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<p><b>Abstract</b>—This paper investigates reduced ordered binary decision diagrams (OBDD) of partially symmetric Boolean functions when using variable orders where symmetric variables are adjacent. We prove upper bounds for the size of such symmetry ordered OBDDs (SymOBDD). They generalize the upper bounds for the size of OBDDs of totally symmetric Boolean functions and nonsymmetric Boolean functions proven by Heap and Mercer [<ref type="bib" rid="bibT036014">14</ref>], [<ref type="bib" rid="bibT036015">15</ref>] and Wegener [<ref type="bib" rid="bibT036037">37</ref>]. Experimental results based on these upper bounds show that the nontrivial symmetry sets of a Boolean function should be located either right up at the beginning or right up at the end of the variable order in order to obtain best upper bounds.</p>
Binary decision diagrams, variable ordering, upper worst case bounds, partial symmetric Boolean functions.
Laura Heinrich-Litan, Paul Molitor, "Least Upper Bounds for the Size of OBDDs Using Symmetry Properties", IEEE Transactions on Computers, vol. 49, no. , pp. 360-368, April 2000, doi:10.1109/12.844348
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