PQLG COLLECTION OF WEB PAGES AND LITERATURE RELATED TO REVERSIBLE AND QUANTUM LOGIC AND COMPUTING

ALPHABETICALLY

1. Prof. Takafumi Aoki, Tohoku University, Japan: EMAIL: aoki@ecei.tohoku.ac.jp
   Phone : +81-22-217-7169 Fax : +81-22-263-9406
2. ADIABATIC:
   1. http://www-cad.eecs.berkeley.edu/~aferrari/classes/ee241/adiabatic/report-mid/node1.html Adiabatic Computation, A. Ferrari, Wed Mar 20 12:14:36 PST 1996. Report.
      
   2. Adiabatic Circuits for Low Power Consumption Student Project, VHDL.
3. UNIVERSITY OF SOUTHERN CALIFORNIA ADIABATIC CMOS:
   1. W.C. Athas & L."J." Svensson, "Reversible Logic Issues in Adiabatic CMOS", Exploratory Design Group, University of Southern California - Information Sciences Institute, Marina del Rey, CA 90292-6695, {athas,svensson}@isi.edu

1. H.G. Baker "(NREVERSAL) of Fortune - The Thermodynamics of Garbage Collection", Int'l Workshop on Memory Management, Y. Bekkers (ed.), Springer 1992, pp. 502-524.
2. CHARLES BENNETT:
   1. Ch.H. Bennett, "Notes on the History of Reversible Computation", IBM J. Res. Develop., Vol. 32, 1988, pp. 16-23.
   2. Ch. H. Bennett and R. Landauer, "The Fundamental Limits of Computation", Scientific American, July 1985, pp. 38-46.
   3. C. Bennett, "Logical reversibility of computation", I.B.M. Journal of Research and Development, 17 (1973), pp. 525-532.
3. U.C. BERKELEY
   1. Charge Recovery and Adiabatic Switching Techniques in Digital Logic Overview of Adiabatic Styles from 1997.
4. BIRNBAUM AND HEWLETT PACKARD:
   1. J. Birnbaum, "Computing Alternatives", Talk given on March 3, 1997 atACM97, March 3, 1997, San Jose, California, by Director of Hewlett- Packard Laboratories, Senior Vice-President of Research and Development.
5. SAMUEL BRAUNSTEIN:
   1. http://www.sees.bangor.ac.uk/~schmuel/comp/node6.html Quantum computation: a tutorial. Samuel L. Braunstein. United Kingdom.
6. Prof. Jon T. Butler, Naval Postgraduate School, USA: EMAIL: butler@cs.nps.navy.mil
   EMAIL butler@aries20.cse.kyutech.ac.jp
   EMAIL butler@candy.cse.kyutech.ac.jp
   HOMEPAGE Publications.

1. Prof. Jan Chomicki: Jan Chomicki's scientific pedigree . HOMEPAGE
   Prof. Jan Chomicki HOMEPAGE
2. CHUANG IN U.C. BERKELEY:
   1. M.A. Nielsen and I.L. Chuang, "Quantum Computation and Quantum Information", Cambridge, 2001.

1. DE VOS, UNIV. GENT, BELGIUM.
   1. Reversible computers WEB PAGE OF DE VOS.
   2. L. Storme, A. De Vos, G. Jacobs, "Group Theoretical Aspects of Reversible Logic Gates", Journal of Universal Computer Science, Vol. 5, 1999, pp. 307-321.
   3. A. De Vos, B. Desoete, A. Adamski, P. Pietrzak, M. Sibinski, T. Widerski "Design of reversible circuits by means of control gates", Integrated Circuit Design, Proc. PATMOS'2000 (10th Workshop Power and Timing Modeling, Optimization and Simulation), Goettingen, Germany, Sept. 13-15, 2000, P. Pirsch and E. Barke (eds.), Springer Verlag, Lecture Notes in Computer Science, vol. 1918, pp.255-264. See Kerntopf.
   4. A. De Vos, "Proposal for an Implementation of Reversible Gates in c-MOS," Int. Journal of Electronics, Vol. 76, 1994, pp. 293-302.
   5. A. De Vos, "Reversible Computing in c-MOS”, Proc. Advanced Training Course on Mixed Design of VLSI Circuits, 1994, pp. 36-41.
   6. A. De Vos, "A 12-Transistor c-MOS Building-Block for Reversible Computers", Int. Journal of Electronics, Vol. 79, 1995, pp. 171-182.
   7. A. De Vos, "Reversible and Endoreversible Computing", Int. Journal of Theor. Phys., Vol. 34, 1995, pp. 2251-2266.
   8. De Vos, A., "Introduction to r-MOS systems"; Proc. 4 th Workshop on Physics and Computation, Boston, 1996, pp. 92-96.
   9. De Vos, A., "Towards reversible digital computers"; Proc. European Conference on Circuit Theory and Design, Budapest, 1997, pp. 923-931.
   10. De Vos, A., "Reversible computing"; Progress in Quantum Electronics, 23 (1999), pp. 1-49.
   11. B. Desoete, A. De Vos, M. Sibinski, T. Widerski, "Feynman's Reversible Logic Gates Implemented in Silicon", Proc. 6 th Intern. Conf. MIXDES, 1999, pp. 497-502.
2. ERIC DREXLER: Eric Drexler: AltaVista Search: Simple Query "Eric Drexler"
   1. Argomenti trattati: nanocomputer, nanotecnologia, entropia Drexler's mechanical logic

