of Chinese Medicine, Beijing 100029, China;1. College of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, PR China;2. Department of Mathematics, Guangxi Normal University, Guilin 541004, PR China;3. School of Mathematics and Statistics, UNSW Sydney, New South Wales 2052, Australia;1. College of Information Engineering, Tarim University, Alar 843300, PR China;2. School of Mathematics and Statistics, Xidian University, Xi’an 710071, PR China;1. Department of Astronautical, Electrical and Energy Engineering, Sapienza University of Rome, Via Eudossiana 18, 00100 Rome, Italy;2. Department of Planning, Design and Technology of Architecture, Sapienza University of Rome, Via Antonio Gramsci 53, 00197 Rome, Italy;3. EURAC Research, Institute for Renewable Energy, Viale Druso 1, I-39100 Bolzano, Italy
Abstract:An approach to calculate the exact transitive closure of a parameterized and normalized affine integer tuple relation is presented. A relation is normalized when it describes graphs of the chain topology only. The exact transitive closure calculation is based on resolving a system of recurrence equations being formed from the input and output tuples of a normalized relation. The approach permits for calculating an exact transitive closure for a relation when the constraints of this closure are represented by both affine and non-linear forms. An example of calculating the exact transitive closure of normalized affine integer tuple relation is presented.
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