Abstract
New reduction methods for solving large systems of logical equations are described and analyzed. Results of computer-aided experiments are presented.
Similar content being viewed by others
REFERENCES
Ledley, R., Programming and Utilizing Digital Computers, New York: McGraw-Hill, 1962. Translated under the title Programmirovanie i ispol'zovanue tsifrovykh vychislitel'nykh mashin, Moscow: Mir, 1966.
Rudeanu, S., Boolean Functions and Equations, Amsterdam: Elsevier, 1974.
Zakrevskii, A.D., Logicheskie uravneniya (Logical Equations), Minsk: Nauka i Tekhnika, 1975.
Bochmann, D., Zakrevskij, A.D., and Posthofi, H., Boolesche Gleichungen, Berlin: VEB Verlag Technik, 1984.
Teoriya diskretnykh upravlyayushchikh ustroistv (Theory of Discrete Control Devices), Zakrevskii, A.D. and Prangishvili, I.V., Eds., Moscow: Nauka, 1982.
Zakrevskii, A.D., Algoritmy sinteza diskretnykh avtomatov (Algorithms for Designing Discrete Automata), Moscow: Nauka, 1971.
Osnovy tekhnicheskoi diagnostiki (Elements of Technical Diagnostics), Parkhomenko, P.P., Ed., Moscow: Energiya, 1976.
Chang, C. and Lee, R., Symbolic Logic and Mechanical Theorem, Proving, New York: Academic, 1973. Translated under the title Matematicheskaya logika i avtomaticheskoe dokazatel'stvo teorem, Moscow: Nauka, 1983.
Zakrevskij, A.D., Pattern Recognition as Solving Logical Equations, SSIT'99 (AMSE), pp. 125–136.
Baumann, M., Rohde, R., and Barthel, R., Cryptoanalysis of the Hagelin M-209 Machine, Proc. 3 Int. Workshop on Boolean Problems, Freiberg (Sachsen), 1998, pp. 109–116.
Nilsson, N.J., Problem-Solving Methods in Artificial Intelligence, New York: McGraw-Hill, 1971. Translated under the title Iskusstvennyi intellekt, metody poiska i reshenii, Moscow: Mir, 1973.
Zakrevskij, A. and Zakrevski, L., Solving Systems of Logical Equations Using Search Tree Minimization Technique, Proc. PDPTA'02 Int. Conf., Las Vegas, USA, 2002, pp. 1145–1150.
Cherry, C. and Vaswani, P.K., A New Type of Computer in Propositional Logic with Greatly Reduced Scanning Procedures, Inf. & Control, 1961, vol. 4, no. 3, pp. 155–168.
Zakrevskij, A. and Vasilkova, I., Reducing Large Systems of Boolean Equations, Proc. 4th Int. Workshop on Boolean Problems, Freiberg, Germany, 2000, pp. 21–28.
Zakrevskij, A.D. and Vasilkova, I.V., Cryptanalysis of the Hagelin Machine: A Solution Method for a System of Logical Equations, in Kompleksnaya zashchita informatsii (Overall Data Protection), Minsk: Inst. Tekh. Kibern., 1999, vol. 2, pp. 129–138.
Zakrevskii, A.D., Reduction of Large Systems of Logical Equations: A Syllogism Method, Avtomat. Vychisl. Tekh., 2000, no. 5, pp. 32–39.
Zakrevskii, A.D., Solution of Systems of Logical Equations by the Local Reduction Method, Dokl. Belarus. Nat. Akad. Nauk, 1999, vol. 43, no. 5, pp. 5–8.
Zakrevskii, A.D., The “Reected Waves” Method for Solving Logical Equations, Proc. III Int. Seminar on Applied Aspects of Automata Theory, Varna, 1975, vol. 1, pp. 81–84.
Zakrevskii, A.D. and Vasil'kova, I.V., Cryptanalysis of the HAGELIN Machine: A Method for Solving Systems of Logical Equations, Proc. Interdepartment Conf. “National Security: Management and Information of Support Technology”, Minsk, 2000, pp. 213–216.
Lukasevich, Ya., Aristotelevskaya sillogistika s tochki zreniya sovremennoi logiki (Aristotle's Syllogistic from the Viewpoint of Modern Logic), Moscow: Inostrannaya Literatura, 1959.
Zakrevskii, A.D., Polysyllogism Theory, Dokl. Belarus. Nat. Akad. Nauk, 1974, vol. 18, no. 2, pp. 114–117.
Zakrevskii, A.D., K formalizatsii polisillogistiki: logicheskii vyvod (Formalization of Polysyllologistic: A Logical Inference), Moscow: Nauka, 1979.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Zakrevskii, A.D. Logical Equations with Applications to Automatic Design and Control. Automation and Remote Control 65, 660–670 (2004). https://doi.org/10.1023/B:AURC.0000023543.02315.f5
Issue Date:
DOI: https://doi.org/10.1023/B:AURC.0000023543.02315.f5