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NP-complete decision problems for quadratic polynomials

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

doi:10.1145/800113.803627
dblp:conf/stoc/MandersA76
fatcat:sim4pz2f6ndkvmrc6vx66uur7a
*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. ...##
###
System design is an NP-complete problem

2001
*
Systems Engineering
*

This paper proves that the System Design

doi:10.1002/sys.1018
fatcat:jihixzdi6bac5iyut2xdou34vi
*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 ...##
###
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

2009
*
Communications of the ACM
*

Josh Grochow wrote

doi:10.1145/1562164.1562186
fatcat:gxquaagohnc7jdxdhaaexzof44
*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] ). ...##
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Transforming NP to P: An Approach to Solve NP Complete Problems
[article]

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. ...

##
###
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

2009
*
Discrete Applied Mathematics
*

The explicit purpose of the present Perspective is to suggest a

doi:10.1016/j.dam.2009.04.022
fatcat:3nvxwk5u4zhqlagcydyknwejmq
*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*. ...##
###
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]

2013
*
arXiv
*
pre-print

First of all, we prove that P=

arXiv:1304.1307v1
fatcat:ettzpnhahjfiboze24dycprzaa
*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. ...##
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A natural encoding scheme proved probabilistic polynomial complete

1983
*
Theoretical Computer Science
*

This is the first non

doi:10.1016/0304-3975(83)90004-x
fatcat:y4fzxxpfmnao5bqs5qcfmevmgu
*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*. ...##
###
David Stifler Johnson: A Tribute by 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

dblp:journals/eatcs/Fortnow16
fatcat:q577fqxvvjeshm3ymhxgoa5roq
*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 ...
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