Title:
Optimized Blist Form (OBF)
Optimized Blist Form (OBF)
| dc.contributor.author | Rossignac, Jarek | |
| dc.date.accessioned | 2008-02-21T23:20:28Z | |
| dc.date.available | 2008-02-21T23:20:28Z | |
| dc.date.issued | 2007-05-23 | |
| dc.description | Tech Report GIT-GVU-07-10 (original number: GIT-GVU-06-18) revised on May 23, 2007. | |
| dc.description.abstract | Any Boolean expressions may be converted into positive-form, which has only union and intersection operators. Let E be a positive-form expression with n literals. Assume that the truth-values of the literals are read one at a time. The numbers s(n) of steps (operations) and b(n) of working memory bits (footprint) needed to evaluate E depend on E and on the evaluation technique. A recursive evaluation performs s(n)=n–1 steps but requires b(n)=log(n)+1 bits. Evaluating the disjunctive form of E uses only b(n)=2 bits, but may lead to an exponential growth of s(n). We propose a new Optimized Blist Form (OBF) that requires only s(n)=n steps and b(n)=⌈log2j⌉ bits, where j=⌈log2(2n/3+2)⌉. We provide a simple and linear cost algorithm for converting positive-form expressions to their OBF. We discuss three applications: (1) Direct CSG rendering, where a candidate surfel stored at a pixel is classified against an arbitrarily complex Boolean expression using a footprint of only 6 stencil bits; (2) the new Logic Matrix (LM), which evaluates any positive form logical expression of n literals in a single cycle and uses a matrix of at most n×j wire/line connections; and (3) the new Logic Pipe (LP), which uses n gates that are connected by a pipe of ⌈log2j⌉ lines and when receiving a staggered stream of input vectors produces a value of a logical expression at each cycle. | en_US |
| dc.identifier.uri | http://hdl.handle.net/1853/20059 | |
| dc.language.iso | en_US | en_US |
| dc.publisher | Georgia Institute of Technology | en_US |
| dc.relation.ispartofseries | GVU Technical Report; GIT-GVU-07-10 | en_US |
| dc.subject | Boolean expressions | en_US |
| dc.subject | Logic matrix | en_US |
| dc.subject | Logic pipe | en_US |
| dc.subject | Op-nodes | en_US |
| dc.subject | Optimized blist form | en_US |
| dc.title | Optimized Blist Form (OBF) | en_US |
| dc.type | Text | |
| dc.type.genre | Technical Report | |
| dspace.entity.type | Publication | |
| local.contributor.author | Rossignac, Jarek | |
| local.contributor.corporatename | GVU Center | |
| local.relation.ispartofseries | GVU Technical Report Series | |
| relation.isAuthorOfPublication | d854d72c-9694-4442-bd2f-fb8859bade72 | |
| relation.isOrgUnitOfPublication | d5666874-cf8d-45f6-8017-3781c955500f | |
| relation.isSeriesOfPublication | a13d1649-8f8b-4a59-9dec-d602fa26bc32 |