Abstract
In a preceding paper an NP-complete problem has been discussed pertaining to a function, called “core function”, which plays an important role in the well known Boolean satisfiability problem (see the first item in the references list). In this paper, some theorems concerning the minimal Boolean implementation of the core function are proved.
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References
Meo, A.R.: On the minimization of core function Acc. Sc. Torino – Memorie Sc. Fis. 29, 155–178, 7 ff. (2005)
Sipser, M.: Introduction to the theory of computation, PWS Publ.Comp. (1997)
Smale, S.: Mathematical problems for the next century. Mathematical Intelligencer 20(2), 7–15 (1998)
Garey, M.R., Johnson, D.S.: Computers and intractability. W.H.Freeman and Co., New York (1979)
Asser, G.: Das Reprasentantenproblem im Pradikatenkalkul der ersten Stufe mit Identitat, Zietschr.f.Mathematisches Logik u. Grundlagen der Math. 1, 252–263 (1955)
Cook, S.A.: The complexity of theorem proving procedures. In: Proc. 3rd Annual ACM Symp. on Theory of Computing, pp. 151–158. ACM Press, New York (1971)
Cook, S.A.: Computational complexity of higher type functions. In: Sarake, I. (ed.) Proceeding of the International Congress of Mathematicians, Kyoto, Japan, pp. 55–60. Springer, Heidelberg (1991)
Godel, K.: A letter to J.von Neumann, in Sipser’s article listed above. In: Clote, P., Krajicek, J. (eds.) Arithmetic, Proof Theory and Computational Complexity, Oxford University Press, Oxford (1993)
Karp, R.M.: Reducibility Among Combinatorial Problems, Complexity of Computer Computations, pp. 85–103. Plenum Press (1972)
Levin, L.: Universal Search Problems. Problemy Peredachi Informatsii (= Problems of Information Transmission) 9(3), 265–266 (in Russian) (1973); A partial English transalation, In: Trakhtenbrot, B.A.: A Survey of Russian Approches to Perebor (Brute-force Search) Algorithms. Annals of the History of Computing 6(4), 384–400 (1984)
Scholz, H.: Problem #1: Ein ungelostes Problem in der symbolisches Logik. Symbolic Logic 17, 160 (1952)
Sipser, M.: The history and status of the P versus NP question. In: Proceedings of the 24th Annual ACM Symposium on Theory of Computing, pp. 603–618. ACM Press, New York (1992)
Baker, T., Gill, J., Solovay, R.: Relativizations of the P =? NP question. IAM J. of Computing 4, 431–442 (1975)
Boppana, R., Sipser, M.: Complexity of finite functions. In: van Leeuwen, J. (ed.) Handbook of heoretical Computer Science, pp. 758–804 (1990)
Krajicek, J.: Bounded arithmetic, propositional logic, and omplexity theory, Encyclopedia of Mathematics and Its Applications, vol. 60. Cambridge University Press, Cambridge (1995)
Pudlak, P.: The lengths of proofs. In: Buss, S.R. (ed.) Handbook of Proof Theory, North-Holland, Amsterdam (1998)
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Meo, A.R. (2008). Some Theorems Concerning the Core Function. In: Degano, P., De Nicola, R., Meseguer, J. (eds) Concurrency, Graphs and Models. Lecture Notes in Computer Science, vol 5065. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68679-8_48
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DOI: https://doi.org/10.1007/978-3-540-68679-8_48
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