CSDL Home IEEE Transactions on Visualization & Computer Graphics 2011 vol.17 Issue No.09 - September

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Issue No.09 - September (2011 vol.17)

pp: 1337-1351

Jaroslaw (Jarek) Rossignac , Georgia Institute of Technology, Atlanta

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TVCG.2010.232

ABSTRACT

An Expanded Boolean Expression (EBE) does not contain any XOR or EQUAL operators. The occurrence of each variable is a different literal. We provide a linear time algorithm that converts an EBE of n literals into a logically equivalent Ordered Boolean List (OBL) and show how to use the OBL to evaluate the EBE in n steps and O(log log n) space, if the values of the literals are each read once in the order prescribed by the OBL. (An evaluation workspace of 5 bits suffices for all EBEs of up to six billion literals.) The primary application is the SIMD architecture, where the same EBE is evaluated in parallel for different input vectors when rendering solid models on the GPU directly from their Constructive Solid Geometry (CSG) representation. We compare OBL to the Reduced Ordered Binary Decision Diagram (ROBDD) and suggest possible applications of OBL to logic verification and to circuit design.

INDEX TERMS

CSG, Boolean expression evaluation cost, OBDD.

CITATION

Jaroslaw (Jarek) Rossignac, "Ordered Boolean List (OBL): Reducing the Footprint for Evaluating Boolean Expressions",

*IEEE Transactions on Visualization & Computer Graphics*, vol.17, no. 9, pp. 1337-1351, September 2011, doi:10.1109/TVCG.2010.232REFERENCES