1. Prof. Andrzej Enhenfeucht: AltaVista Search: Simple Query "Andrzej Ehrenfeucht"
2. QUANTUM ERROR CORRECTING CODES WEB PAGE:
   1. Quantum Error-Correcting Codes.
3. EXTROPIANS AND SIMILAR FRINGES:
   1. The Posthuman Body

1. Dr. Bogdan Falkowski, EMAIL: EFALKOWSKI@ntu.edu.sg
2. MICHAEL FRANK, UNIV. of FLORIDA: M. Frank, WWW page
3. Michael Frank, University of Florida.
4. Nanotechnology from Frank.
   1. http://www.cise.ufl.edu/~mpf/rc.html Amorphous and nano computing.
   2. Physical Limits of Computing
   3. M. Frank, "Physical Limits of Computing," CIS 4930.1194X / 6930.1078X, Spr. '00. WWW page
   4. Michael Frank, University of Florida.
   5. Nanotechnology from Frank.
5. ED FREDKIN:
   
6. Prof. Edward Fredkin: HOMEPAGE
   1. E. Fredkin, T. Toffoli, "Conservative Logic", Int. Journal of Theor. Phys., 21 (1982), pp. 219-253.
   2. E.F. Fredkin, T. Toffoli, - Design Principles for Achieving High-Performance Submicron Digital Technologies, DARPA Proposal, Nov. 1978
7. RICHARD FEYNMAN:
   1. R.Feynman, "Quantum Mechanical Computers", Optics News, 11 (1985), pp. 11-20.
   2. R. Feynman, "There's plenty of space at the bottom: an invitation To Enter a New Field of Physics," Nanotechnology, Ed BC Crandal and J.Lewis, the MIT Press 1992, pp. 347-363
   3. Feynman, R., "Feynman lectures on computation" (A. Hey and R. Allen, eds); Addison-Wesley, Reading (1996).

1. GERSHENFELD:
   1. http://www.sciam.com/1998/0698issue/0698gershenfeld.html Quantum Computing with Molecules, By taking advantage of nuclear magnetic resonance, scientists can coax the molecules in some ordinary liquids to serve as an extraordinary type of computer by Neil Gershenfeld and Isaac L. Chuang
2. Dr. Ryszard Gokieli: HOMEPAGE
3. Prof. P. Glenn Gulak, University of Toronto, Canada: EMAIL: gulak@eecg.toronto.edu
   Phone : +1-416-978-8671 Fax : +1-416-971-2286

1. JOHN STORRS HALL:
   1. Hall, J. S. (1994): "Nanocomputers and Reversible Logic"', Nanotechnology, V. 5 no. 3 pp. 157ff
   2. Hall, J. S. (1994): "A Reversible Instruction Set Architecture and Algorithms", Proc. Physics of Computation Workshop, IEEE Press.
   3. Hall, J. S. (1993): "Nanocomputers and Reversible Logic", Third Foresight Conference on Nanotechnology, Palo Alto. (invited address)
   4. Hall, J. S. (1993): "An Electroid Switching Model for Reversible Computer Architectures", Proc. 1992 Physics of Computation Workshop, IEEE Press
   5. John Storrs Hall
2. Prof. Takahiro Hanyu, Dept. of Computer & Mathematical Sciences, Tohoku Univ.: EMAIL hanyu@kameyama.ecei.tohoku.ac.jp
   Graduate School of Information Sciences
   Tohoku University, Aoba-ku, Sendai 980-77 Japan
   Phone : +81-22-217-7153 (Direct)
   Fax : +81-22-263-9401 (Direct)
3. Prof. Yutaka Hata, Himeji Institute of Technology, Japan: EMAIL: hata@comp.eng.himeji-tech.ac.jp
4. Byte, July-August 1995 , The Square Root of NOT, Brian Hayes

