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Nonlinear pseudo-boolean equations and inequalities

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Pseudo-Boolean Methods for Bivalent Programming

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References

  1. G. BIRKHOFF: Lattice Theory. Amer. Math. Soc. Coll. Publ. New York 1948 (reprint 1961).

    MATH  Google Scholar 

  2. M. CARVALLO: Principes et applications de l'analyse booléenne. Gauthier-Villars, Paris 1965.

    MATH  Google Scholar 

  3. G.B. DANTZIG: Linear Programming and Extensions, Ch.26. Princeton Univ. Press, Princeton, 1963.

    Book  MATH  Google Scholar 

  4. R. FORTET: L'algèbre de Boole et ses applications en recherche opérationnelle. Cahiers Centre Etudes Rech. Opér., 1, No. 4, 5–36 (1959).

    MathSciNet  MATH  Google Scholar 

  5. Ju.I. GRIGORIAN: Algorithm for the Solution of Logical Equations (in Russian). Jurn. vycislit. mat. i mat. fiziki, 2, 186–189 (1962).

    Google Scholar 

  6. M. ITOH: On Boolean Equations with Many Unknowns and the Generalized Poretsky's Formula. Rev. Univ. Nac. Tucumán, 12, 107–112 (1959).

    Google Scholar 

  7. P.L. IVANESCU: Systems of Pseudo-Boolean Equations and Inequalities. Bull. Acad. Polon. Sci. Ser. Math. Astronom. Phys., 12, 673–680 (1964).

    MathSciNet  MATH  Google Scholar 

  8. P.L. IVANESCU: The Method of Succesive Eliminations for Pseudo-Boolean Equations. Bull. Acad. Polon. Ser. Sci. Math. Astronom. Phys., 12, 681–683 (1964).

    MathSciNet  MATH  Google Scholar 

  9. P.L. IVANESCU and S. RUDEANU: The Theory of Pseudo-Boolean Programming. I. Linear Pseudo-Boolean Equations and Inequalities. SIAM Journal (in press).

    Google Scholar 

  10. J. KLÍR: Solutions of System of Boolean Equations (in Czech.), Apl. Mat. 7, 265–273 (1962).

    MathSciNet  MATH  Google Scholar 

  11. R.S. LEDLEY: Digital Computers and Control Engineering. Mc. Graw Hill, New York, 1960.

    Google Scholar 

  12. L. LÖWENHEIM: Über Auflösungsproblem im logischen Klassenkalkul. Sitzungsber. Berl. Math. Geselschaft, 7, 89–94 (1908).

    MATH  Google Scholar 

  13. K.K. MAITRA: A Map Approach to the Solution of a Class of Boolean Functional Equations. Communic. Electr. No. 59, 34–36 (1962).

    Google Scholar 

  14. M. NADLER and B. ELSPAS: The Solution of Simultaneous Boolean Equations. IRE Trans. Communication Theory 7, No. 3 (1960).

    Google Scholar 

    Google Scholar 

  15. L. NÉMETI: Das Reihenfolgsproblem in der Fertigungsprogrammierung und Linearplanung mit logischen Bedingungen. Mathematica (Cluj), 6(29), 87–99, (1964).

    MATH  Google Scholar 

  16. L. NÉMETI, F. RADÓ: Ein Wartezeitproblem in der Programmierung der Produktion. Mathematika (Cluj), 5(28), 65–95 (1963).

    MathSciNet  MATH  Google Scholar 

  17. J. POSTLEY: A Method for the Evaluation of a System of Boolean Algebraic Equations. Math. Tables and Other Aids to Computations, 9, 5–8 (1955).

    Article  MathSciNet  MATH  Google Scholar 

  18. F. RADÓ: Linear Programming with Logical Conditions (in Romanian). Comunicârile Acad. RPR, 13, 1039–1042 (1963).

    MathSciNet  MATH  Google Scholar 

  19. F. RADÓ: Un algorithme pour résoudre certains problèmes de programmation mathématiques. Mathematica (Cluj), 6(29), 105–116 (1964).

    MathSciNet  MATH  Google Scholar 

  20. N. ROUCHE: Some Properties of Boolean Equations. IRE Trans. Electronic Computers, 7, 291–298 (1958).

    Article  Google Scholar 

  21. S. RUDEANU: On the Solution of Boolean Equations by the Löwenheim Method (in Romanian). Stud. Cerc. Mat., 13, 295–308 (1962).

    MathSciNet  MATH  Google Scholar 

  22. S. RUDEANU: Remarks on Motinori Goto's Papers on Boolean Equations. Rev. Roumaine Math. Pures Appl., 10, 311–317 (1965).

    MathSciNet  MATH  Google Scholar 

  23. S. RUDEANU: Irredundant Solutions of Boolean and Pseudo-Boolean Equations. Rev. Roumaine Math. Pures Appl. (in press).

    Google Scholar 

  24. E.L. SCHUBERT: Simultaneous Logical Equations. Comm. and Electronics, No. 46, 1080–1083 (1960).

    Google Scholar 

  25. W. SEMON: A Class of Boolean Equations. Sperry Rand. Research Corp., SRCC-RR-62-17, August 1962.

    Google Scholar 

  26. A. SVOBODA and K. ČULIK: An Algorithm for Solving Boolean Equations (in Russian). Avtomat. i Telemeh. 25, 374–381, (1964).

    MathSciNet  MATH  Google Scholar 

  27. A. ŽELEZNIKAR: Behandlung logistischer Probleme mit Ziffernrechner. Glasnik Mat.-Fiz.-Astronom, 17, 171–179 (1962).

    MathSciNet  MATH  Google Scholar 

  28. H. ZEMANEK: Die Lösung von Gleichungen in der Schaltalgebra. Arch. Elektr. Ubertragung, 12, 35–44 (1958).

    Google Scholar 

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© 1966 Springer-Verlag

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Ivănescu, P.L., Rudeanu, S. (1966). Nonlinear pseudo-boolean equations and inequalities. In: Pseudo-Boolean Methods for Bivalent Programming. Lecture Notes in Mathematics, vol 23. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0077206

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  • DOI: https://doi.org/10.1007/BFb0077206

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