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United States Patent (10) Patent No.: US 7.254,304 B2 Westphal (45) Date of Patent: Aug

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United States Patent (10) Patent No.: US 7.254,304 B2 Westphal (45) Date of Patent: Aug USOO72543 04B2 (12) United States Patent (10) Patent No.: US 7.254,304 B2 Westphal (45) Date of Patent: Aug. 7, 2007 (54) DEVICES AND TECHNIQUES FOR LOGICAL 5,220,642 A * 6/1993 Takahashi et al. ............ TO6/40 PROCESSING 5,414,789 A 5/1995 Tamil et al. ... 385,122 5.448,484 A * 9/1995 Bullock et al. ............. 701 117 (76) Inventor: Jonathan Westphal, 7620 Valley Vista 5,544,280 A 8/1996 Liu et al. ...................... 395.24 Rd., Pocatello, ID (US) 83201 6,272,261 B1* 8/2001 Matsuoka ...... ... 382.276 6.424,773 B1* 7/2002 Watanabe ................... 385,122 (*) Notice: Subject to any disclaimer, the term of this patent is extended or adjusted under 35 U.S.C. 154(b) by 531 days. OTHER PUBLICATIONS (21) Appl. No.: 10/398,312 Kunihuro Ichimura, “Photochromic Polymers', John C. Crano and Robert J. Gugilelmetti, eds. Organic Photochromic and (22) PCT Filed: Oct. 5, 2001 Thermochromic Compounds, vol. 2, Kluwer, New York, 1999, pp. 9-63. (86). PCT No.: PCT/US01/31217 * cited by examiner S 371 (c)(1), (2), (4) Date: Sep. 9, 2003 Primary Examiner Mark Hellner (74) Attorney, Agent, or Firm Allen, Dyer, Doppelt (87) PCT Pub. No.: WO02/29520 Milbrath & Gilchrist, P.A. PCT Pub. Date: Apr. 11, 2002 O O (57) ABSTRACT (65) Prior Publication Data US 2004/OO75885 A1 Apr. 22, 2004 The invention is directed to apparatus, methods, systems and Related U.S. Application Data computer programs which permit a simplification or reduc tion of the description of a complex digital circuit. This is (60) Provisional6, 2000 application No. 60/238,007, filed on Oct. accomplishedlished by usingusi a completelyletel new system off propo s sitional logic (13B), representing the logic of a logical (51) Int. Cl. circuit to be designed as points and vectors in a vector space, GO2F 3/00 (2006.01) simplifying the logic so represented to a simpler form using (52) U.S. Cl. ....................................... 385/122:359/108 vector transformations, and designing the circuit using the (58) Field of Classification Search ................ 3.85/122; simpler form. The invention is also directed to apparatus, 706/40: 701/117; 382/276; 35.9/108 methods, systems and devices which will implement the See application file for complete search history. vector logic system in optical forms, including free-space (56) References Cited optical methods, flat-optical methods, colorimetric methods, and methods using a polarization-based AND-gate. U.S. PATENT DOCUMENTS 5,131,055 A 7, 1992 Chao ........................... 382,32 1 Claim, 63 Drawing Sheets pvQ /1 3400 3414 3412 Ops U.S. Patent Aug. 7, 2007 Sheet 1 of 63 US 7.254,304 B2 Figure 1 A Space for Propositions U.S. Patent Aug. 7, 2007 Sheet 2 of 63 US 7.254,304 B2 Figure 2 The Propositions p and q v q U.S. Patent Aug. 7, 2007 Sheet 3 of 63 US 7.254,304 B2 Figure 3 Two-Letter Alternational Clauses U.S. Patent Aug. 7, 2007 Sheet 4 of 63 US 7.254,304 B2 (p,q) C (p,q) p p (p,q) d (p,q) Figure 4 The ANS-plane U.S. Patent Aug. 7, 2007 Sheet S of 63 US 7.254,304 B2 Figure 5 Modus Ponens in the CNS-plane U.S. Patent Aug. 7, 2007 Sheet 6 of 63 US 7.254,304 B2 Figure 6 Modus Tollens in the CNS-plane U.S. Patent Aug. 7, 2007 Sheet 7 of 63 US 7.254,304 B2 Figure 7 The Disjunctive Syllogism in the CNS-plane U.S. Patent Aug. 7, 2007 Sheet 8 of 63 US 7.254,304 B2 pVC q 802 pVQ OXN-804 C 806 pC Figure 8 Harmony of ANS-and CNS-planes U.S. Patent Aug. 7, 2007 Sheet 9 of 63 US 7.254,304 B2 Figure 9 pp -, pc W p. U.S. Patent Aug. 7, 2007 Sheet 10 of 63 US 7.254,304 B2 Figure 10 2D Representation of the 3D ANS-Space U.S. Patent Aug. 7, 