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; das ist, 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 "natürlich" 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.

Inhalt 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 Verweise 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 {Anzeigestil x} und {Anzeigestil y} , does {Anzeigestil y} have a divisor congruent to 1 modulo {Anzeigestil 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: given {Anzeigestil n} positive integers whose sum is less than {Anzeigestil 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". Zeitschrift der ACM. 22 (1): 155–171. doi:10.1145/321864.321877. S2CID 14352974. ^ Grädel, Erich; Kolaitis, Phokion G.; Libkin, Leonid; 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. Berlin: Springer-Verlag. p. 348. ISBN 978-3-540-00428-8. Zbl 1133.03001. ^ Schäfer, Thomas J. (1978). "Die Komplexität von Erfüllbarkeitsproblemen" (Pdf). Proz. 10th Ann. ACM Symp. on Theory of Computing. pp. 216–226. HERR 0521057. ^ Adleman, Leonard; 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). Rechenkomplexität. Addison-Wesley. p. 236. ISBN 9780201530827. ^ Eiter, Thomas; Gottlob, Georg (2002). "Hypergraph transversal computation and related problems in logic and AI". In Flesca, Sergio; Greco, Sergio; Leone, Nicola; Ianni, Giovambattista (Hrsg.). Logics in Artificial Intelligence, European Conference, JELIA 2002, Cosenza, Italien, September, 23-26, Verfahren. Vorlesungsunterlagen in Informatik. Vol. 2424. Springer. pp. 549–564. doi:10.1007/3-540-45757-7_53. ^ Kabanets, Valentine; Cai, Jin-Yi (2000). "Circuit minimization problem". Proz. 32nd Symposium on Theory of Computing. Portland, Oregon, Vereinigte Staaten von Amerika. pp. 73–79. doi:10.1145/335305.335314. S2CID 785205. ECCC TR99-045. ^ Eiter, Thomas; 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. HERR 2437000. S2CID 10096898. ^ Sleator, Daniel D.; Tarjan, Robert E.; Thurston, William P. (1988). "Rotation distance, triangulations, and hyperbolic geometry". Zeitschrift der American Mathematical Society. 1 (3): 647–681. doi:10.2307/1990951. JSTOR 1990951. HERR 0928904. ^ Skiena, Stefan; Schmied, Warren D.; Lemke, Paul (1990). "Reconstructing Sets from Interpoint Distances (Extended Abstract)". In Seidel, Raimund (ed.). Proceedings of the Sixth Annual Symposium on Computational Geometry, Berkeley, CA, Vereinigte Staaten von Amerika, Juni 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". Mathematik der Operationsforschung. 36 (4): 743–753. doi:10.1287/moor.1110.0515. HERR 2855867. ^ Lackenby, Markus (2021). "The efficient certification of knottedness and Thurston norm". Fortschritte in der Mathematik. 387: Paper No. 107796. arXiv:1604.00290. doi:10.1016/j.aim.2021.107796. HERR 4274879. S2CID 119307517. ^ Demaine, Erich 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. HERR 2354878.. ^ Jurdziński, Marcin (1998). "Deciding the winner in parity games is in UP {displaystyle cap } co-UP". Briefe zur Informationsverarbeitung. 68 (3): 119–124. doi:10.1016/S0020-0190(98)00150-1. HERR 1657581. ^ Condon, Anne (1992). "The complexity of stochastic games". Information und Berechnung. 96 (2): 203–224. doi:10.1016/0890-5401(92)90048-K. HERR 1147987. ^ Grohe, Martin; Neuen, Daniel (Juni 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 (Hrsg.). Mathematical Foundations of Computer Science 2002, 27th International Symposium, MFCS 2002, Warsaw, Poland, August 26-30, 2002, Verfahren. Vorlesungsunterlagen in Informatik. Vol. 2420. Springer. pp. 59–67. doi:10.1007/3-540-45687-2_4. ^ Gallian, Joseph A. (Dezember 17, 2021). "A dynamic survey of graph labeling". Elektronische Zeitschrift für Kombinatorik. 5: Dynamic Survey 6. HERR 1668059. ^ Nishimura, N.; Ragde, P.; Thilikos, D.M. (2002). "On graph powers for leaf-labeled trees". Zeitschrift für Algorithmen. 42: 69–108. doi:10.1006/jagm.2001.1195.. ^ Fellows, Michael R.; Rosamond, Frances A.; Rotics, Udi; Szeider, Stefan (2009). "Clique-width is NP-complete". SIAM-Journal für diskrete Mathematik. 23 (2): 909–939. doi:10.1137/070687256. HERR 2519936.. ^ Gassner, Elisabeth; Jünger, Michael; Percan, Merijam; Schäfer, Markus; Schulz, Michael (2006). "Simultaneous graph embeddings with fixed edges". Graph-Theoretic Concepts in Computer Science: 32nd International Workshop, WG 2006, Bergen, Norway, Juni 22-24, 2006, Revised Papers (Pdf). Vorlesungsunterlagen in Informatik. Vol. 4271. Berlin: Springer. pp. 325–335. doi:10.1007/11917496_29. HERR 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. HERR 1107721. ^ Papadimitriou, Christos H. (1994). "On the complexity of the parity argument and other inefficient proofs of existence". Zeitschrift für Computer- und Systemwissenschaften. 48 (3): 498–532. doi:10.1016/S0022-0000(05)80063-7. HERR 1279412. ^ Papadimitriou, Christos H.; Yannakakis, Mihalis (1996). "On limited nondeterminism and the complexity of the V-C dimension". Zeitschrift für Computer- und Systemwissenschaften. 53 (2, Teil 1): 161–170. doi:10.1006/jcss.1996.0058. HERR 1418886. External links Complexity Zoo: Class NPI Basic structure, Turing reducibility and NP-hardness Lance Fortnow (24 Marsch 2003). "Grundlagen der Komplexität, Lektion 16: Ladner's Theorem". Abgerufen 1 November 2013. Kategorien: Complexity classes

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