1. COLIN JOHNSON:
   1. Reversible logic saves power, By R. Colin Johnson

1. Prof. Kameyama, Tohoku Univ.:
   EMAIL: ismvl98@vlsichip.kameyama.ecei.tohoku.ac.jp
   EMAIL: michi@kameyama.ecei.tohoku.ac.jp
   Program Chair of the 28th ISMVL
   PHONE: (+81)22-217-7152
   [022-217-7152 in Japan]
   FAX: (+81)22-263-9405
   
   HOMEPAGE
   
   http://www.higuchi.ecei.tohoku.ac.jp/research/paper/paper-list.html
   http://www.higuchi.ecei.tohoku.ac.jp/research/research.html
2. PAWEL KERNTOPF:
   1. P. Kerntopf, "Logic Synthesis Using Reversible Gates," Proc. 3rd Symposium on Logic, Design and Learning, Portland, Oregon, May 31, 2000.
   2. P. Kerntopf, "A Comparison of Logical Efficiency of Reversible and Conventional Gates," 9th IEEE Workshop on Logic Synthesis,
   3. P. Kerntopf, "On Efficiency of Reversible Logic (3,3) Gates." Proc. 7th Intl. Conf. MIXDES, 2000, pp. 185-190.
3. Z. Kohavi, "Switching Functions and Finite Automata Theory", Prentice Hall.
4. QUANTUM COMPUTATION GROUP AT KOREAN ADVANCED INSTITUTE OF SCIENCE AND TECHNOLOGY.
   1. http://mrm.kaist.ac.kr/qc/main.html Homepage of the Quantum Computation at Korea Advanced Institute of Science and Technology
   2. J. Lim, D. Kim, and S. Chae, "Reversible Energy Recovery Logic Circuits and Its 8-Phase Clocked Power Generator for Ultra-Low-Power Applications," IEICE Trans. Electron, OL.E82 C, No. 4 April 1999.
   3. Category:Integrated Electronics Title:Reversible Energy Recovery Logic Circuits and Its 8-Phase Clocked Power Generator for Ultra-Low-Power Applications, Author:Joonho LIM,Dong-Gyu KIM,Soo-Ik CHAE
   4. Research Interests Ultra Low Power Computation. We are exploring new ideas in adiabatic switching & reversible computation
   5. What is reversible logic? Welcome to Low Power Research Homepage. What is RERL(Reversible Energy Recovery Logic)?
   6. Ultra-Low Power CMOS Design Using Reversible Logic

1. R.LANDAUER:
   1. R. Landauer, "Irreversibility and heat generation in the computational process"; I.B.M. Journal of Research and Development, 5 (1961), pp. 183-191.
   2. R. Keyes, and R. Landauer, "Minimal energy dissipation in logic"; I.B.M. Journal of Research and Development, 14 (1970), pp. 153-157.
2. LOW POWER:
   1. Selected Publications (Power Conscious Design) K. Roy and S. Prasad, ``Circuit Activity Based CMOS Logic Synthesis for for Low Power Reliable...
      
   2. Brzozowski: Low Power
   3. Signal entropy and the thermodynamics of computation
   4. Johan Klockars's Bookmarks
   5. Andreas' Hardware Design Page
   6. Physics News Update 1993 Index
   7. Tutorial on Behavioral Synthesis Power Optimization
   8. Re:FPGAs and Heat (Re: Paranoid Musings
3. LUNDSTROM FROM PURDUE:
   1. http://shay.ecn.purdue.edu/~ee595n/Handouts/Lecture30.pdf Mark Lundstrom, Electrical and Computer Engineering, Purdue University, West Lafayette, IN. Device Physics of Nanoscale MOSFETs.

