NP-intermediate (Redirected from Ladner's theorem) Jump to navigation Jump to search In computational complexity, problems that are in the complexity class NP but are neither in the class P nor NP-complete are called NP-intermediate, and the class of such problems is called NPI. Ladner's theorem, shown in 1975 by Richard E. Ladner,[1] is a result asserting that, if P ≠ NP, then NPI is not empty; questo è, NP contains problems that are neither in P nor NP-complete. Since it is also true that if NPI problems exist, then P ≠ NP, it follows that P = NP if and only if NPI is empty.

Under the assumption that P ≠ NP, Ladner explicitly constructs a problem in NPI, although this problem is artificial and otherwise uninteresting. It is an open question whether any "naturale" problem has the same property: Schaefer's dichotomy theorem provides conditions under which classes of constrained Boolean satisfiability problems cannot be in NPI.[2][3] Some problems that are considered good candidates for being NP-intermediate are the graph isomorphism problem, factoring, and computing the discrete logarithm.

Contenuti 1 List of problems that might be NP-intermediate 1.1 Algebra and number theory 1.2 Boolean logic 1.3 Computational geometry and computational topology 1.4 Game theory 1.5 Graph algorithms 1.6 Miscellaneous 2 Riferimenti 3 External links List of problems that might be NP-intermediate Algebra and number theory Factoring integers Discrete Log Problem and others related to cryptographic assumptions Isomorphism problems: Group isomorphism problem, Group automorphism, Ring isomorphism, Ring automorphism Linear divisibility: given integers {stile di visualizzazione x} e {stile di visualizzazione y} , does {stile di visualizzazione y} have a divisor congruent to 1 modulo {stile di visualizzazione x} ?[4][5] Boolean logic IMSAT, the Boolean satisfiability problem for "intersecting monotone CNF": conjunctive normal form, with each clause containing only positive or only negative terms, and each positive clause having a variable in common with each negative clause[6] Minimum Circuit Size Problem[7] Monotone self-duality: given a CNF formula for a Boolean function, is the function invariant under a transformation that negates all of its variables and then negates the output value?[8] Computational geometry and computational topology Computing the rotation distance[9] between two binary trees or the flip distance between two triangulations of the same convex polygon The turnpike problem of reconstructing points on line from their distance multiset[10] The cutting stock problem with a constant number of object lengths[11] Knot triviality[12] Finding a simple closed quasigeodesic on a convex polyhedron[13] Game theory Determining winner in parity games, in which graph vertices are labeled by which player chooses the next step, and the winner is determined by the parity of the highest-priority vertex reached[14] Determining the winner for stochastic graph games, in which graph vertices are labeled by which player chooses the next step, or whether it is chosen randomly, and the winner is determined by reaching a designated sink vertex.[15] Graph algorithms Graph isomorphism problem[16] Planar minimum bisection[17] Deciding whether a graph admits a graceful labeling[18] Recognizing leaf powers and k-leaf powers[19] Recognizing graphs of bounded clique-width[20] Finding a simultaneous embedding with fixed edges[21] Miscellaneous Problems in TFNP[22] Pigeonhole subset sum: dato {stile di visualizzazione n} positive integers whose sum is less than {stile di visualizzazione 2 ^{n}-1} , find two distinct subsets with the same sum[23] Finding the Vapnik–Chervonenkis dimension of a given family of sets[24] References ^ Ladner, Richard (1975). "On the Structure of Polynomial Time Reducibility". Giornale dell'ACM. 22 (1): 155–171. doi:10.1145/321864.321877. S2CID 14352974. ^ Grädel, Erich; Kolaitis, Phokion G.; Libkin, Leonide; Marx, Maarten; Spencer, Joel; Vardi, Moshe Y.; Venema, Yde; Weinstein, Scott (2007). Finite model theory and its applications. Texts in Theoretical Computer Science. An EATCS Series. Berlino: Springer-Verlag. p. 348. ISBN 978-3-540-00428-8. Zbl 1133.03001. ^ Schäfer, Thomas J. (1978). "La complessità dei problemi di soddisfacibilità" (PDF). Proc. 10th Ann. ACM Symp. on Theory of Computing. pp. 216–226. SIG 0521057. ^ Adleman, Leonardo; Manders, Kenneth (1977). "Reducibility, randomness, and intractibility". Proceedings of the 9th ACM Symp. on Theory of Computing (STOC '77). doi:10.1145/800105.803405. ^ Papadimitriou, Christos H. (1994). Complessità computazionale. Addison-Wesley. p. 236. ISBN 9780201530827. ^ Eiter, Tommaso; Gottlob, Georg (2002). "Hypergraph transversal computation and related problems in logic and AI". In Flesca, Sergio; Greco, Sergio; Leone, Nicola; Ianni, Giovambattista (eds.). Logics in Artificial Intelligence, European Conference, JELIA 2002, Cosenza, Italia, settembre, 23-26, Atti. Appunti delle lezioni in Informatica. vol. 2424. Springer. pp. 549–564. doi:10.1007/3-540-45757-7_53. ^ Kabanets, Valentine; Cai, Jin-Yi (2000). "Circuit minimization problem". Proc. 32nd Symposium on Theory of Computing. Portland, Oregon, Stati Uniti d'America. pp. 73–79. doi:10.1145/335305.335314. S2CID 785205. ECCC TR99-045. ^ Eiter, Tommaso; Makino, Kazuhisa; Gottlob, Georg (2008). "Computational aspects of monotone dualization: a brief survey". Discrete Applied Mathematics. 