Abstract
Parity Ordered Binary Decision Diagrams (⊕OBDDs) are a data structure for boolean functions that extends the well-known OBDDs and reduces the representation size for several functions. Both data structures share the problem that the representation size strongly depends on the chosen variable order. For ⊕OBDDs the number of edges and thus the representation size is also influenced by the choice of the basis of the represented vector space. In this paper the hardness of some minimization problems for ⊕OBDDs is proven, namely, that there is no polynomial time approximation scheme for minimizing the number of nodes by choosing the variable order and for minimizing the number of edges, where the variable order may be changed or is fixed, unless P=NP.
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Sieling, D. Minimization Problems for Parity OBDDs. Theory Comput Syst 44, 391–413 (2009). https://doi.org/10.1007/s00224-007-9084-8
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DOI: https://doi.org/10.1007/s00224-007-9084-8