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NP-complete decision problems for quadratic polynomials

Kenneth Manders, Leonard Adleman
1976 Proceedings of the eighth annual ACM symposium on Theory of computing - STOC '76  
In this a r t i c l e we show the NP-completeness of some simple number-theoretic problems. Natural simplifications of these problems invariably are known to be in P.  ...  Our research was motivated by the question whether one could study non-determini s t i c computation without loss of generality on a restricted, number theoretically significant class of nondeterministic  ...  ABSTRACT In this a r t i c l e we show the NP-completeness of some simple number-theoretic problems. Natural simplifications of these problems invariably are known to be in P.  ... 
doi:10.1145/800113.803627 dblp:conf/stoc/MandersA76 fatcat:sim4pz2f6ndkvmrc6vx66uur7a

System design is an NP-complete problem

William L. Chapman, Jerzy Rozenblit, A. Terry Bahill
2001 Systems Engineering  
This paper proves that the System Design Problem is NP-complete by reduction from the Knapsack Problem, which is known to be NP-complete.  ...  It requires selecting subsystems from an allowable set and matching the interfaces between them.  ...  An earlier version of this paper was published in the Proceedings of the IEEE International Conference on Systems Man and Cybernetics, San Antonio, TX, October 1994, pp. 1880-1884  ... 
doi:10.1002/sys.1018 fatcat:jihixzdi6bac5iyut2xdou34vi

Page 3950 of Mathematical Reviews Vol. , Issue 92g [page]

1992 Mathematical Reviews  
By using the technique proving this result, the intractability of several number-theoretic decision problems, i.e., decision problems defined naturally from number-theoretic problems, is investigated.  ...  We prove that the OTSG problem is NP-complete. Therefore an efficient solution to the problem should not be expected in the general case.” 92g:68060 68Q25 68U05 Dielissen, Victor J.  ... 

The status of the P versus NP problem

Lance Fortnow
2009 Communications of the ACM  
Josh Grochow wrote an early draft of Section 9. The anonymous referees provided critical advice. Some of the material in this article has appeared in my earlier surveys and my blog [14] .  ...  An efficient solution to any NP-complete problem would imply P = NP and an efficient solution to every NP-complete problem.  ...  In the 1970's, theoretical computer scientists showed hundreds more problems NP-complete (see [17] ).  ... 
doi:10.1145/1562164.1562186 fatcat:gxquaagohnc7jdxdhaaexzof44

Transforming NP to P: An Approach to Solve NP Complete Problems [article]

Wenhong Tian, GuoZhong Li, Xinyang Wang, Qin Xiong, Yaqiu Jiang
2015 arXiv   pre-print
NP complete problem is one of the most challenging issues.  ...  This approach helps to solve originally NP complete problems with practical applications. It may shine light on solving other NP complete problems in similar way.  ...  Acknowledgments This research is sponsored by the National Natural Science Foundation of China (NSFC) (Grand Number:61450110440). Dr.  ... 
arXiv:1505.00058v1 fatcat:szvyuomx4fhdbgs6wgrquergw4

Page 1822 of Mathematical Reviews Vol. 56, Issue 5 [page]

1978 Mathematical Reviews  
A p-reduction is said to be parsimonious if it preserves “the number of solutions” of given NP-complete problems.  ...  The authors conjecture: “Every two-NP-complete problems are p-isomorphic’. The conjecture would imply PNP, since if PA NP then nonempty finite sets are NP-complete.  ... 

Page 4676 of Mathematical Reviews Vol. , Issue 83k [page]

1983 Mathematical Reviews  
The problem for an arbitrary number of strings is shown to be NP-complete and so is unlikely to have a polynomial time algorithm.”  ...  In this paper the authors show that the SCS problem is NP-complete for an alphabet of size >2. V. B. Alekseev (Moscow) Sidorenko, A.  ... 