156 (11): 2035–2049. doi:10.1016/j.dam.2007.04.017. SIG 2437000. S2CID 10096898. ^ Sleator, Daniel D.; Tarjan, Robert E.; Thurston, Guglielmo P. (1988). "Rotation distance, triangulations, and hyperbolic geometry". Giornale della Società matematica americana. 1 (3): 647–681. doi:10.2307/1990951. JSTOR 1990951. SIG 0928904. ^ Skiena, Stefano; fabbro, Warren D.; Lemke, Paolo (1990). "Reconstructing Sets from Interpoint Distances (Extended Abstract)". In Seidel, Raimund (ed.). Proceedings of the Sixth Annual Symposium on Computational Geometry, Berkeley, circa, Stati Uniti d'America, Giugno 6-8, 1990. ACM. pp. 332–339. doi:10.1145/98524.98598. ^ Jansen, Klaus; Solis-Oba, Roberto (2011). "A polynomial time OPT + 1 algorithm for the cutting stock problem with a constant number of object lengths". Mathematics of Operations Research. 36 (4): 743–753. doi:10.1287/moor.1110.0515. SIG 2855867. ^ Lackenby, marc (2021). "The efficient certification of knottedness and Thurston norm". Progressi in matematica. 387: Paper No. 107796. arXiv:1604.00290. doi:10.1016/j.aim.2021.107796. SIG 4274879. S2CID 119307517. ^ Demaine, Eric D.; O'Rourke, Joseph (2007). "24 Geodesics: Lyusternik–Schnirelmann". Geometric folding algorithms: Linkages, origami, polyhedra. Cambridge: Cambridge University Press. pp. 372–375. doi:10.1017/CBO9780511735172. ISBN 978-0-521-71522-5. SIG 2354878.. ^ Jurdziński, Marcin (1998). "Deciding the winner in parity games is in UP {cappuccio in stile display } co-UP". Lettere di elaborazione delle informazioni. 68 (3): 119–124. doi:10.1016/S0020-0190(98)00150-1. SIG 1657581. ^ Condon, Anne (1992). "The complexity of stochastic games". Informazione e calcolo. 96 (2): 203–224. doi:10.1016/0890-5401(92)90048-K. SIG 1147987. ^ Grohe, Martino; Neuen, Daniele (Giugno 2021). "Recent advances on the graph isomorphism problem". Surveys in Combinatorics 2021. Cambridge University Press. pp. 187–234. arXiv:2011.01366. doi:10.1017/9781009036214.006. S2CID 226237505. ^ Karpinski, Marek (2002). "Approximability of the minimum bisection problem: an algorithmic challenge". In Diks, Krzysztof; Rytter, Wojciech (eds.). Mathematical Foundations of Computer Science 2002, 27th International Symposium, MFCS 2002, Warsaw, Poland, agosto 26-30, 2002, Atti. Appunti delle lezioni in Informatica. vol. 2420. Springer. pp. 59–67. doi:10.1007/3-540-45687-2_4. ^ Gallian, Joseph A. (Dicembre 17, 2021). "A dynamic survey of graph labeling". Giornale elettronico di combinatoria. 5: Dynamic Survey 6. SIG 1668059. ^ Nishimura, N.; Ragde, P.; Thilikos, D.M. (2002). "On graph powers for leaf-labeled trees". Diario di algoritmi. 42: 69–108. doi:10.1006/jagm.2001.1195.. ^ Fellows, Michael R.; Rosamond, Frances A.; Rotics, Udi; Szeider, Stefano (2009). "Clique-width is NP-complete". SIAM Journal sulla matematica discreta. 23 (2): 909–939. doi:10.1137/070687256. SIG 2519936.. ^ Gassner, Elisabeth; Jünger, Michael; Percan, Merijam; Schäfer, Marco; Schulz, Michael (2006). "Simultaneous graph embeddings with fixed edges". Graph-Theoretic Concepts in Computer Science: 32nd International Workshop, WG 2006, Bergen, Norway, Giugno 22-24, 2006, Revised Papers (PDF). Appunti delle lezioni in Informatica. vol. 4271. Berlino: Springer. pp. 325–335. doi:10.1007/11917496_29. SIG 2290741.. ^ Megiddo, Nimrod; Papadimitriou, Christos H. (1991). "On total functions, existence theorems and computational complexity" (PDF). Theoretical Computer Science. 81 (2): 317–324. doi:10.1016/0304-3975(91)90200-l. SIG 1107721. ^ Papadimitriou, Christos H. (1994). "On the complexity of the parity argument and other inefficient proofs of existence". Giornale di scienze informatiche e dei sistemi. 48 (3): 498–532. doi:10.1016/S0022-0000(05)80063-7. SIG 1279412. ^ Papadimitriou, Christos H.; Yannakakis, Mihalis (1996). "On limited nondeterminism and the complexity of the V-C dimension". Giornale di scienze informatiche e dei sistemi. 53 (2, parte 1): 161–170. doi:10.1006/jcss.1996.0058. SIG 1418886. External links Complexity Zoo: Class NPI Basic structure, Turing reducibility and NP-hardness Lance Fortnow (24 Marzo 2003). "Fondamenti di complessità, Lezione 16: Ladner's Theorem". Recuperato 1 novembre 2013. Categorie: Complexity classes

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