Boolean differential calculus concepts are analogous to those of classical
differential calculus, notably studying the changes in functions and variables with respect to another/others.[1]
Since then, significant advances were accomplished in both, the theory and in the application of the BDC in switching circuit design and
logic synthesis.
Boolean
differential operators play a significant role in BDC. They allow the application of
differentials as known from classical
analysis to be extended to logical functions.
The differentials of a Boolean variable models the relation:
There are no constraints in regard to the nature, the causes and consequences of a change.
The differentials are binary. They can be used just like common
binary variables.
^Huffman, David Albert (1958-01-15). "Solvability criterion for simultaneous logical equations". Quarterly Progress Report. Cambridge, MA, USA: MIT Research Laboratory of Electronics (48): 87–88. AD 156-161. (2 pages)
^
abcSellers Jr., Frederick F.; Hsiao, Mu-Yue; Bearnson, Leroy W. (November 1968). Error Detecting Logic for Digital Computers (1st ed.). New York, USA:
McGraw-Hill Book Company. pp. 17–37.
LCCN68-16491.
OCLC439460. (21 of xviii+295 pages)
^
abThayse, André (February 1971).
"Boolean Differential Calculus"(PDF). Philips Research Reports. Brussels, Belgium:
Philips Research Laboratory. 26 (2): 229–246. R764. Archived from
the original(PDF) on 2017-03-08. Retrieved 2017-10-16. […] Abstract: After a brief outline of classical concepts relative to Boolean differential calculus, a theoretical study of various differential operators is undertaken. Application of these concepts to several important problems arising in switching practice is mentioned. […] Acknowledgement: The author is especially grateful to Dr
M. Davio for his encouragement and support and for several ideas in the presentation. […] (18 pages)
^Steinbach, Bernd[in German]; Posthoff, Christian (2013-07-01). Thornton, Mitchell A. (ed.). Boolean Differential Equations. Synthesis Lectures on Digital Circuits and Systems (1st ed.). San Rafael, CA, USA: Morgan & Claypool Publishers.
doi:
10.2200/S00511ED1V01Y201305DCS042.
ISBN978-1-62705-241-2. Lecture #42. (158 pages)
^Scheuring, Rainer; Wehlan, Herbert "Hans" (1991-09-01). Franke, Dieter; Kraus, Franta (eds.). "On the Design of Discrete Event Dynamic Systems by Means of the Boolean Differential Calculus". First IFAC Symposium on Design Methods of Control Systems. Zürich, Switzerland:
International Federation of Automatic Control (IFAC) /
Pergamon Press. 2: 723–728.
doi:
10.1016/S1474-6670(17)54214-7. (6 pages)
^Ânuškevič [Yanushkevich], Svitlana N. [Svetlana N.] (1998). Logic Differential Calculus in Multi-Valued Logic Design. Journal Prace Naukowe Politechniki Szczecińskiej (PhD thesis) (1st ed.). Szczecin, Poland: Instytut Informatyki, Technical University of Szczecin.
ISBN978-8-387423-16-2.
ISSN1506-3054.
ISBN8-387423-16-5. (326 pages)
^Steinbach, Bernd[in German]; Posthoff, Christian (2017-06-07). Thornton, Mitchell A. (ed.). Boolean Differential Calculus. Synthesis Lectures on Digital Circuits and Systems (1st ed.). San Rafael, CA, USA: Morgan & Claypool Publishers.
doi:
10.2200/S00766ED1V01Y201704DCS052.
ISBN978-1-62705-922-0. Lecture #52. (216 pages)
Further reading
Davio, Marc; Piret, Philippe M. (July 1969). "Les dérivées Booléennes et leur application au diagnostic" [Boolean derivatives and their application and diagnosis]. Philips Revue (in French). Brussels, Belgium:
Philips Research Laboratory, Manufacture Belge de Lampes et de Materiel Electronique (MBLE Research Laboratory). 12 (3): 63–76. (14 pages)
Bochmann, Dieter[in German] (1977). "Boolean differential calculus (a survey)". Engineering Cybernetics.
Institute of Electrical and Electronics Engineers (IEEE). 15 (5): 67–75.
ISSN0013-788X. (9 pages) Translation of:
Bochmann, Dieter[in German] (1977). "[Boolean differential calculus (survey)]". Известия Академии наук СССР – Техническая кибернетика (Izvestii︠a︡ Akademii Nauk SSSR – Tekhnicheskai︠a︡ kibernetika) [Proceedings of the Academy of Sciences of the USSR – Engineering Cybernetics] (in Russian) (5): 125–133. (9 pages)
Kühnrich, Martin (1986) [1984-07-31 (submission)]. "Differentialoperatoren über Booleschen Algebren" [Differential operators on Boolean algebras]. Zeitschrift für mathematische Logik und Grundlagen der Mathematik (in German). Berlin, Germany (East). 32 (17–18): 271–288.
doi:
10.1002/malq.19860321703. #18. (18 pages)
Dresig, Frank (1992). Gruppierung – Theorie und Anwendung in der Logiksynthese [Grouping – Theory and application in logic synthesis]. Fortschritt-Berichte VDI. 9 (in German). Vol. 145. Düsseldorf, Germany:
VDI-Verlag.
ISBN3-18-144509-6.
DNB-IDN940164671. (NB. Also: Chemnitz, Technische Universität, Dissertation.) (147 pages)
Scheuring, Rainer; Wehlan, Herbert "Hans" (1993). "Control of Discrete Event Systems by Means of the Boolean Differential Calculus". In Balemi, Silvano; Kozák, Petr; Smedinga, Rein (eds.). Discrete Event Systems: Modeling and Control. Progress in Systems and Control Theory (PSCT). Vol. 13. Basel, Switzerland:
Birkhäuser Verlag. pp. 79–93.
doi:
10.1007/978-3-0348-9120-2_7. (15 pages)