Page 2834 of Mathematical Reviews Vol. , Issue 86g [page]

1986 Mathematical Reviews  
Shen, Bai Ying (PRC-NAN) 86g:03069 Inverse functions of number-theoretic functions. III. (Chinese) An English summary appears in Chinese Ann. Math. Ser. B 5 (1984), no. 3, 397. Chinese Ann. Math.  ...  Author summary (translated from the Chinese): “We continue the investigation of inverses of number-theoretic functions begun in parts I and II [S. K.  ... 

Page 2653 of Mathematical Reviews Vol. , Issue 87e [page]

1987 Mathematical Reviews  
In this paper, the authors show that many graph-theoretic (and other) NP-complete problems become log-space complete for NTISP(poly, f(m)) when restricted to problem instances of band- width f(n).  ...  Summary: “A number of natural enumeration problems in ge- ometry and combinatorics are shown to be complete in the class #P introduced by Valiant.  ... 

Page 2618 of Mathematical Reviews Vol. , Issue 85f [page]

1985 Mathematical Reviews  
It is well known that the problem of determining the chro- matic number for a general graph falls in the class of NP-complete problems.  ...  NP-completeness is proved by polynomial reduction of the known NP-complete problem “exact cover by 3-sets” to the new problem.  ... 

Some theoretical challenges in digital geometry: A perspective

Tetsuo Asano, Valentin E. Brimkov, Reneta P. Barneva
2009 Discrete Applied Mathematics  
The explicit purpose of the present Perspective is to suggest a number of strategic objectives for theoretical research, with an emphasis on the combinatorial approach in image analysis.  ...  Most of the proposed objectives relate to the need to make the theoretical foundations of combinatorial image analysis better integrated within a number of well-established subjects of theoretical computer  ...  Roughly speaking, an NP-hard problem is at least as hard as the corresponding NP-complete decision version of the problem.  ... 
doi:10.1016/j.dam.2009.04.022 fatcat:3nvxwk5u4zhqlagcydyknwejmq

Page 4751 of Mathematical Reviews Vol. , Issue 94h [page]

1994 Mathematical Reviews  
It is well known that (1.1) belongs to the class of NP-complete problems and plays an important role in the proof and classification of NP problems in general.  ...  The authors study a number of complexity-theoretic classes of functions.  ... 

On the structure of the class NP [article]

Anatoly D. Plotnikov
2013 arXiv   pre-print
First of all, we prove that P= NP and establish that it needs to consider the problem "P vs UF" instead the problem "P vs NP".  ...  A new class UF of problems is introduced, strictly included in the class NP, which arises in the analysis of the time verifying the intermediate results of computations.  ...  In the class NP, universal or NP-complete problems are allocated. The problem Z is called NP-complete if any problem of NP reduced in polynomial time to the problem of Z.  ... 
arXiv:1304.1307v1 fatcat:ettzpnhahjfiboze24dycprzaa

A natural encoding scheme proved probabilistic polynomial complete

Umesh V. Vazirani, Vijay V. Vazirani
1983 Theoretical Computer Science  
This is the first non number-theoretic: problem that is UR-complete but not known to be NP-complete.  ...  We prove a natural encoding scheme to be intractable (by showing it UR-complete, a technique which may be used when 21 problem does not yield to a proof of NP-completeness).  ...  In open problem No 5 of their-paper, they ask for an example of a non number-theoretic problem that is UR-complete but not known to b/z NP-complete.  ... 
doi:10.1016/0304-3975(83)90004-x fatcat:y4fzxxpfmnao5bqs5qcfmevmgu

David Stifler Johnson: A Tribute by Lance Fortnow

Lance Fortnow
2016 Bulletin of the European Association for Theoretical Computer Science  
A decade ago I had plans to write a book on the history of the P versus NP problem and interviewed a number of theorists including David Johnson.  ...  The notes aren't complete but I'll try and tell his story the best I can. I apologize in advance for any mistakes that follow.  ...  Knuth discusses the results of the poll in an essay in the January 1974 SIGACT News and after describing a number of humorous proposals The "winning" write-in vote is the term NP-hard, which was put forward  ... 
dblp:journals/eatcs/Fortnow16 fatcat:q577fqxvvjeshm3ymhxgoa5roq
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