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   1. MARGOLUS FROM MIT:
      Prof. Norman Margolus, MIT: HOMEPAGE
      1. N. Margolus, "Physics and Computation", Ph. D. Thesis, Massachussets Institute of Technology, USA 1988.
   2. RALPH MERKLE:
      1. The Technical Feasibility of Cryonics, PART 3 of 5. by Ralph C. Merkle
      2. NASA applications of molecular nanotechnology, Al Globus, David Bailey, Jie Han, Richard Jaffe, Creon Levit, Ralph Merkle, and Deepak Srivastava Published in The Journal of the British Interplanetary Society, volume 51, pp. 145-152, 1998.
      3. Two Types of Mechanical Reversible Logic, by Ralph C. Merkle, Xerox PARC
      4. Reversible Electronic Logic Using Switches, by Ralph C. Merkle
      5. Helical logic by Ralph C. Merkle Xerox PARC 3333 Coyote Hill Road Palo Alto, CA 94304 merkle@xerox.com www.merkle.com. and. K. Eric Drexler...
         
      6. Papers by Ralph C. Merkle
      7. R C. Merkle and K. Eric Drexler, "Helical Logic", WWW.
      8. R C. Merkle, "Reversible electronic logic using switches," Nanotechnology, 4 (1993) pp. 21-40
      9. R. C. Merkle, "Two types of mechanical reversible logic," Nanotechnology, 4 (1993), pp. 114-131.
   3. LUTZ MICHEEL AND WRIGHT LABS:
      1. L.J. Micheel, A.H. Taddiken and A.C. Seabaugh, "Multiple-Valued Logic Computation Using Micro- and Nanoelectronic Devices," Proc. ISMVL, IEEE, 1993, pp. 164-169
   4. MIT:
      1. http://xyz.plh.af.mil/Talks/MIT99/sld035.htm Large macroscopic array of mesoscopic quantum computers
      2. MIT Reports to the President 1995-96
      3. Physics of Computing 1998/99 3. Information theory and reversible computing. Reversible computing from AltaVista. Reversible logic. MIT Information Mechanics lab. MIT laboratory...
         
   5. MOLECULAR COMPUTING:
      1. Molecular Computing, The Next Information Systems Revolution Part 2 of an overview of a family of new technologies that is soon going to turn the computer and consumer electronics industries upside down. by Franco Vitaliano
   6. MORITA FROM JAPAN:
      1. List of Selected Papers of Kenichi MORITA (Chronological Order, 1986 - )
   7. MUZYCHENKO AND SYMMETRIC FUNCTIONS:
      1. O.N. Muzychenko, "Uniform and Regular Structures for Realization of Symmetric Functions of the Algebra of Logic", Automation and Remote Control, Vol. 59, No.4, 1998, pp. 581-592

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   1. NANOTECHNOLOGY:
      1. Transhuman Technologies - Nanotechnology
      2. A Proposed MNT Active Cell By Forrest Bishop Copyright (c) 1996,
      3. Team uses groupware to build nanocomputer on the Net
      4. http://vortex.tn.tudelft.nl/publi/1997/nano97/nano97.html
      5. http://www.nanomedicine.com/6.5.html"
      6. Molecular Engineering and Nanotechnology Guides
      7. Nanotechnology
      8. sci.nanotech archives by thread
      9. sci.nanotech archives: Re: Update #5
      10. sci.nanotech archives by thread

