Abstract
Problems of inversion of discrete functions that are deterministically computable for polynomial time is considered. The propositional approach, which is based on the technique of representation of algorithms as systems of logical equations, is applied.
Similar content being viewed by others
References
A. A. Semenov and E. V. Buranov, “Emdeding of the Problem of Cryptoanalysis of Symmetric Ciphers in Propositional Logic,” in Computational Technologies (Joint Issue with Journal “Regional’nyi Vestnik Vostoka”) 8, 118–126 (2003).
A. A. Semenov, “A Logical-Heuristic Approach in Cryptoanalysis of generators of Double Sequences,” in Proceedings of International Conference PAVT’07 (Izd-vo YuUrGU, Chelyabinsk, 2007), Vol. 1, pp. 170–180 [in Russian].
O. S. Zaikin and A. A. Semenov, “Technology of Large-Block Parallelism in SAT-Problems,” Problemy Upravleniya, No. 1, 43–50 (2008).
A. A. Semenov and O. S. Zaikin, “Incomplete Algorithms in Large-Block Parallelism of Combinatorial Problems,” Vychisl. Metody Program. 9(1), 112–122 (2008).
SatLive [http://www.satlive.org].
E. M. Clark, O. Gramberg, and D. Peled, Verification of Models of Programs: Model Checking (MTsNMO, Moscow, 2002) [in Russian].
N. Catland, Computability. Introduction to the Theory of Recursive Functions (Mir, Moscow, 1983) [in Russian].
M. R. Garey and D. S. Johnson, Computers and Intractability: The Guide to the Theory of NP-Completeness (Freeman, San Francisco, 1979; Mir, Moscow, 1982).
A. A. Semenov, “On Complexity of Inverting a Discrete Function from a Class,” Diskretnyi Analiz i Issledovanie Operatsii, Ser. 1. 11(4), 44–55 (2004).
S. V. Yablonskii, Introduction to Discrete Mathematics (Nauka, Moscow, 1986) [in Russian].
S. A. Cook, “The Complexity of Theorem-Proving Procedures” in Proceedings of 3rd Annual ACM Symposium on Theory of Computing, ACM, Ohio, USA, 1971, pp. 151–159.
C. H. Papadimitriou, and K. Steiglitz, Combinatorial Optimization: Algorithms and Complexity (Prentice-Hall, Englewood Cliffs, 1982; Mir, Moscow, 1985).
J. Simon, On Some Central Problems in Computational Complexity, Doctoral Thesis. Dept. of Computer Science (Cornel University, Ithaca, N.Y., 1975).
G. S. Tseitin, “On the Complexity of Inference in Propositional Calculus,” Zap. Nauchn. Seminarov LOMI AN SSSR 8, 234–259 (1968).
G. Tseitin, “On the Complexity of Derivation in Propositional Calculus,” Studies in Constructive Mathematics and Mathematical Logic, No. 2, 115–125 (1968).
F. Massacci and L. Marraro, “Logical Cryptanalysis as a SAT Problem: the Encoding of the Data Encryption Standard,” Preprint No. Dipartimento di Imformatica e Sistemistica. Universita di Roma “La Sapienza”, 1999.
M. Davis, G. Logemann, and D. Loveland, “A Machine Program for Theorem Proving,” Commun. ACM 5, 394–397 (1962).
J. P. Marqeus-Silva and K. A. Sakallah, “GRASP: A Search Algorithm for Propositional Satisfiability,” IEEE Trans. Comput. 48(5), 506–521 (1999).
MiniSat: [http://www.cs.chalmers.se/Cs/Research/FormalMethods/MiniSat/MiniSat.html].
M. Moskewicz and C. Madigan, et al., “Chaff: Engineering an Efficient SAT Solver,” in Proceedings of Design Automation Conference (DAC). LAS Vegas, USA, 2001.
E. Goldberg and Y. Novikov, “BerkMin: A Fast and Robust SAT Solver,” in Design Automation and Test in Europe (DATE) (Paris, 2002), pp. 142–149.
Ch. Meinel and T. Theobald, Algorithms and Data Structures in VLSI-Design: OBDD-Foundations and Applications (Springer, Berlin, 1998).
R. E. Bryant, “Graph-Based Algorithms for Boolean Function Manipulation,” IEEE Trans. Comput. 35(8), 677–691 (1986).
C. Y. Lee, “Representation of Switching Circuits by Binary-Decision Programs,” Bell Syst. Techn. J. 38, 985–999 (1959).
A. Tay, P. Gribomont, J. Lui, et al., Logical Approach to Artificial Intelligence (Mir, Moscow, 1991) [in Russian].
A. Kolmeroe, A. Kanui, and M. Kanegem, “Prolog—Theoretical Foundations and Modern Development,” in Logical Programming (Mir, Moscow, 1988), pp. 27–133 [in Russian].
L. Stockmeyer, “Classifying of Computational Complexity of Problems,” J. Symbolic Logic 52(1), 1–43 (1987).
J. F. Groote and H. Zantema, “Resolution and Binary Decision Diagrams Cannot Simulate Each Other Polynomially,” J. Discr. Appl. Math. 130(2), 157–171 (2003).
D. Kocks, D. Little, and D. Shi, Ideals, Manifolds, and Algorithms (Mir, Moscow, 2000) [in Russian].
R. G. Nigmatullin, Complexity of Boolean Functions (Nauka, Moscow, 1991) [in Russian].
L. G. Valiant, “The Complexity of Enumeration and Reliability Problems,” SIAM J. Comput. 8(3), 410–421 (1979).
T. Cormen, Ch. Laserson, and R. Rivest, Algorithms. Construction and Analysis (MTsNMO, Moscow, 2001) [in Russian].
Author information
Authors and Affiliations
Additional information
Original Russian Text © A.A. Semenov, 2009, published in Izvestiya Akademii Nauk. Teoriya i Sistemy Upravleniya, 2009, No. 5, pp. 47–61.
Rights and permissions
About this article
Cite this article
Semenov, A.A. Decomposition representations of logical equations in problems of inversion of discrete functions. J. Comput. Syst. Sci. Int. 48, 718–731 (2009). https://doi.org/10.1134/S1064230709050062
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1064230709050062