2007 Sheet 11 of 63 US 7.254,304 B2 Figure 11 The CNS-Space with Three Variables: the Hypothetical Syllogism U.S. Patent Aug. 7, 2007 Sheet 12 of 63 US 7.254,304 B2 p C r Premise 1 -1 1 O + pvQ Premise 2 0 - 1 O Cvr Conclusion = -1 O 1 pvr Figure 12A Figure 12B Hypothetical Syllogism in a 3D CNS-Space U.S. Patent Aug. 7, 2007 Sheet 13 of 63 US 7.254,304 B2 StartiSE" Direction EEnd (o) (av)) by a p? EvG) N-q e (Every--p p?y Eve? Figure 13A U.S. Patent Aug. 7, 2007 Sheet 14 of 63 US 7.254,304 B2 Figure 13C U.S. Patent Aug. 7, 2007 Sheet 15 of 63 US 7.254,304 B2 S. S. N/K7 O C SVs O d CD Ol Cl S O) L U.S. Patent Aug. 7, 2007 Sheet 16 of 63 US 7.254,304 B2 pdrs pdf Figure 15 A Four-Clause Schema Simplified pqr vpdf V par V pdf.-H.Qr V pr U.S. Patent Aug. 7, 2007 Sheet 17 of 63 US 7.254,304 B2 pars QS. pGrS. pars Figure 16A Figure 16B U.S. Patent Aug. 7, 2007 Sheet 18 of 63 US 7.254,304 B2 pars QS. pqrS. pdrs pqrs pqf pGS pqrs pers Figure 17 Four-Variable V-diagram with Simplification of pqrs v pars v pars v pars V pa?s V pars". prS v qS U.S. Patent Aug. 7, 2007 Sheet 19 of 63 US 7.254,304 B2 pars qrS. pdr S. pqrs pqrS - pdf pqS or at pdfs pdrS Figure 18A Fix Rule d = 2 ur pqr v pa? V pdr V pdf v par v par V par. ". p v q V r r p 1 - 1 s 1 - 1 - 1 U.S. Patent Aug. 7, 2007 Sheet 20 of 63 US 7.254,304 B2 pars GrS. pGrS. pars pCrs pdf pGS pqrs pdrs Figure 19 Fix Rule d = 3 ele us pdrs v parSV pdfs v pdrs v parS V pars v pdrs v parS. p U.S. Patent Aug. 7, 2007 Sheet 21 of 63 US 7.254,304 B2 pars qrS. prS. pars pCrS ser pdf pqS pa?s pdrs U.S. Patent Aug. 7, 2007 Sheet 22 of 63 US 7.254,304 B2 pars GrS. pqrS. pqrS pqrs pqf pCS pqrs pdrs Figure 21 Simplification of Developed pg v pÉy qr V qf pqr v par v par v par v par V par. "... pg V prV pr U.S. Patent Aug. 7, 2007 Sheet 23 of 63 US 7.254,304 B2 pars GrS. pdrS. pars pqrs -- pqf paS pdfs pors Figure 22 Simplification of Undeveloped pav Ór V pav qf U.S. Patent Aug. 7, 2007 Sheet 24 of 63 US 7.254,304 B2 pqrpr pars qrs pqrS. - prS Sis pqr prSS NGr. pqrp?-s-pq or qr pars s L = p(rpf =pqp par - pg Figure 23 Simplification of par v pf v pCSV prV pdfs U.S. Patent Aug. 7, 2007 Sheet 25 of 63 US 7.254,304 B2 pqrs Figure 24 Equivalence of par and pq in par V pf U.S. Patent Aug. 7, 2007 Sheet 26 of 63 US 7.254,304 B2 Figure 25 ConsenSUS Theorem Figure 26 the Dual of qpConsensus v prw qr isTheorem: (q v p)(p v () (q.v r) U.S. Patent Aug. 7, 2007 Sheet 27 of 63 US 7.254,304 B2 Figure 27 : Superfluity of pas in pdr Vpr V pas U.S. Patent Aug. 7, 2007 Sheet 28 of 63 US 7.254,304 B2 Figure 28 Y Target Circuit: ABC + AC + ABD+AC + ABCD G=5, = 12, R=7 Figure 29 A Simplest Circuit Equivalent to the Target Circuit (ABC + AC + ABD +AC + ABCD) = (AB+ AC + AC + ABD) G=4, -9, R=2 U.S. Patent Aug. 7, 2007 Sheet 29 of 63 US 7.254,304 B2 Figure 30 Optical Computation of moduS ponens -- Implication ------ Half-implication U.S. Patent Aug. 7, 2007 Sheet 30 of 63 US 7.254,304 B2 Beam 3104 =1 St.pvc A 0.5 s. <-----a pvg 3112 =1 C<SHBeam = 1 3110 Figure 31 Interferometric Processing for modus ponens U.S. Patent Aug. 7, 2007 Sheet 31 of 63 US 7.254,304 B2 U.S. Patent Aug. 7, 2007 Sheet 32 of 63 US 7.254,304 B2 Figure 33 Displacement of O top v q; p is q U.S. Patent Aug. 7, 2007 Sheet 33 of 63 US 7.254,304 B2 341 4 3412 ( ( 3404 Ops S O .5 1 1.5 2 Figure 35 U.S. Patent Aug. 7, 2007 Sheet 34 of 63 US 7.254,304 B2 as: 32 3632. $ -3606 p 36.36 3638 ( ( 'S Opk-k-k€- 2-N-3634 3604 Figure 36 U.S. Patent Aug. 7, 2007 Sheet 35 of 63 US 7.254,304 B2 3702 - 370 8 p Opas: -3634 M 3704 3720 3726 f \ M SSM S3724 3630 3640 3718 SN-3710 C Figure 37 U.S. Patent Aug. 7, 2007 Sheet 36 of 63 US 7.254,304 B2 pd p0 pd pd Figure 38 U.S. Patent Aug. 7, 2007 Sheet 37 of 63 US 7.254,304 B2 U.S. Patent Aug. 7, 2007 Sheet 38 of 63 US 7.254,304 B2 pvQ Q pVg Figure 41 U.S.
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