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   P
   
   1. Y.N. Patt, "A Complex Logic Module for the Synthesis of Combinational Switching Circuits", Proc. 30 th AFIPS Spring Joint Computer Conf., 1967, pp. 699-706.
   2. PERES:
      1. A. Peres, "Reversible Logic and Quantum Computers", Physical Review A, 32 (1985), pp. 3266-3276. [31]
   3. PICTON:
      1. P. Picton, "Optoelectronic, Multivalued, Conservative Logic", Int. Journal of Optical Computing, Vol. 2, 1991, pp. 19-29.
      2. PICTON: MULTIPLE- VALUED LOGIC JOURNAL
      3. Multiple Valued Logic Paper by Picton.
      4. P. Picton, "Multi-valued Sequential Logic Design Using Fredkin Gates", MVL Journal, vol.1, 1996, pp.241-251.
      5. P. D. Picton, "A Universal Architecture for Multiple-Valued Reversible Logic", WWW link
      6. P. Picton, "A Universal Architecture for Multiple-valued Reversible Logic," MVL Journal, 5 (2000), pp.27-37.
      7. P. Picton, "Modified Fredkin Gates in Logic Design," Microelectronics Journal, 25 (1994), pp. 437-441.
   4. PQLG - PORTLAND QUANTUM LOGIC GROUP:
      1. M. Chrzanowska-Jeske, Y. Xu, and M. Perkowski, ``Logic Synthesis for a Regular Layout,'' VLSI Design, Vol. 10, No. 1, pp. 35 - 55, 1999.
      2. M. A. Perkowski, "A Fundamental Theorem for EXOR Circuits," Proc. of IFIP W.G. 10.5 Workshop on Applications of the Reed-Muller Expansion in Circuit Design," Hamburg, Germany, September 16-17, pp. 52 - 60, 1993.
      3. M. Perkowski, B. Falkowski, M. Chrzanowska-Jeske, and R. Drechlser, ``Efficient Algorithms for Creation of Linearly-Independent Decision Diagrams and their Mapping to Regular Layouts''. VLSI Design. In print
      4. Marek Perkowski, Pawel Kerntopf, Andrzej Buller, Malgorzata Chrzanowska-Jeske, Alan Mishchenko, Xiaoyu Song, Anas Al-Rabadi, Lech Jozwiak, Alan Coppola, "Regularity and Symmetry as a Base for Efficient Realization of Reversible Logic Circuits," submitted.
      5. M.A. Perkowski, M. Chrzanowska-Jeske, and Y. Xu, ``Multi-Level Programmable Arrays for Sub-Micron Technology based on Symmetries,'' Proc. ICCIMA'98 Conference, pp. 707-720, February 1998, Australia, published by World Scientific.
      6. M.A. Perkowski. A. Al-Rabadi, P. Kerntopf, M. Chrzanowska-Jeske and A.Mishchenko, "Three Dimensional Realization of Multi-Valued Symmetric Functions using Reversible Logic". Submitted to ULSI 2001.
      7. M. Perkowski, P. Kerntopf, A. Buller, M. Chrzanowska-Jeske, A. Mishchenko, X. Song, A. Al-Rabadi, L. Jozwiak, A. Coppola, "Regular Realization of Symmetric Functions using Reversible Logic", submitted to Euro-Micro 2001.
      8. E. Pierzchala, M. A. Perkowski, S. Grygiel, "A Field Programmable Analog Arrray for Continuous, Fuzzy and Multi-Valued Logic Applications," Proc. ISMVL'94, pp. 148 - 155, Boston, MA, May 25-27, 1994.
      9. A. Sarabi, N. Song, M. Chrzanowska-Jeske, M. A. Perkowski, "A Comprehensive Approach to Logic Synthesis and Physical Design for Two- Dimensional Logic Arrays," Proc. DAC'94, San Diego, June 1994, pp. 321 - 326.

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   1. QUANTUM COMPUTATION:
      1. http://www.physics.uq.edu.au:8001/people/toombes/Kane/index.htm Solid State Nuclear Spin Quantum Computers, 2/06/98.
      2. http://www.techweb.com/se/directlink.cgi?EET19980504S0062 EE Times, May 04, 1998, Issue: 1005, Section: News, Quantum computing takes practical leap
      3. Quantum Computation Archive
      4. 1.3 Quantum Computation
      5. Amazon.com: Table of Contents: Introduction to Quantum Computers
      6. XRCE People: Marc Dymetman

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   R
   
   1. M.R. Rayner, D.J. Newton, "On the Symmetry of Logic", Journal of Physics A: Mathematical and General, 28 (1995), pp. 5623-5631.
   2. A.L. Ressler, - Practical Circuits Using Conservative Reversible Logic, Bachelor's Thesis, MIT 1979.
   3. ROSKA:
      1. ROSKA: Roska
   4. HARVEY RUBIN:
      1. Harvey Rubin: Reversible Computation Using DNA

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4. PETER SHOR:
   1. http://www.research.att.com/~shor/linklist.html Peter Shor's Links, Quantum Computation Pages.
5. SINGHAI: Bookmarks for Ashish Singhai
6. SANTA FE:
   1. Santa Fe.
7. G. Stix, "Riding the back of electrons"; Scientific American, 279 (September 1998), pp. 20-21.
8. J. Shamir, H. J. Caulfield,
9. W. Micelli, W., and R.I. Seymour, "Optical Computing and the Fredkin Gates", Applied Optics, 25, pp. 1604-1607, 1986.
10. SMOLIN:
    1. J.A. Smolin, and D.P. DiVincenzo, "Five Two-Bit Quantum Gates are sufficient to Implement the Quantum Fredkin Gate", Physical Review A, 53, pp. 2855-2856.
11. STANDORD-BERKELEY-MIT-IBM:
    1. Stanford, Berkeley, MIT, IBM - NMR QUANTUM COMPUTATION PROJECT WEB PAGE.
12. TSUTOMU SASAO:
    Prof. Tsutomu Sasao, University of Kyushu, Japan: HOMEPAGE
    1. Sasao and Kinoshita consider the gates where the number of 1's in the inputs is equal to the number of 1's in the outputs. No fanout is permitted. Constant 1 is expensive. In the last paper, they consider the case where the number of 0's in the inputs is equal to the number of 0's in the outputs in addition to the restrictions above.
    2. TI = On magnetic bubble logic circuits
       
       AU = Kinoshita, K., Sasao, T., Matsuda, J. (Dept. of Electronic Engng., Osaka Univ., Osaka, Japan)
       
       SO = IEEE Trans. Comput. (USA), vol.C-25, no.3, 247-53, MARCH 1976
       
       AB = This paper is concerned with the realisation of logic functions by using two-input magnetic bubble logic elements. A magnetic bubble logic element is the multiple-output logic element whose number of '1''s of the output is equal to that of corresponding input, and fanout of each output terminal of the element is restricted to one. In order to realize some functions, it is necessary to use the generators which correspond to constant-supplying elements. First, the number of generators which are necessary and sufficient to realize an arbitrary functions is obtained for a given set of elements. In particular, it is shown that an arbitrary function can be realized by using I/sub B/ elements and at most two generators. Since the I/sub B/ element is a universal element in the above sense and is considered to be rather easily realized by magnetic bubble interactions, the I/sub B/ logic circuits are mainly discussed. The I/sub B/ minimum circuit defined is a circuit which consists of minimum number of generators and minimum number of I/sub B/ elements. In the last half of this paper, it is shown that the minimum circuits of most functions have the characteristic circuit structure called '1-4 form.'.
    3. TI = Cascade realization of 3-input 3-output conservative logic circuits
       
       AU = Sasao, T., Kinoshita, K. (Dept. of Electronic Engng., Osaka Univ., Osaka, Japan)
       
       SO = IEEE Trans. Comput. (USA), vol.C-27, no.3, 214-21, MARCH 1978
       
       AB = A conservative logic element (CLE) is a multiple-output logic element whose weight of an input vector is equal to that of the corresponding output vector, and is a generalized model of magnetic bubble logic elements, fluid logic elements, and so on. This paper considers the problem of realizing arbitrary 3-input 3-output conservative logic elements (3-3 CLCs) by cascade connections of 3-input 3-output CLEs called 'primitives'. It is shown that the necessary and sufficient number of different primitives to realize an arbitrary 3-3 CLC is three in the case when the crossovers of lines are permitted, and four in the case when the crossovers of lines are not permitted.
    4. TI = Realization of minimum circuits with two-input conservative logic elements
       
       AU = Sasao, T., Kinoshita, K. (Dept. of Electronic Engng., Osaka Univ., Osaka, Japan)
       
       SO = IEEE Trans. Comput. (USA), vol.C-27, no.8, 749-52, Aug. 1978
       
       AB = This correspondence is concerned with the realization of logical functions by using two input three output conservative logic elements called I/sub B/. A conservative logic element is a multiple-output logic element whose number of '1s' of the input is equal to that of the corresponding output, and whose fan out of each output terminal is restricted to one. In order to realize arbitrary functions, it is necessary to use constant-supplying elements C/sub 1/s. The minimum circuit is a circuit which consists of minimum number of C/sub 1/s and minimum number of I/sub B/ elements. This correspondence gives lower bounds on the number of I/sub B/ elements in the circuit and two minimum decomposition theorems. These results are useful for the verification of the minimality of a given circuit and for the realization of minimum circuits. Several examples illustrate this.
    5. TI = Conservative logic elements and their universality
       
       AU = Sasao, T., Kinoshita, K. (Dept. of Electronic Engng., Osaka Univ., Osaka, Japan)
       
       SO = IEEE Trans. Comput. (USA), vol.C-28, no.9, 682-5, Sept. 1979
       
       AB = A conservative logic element (CLE) is a multiple-output logic element whose weight of an input vector is equal to that of the corresponding output vector, and fan-out of each output terminal is restricted to one.
       
       A CLE is a generalized model of magnetic bubble logic elements, etc. In order to realize an arbitrary function, it is necessary to use constant-supplying elements (CSEs).