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Open problems in number theoretic complexity, II [chapter]

Leonard M. Adleman, Kevin S. McCurley
1994 Lecture Notes in Computer Science  
Our list of open problems is derived from an earlier`open problems' paper we wrote in 1986 AM86] .  ...  While it seems inappropriate to spend a great deal of time giving rigorous de nitions of the complexity-theoretic notions used in this paper, it seems worthwhile to provide some guidance.  ... 
doi:10.1007/3-540-58691-1_70 fatcat:3netr75u7nhsncaz3gsliuncm4

Page 2418 of Mathematical Reviews Vol. , Issue 2004c [page]

2004 Mathematical Reviews  
Theoret. Comput. Sci. 295 (2003), no. 1-3, 141-151. Summary: “This paper contains answers to several problems in the theory of the computational complexity of infinite words.  ...  If there are k automata and each has o states, the number of states of the product automaton is o* and the problem is easily solved in time proportional to this number.  ... 

On computational complexity of construction of c -optimal linear regression models over finite experimental domains

Jaromír Antoch, Michal Černý, Milan Hladík
2012 Tatra Mountains Mathematical Publications  
Finally, we point out some complexity-theoretic properties of the SAC algorithm for c-optimality.  ...  Assuming some complexity-theoretic conjectures, we show that the approximate version of c-optimality does not have an efficient parallel implementation.  ...  Recall also that it is known that NC ⊆ P, but it is an open complexity-theoretic question whether the inclusion is proper. The problem NC = ?  ... 
doi:10.2478/v10127-012-0002-3 fatcat:3jcxi2gzfbbozgxnncspghr2zq

Page 3743 of Mathematical Reviews Vol. , Issue 81I [page]

1981 Mathematical Reviews  
This result does not imply that natural numbers can be factored in polynomial time, since our measure of complexity ignores the size of the numbers in- volved.  ...  “In this note, we consider the inherent difficulty of the factoring problem from the point of view of another natural measure of complexity, namely the number of arithmetic steps (addition, sub- traction  ... 

Page 1270 of Mathematical Reviews Vol. , Issue 99b [page]

1991 Mathematical Reviews  
This is of importance because the central open problems such as P versus NP are connected to the lack of powerful proof methods for lower bounds in complexity theory.  ...  Their idea is to reduce problems of proving lower bounds on complexity to the problem of proving lower bounds on the length of proofs in certain restricted proof systems.  ... 

Study on Computer Software Applied in Teaching of Design of Chemical Engineering Principles

Tingting Tang, Jun Wang
2019 OALib  
The basic functions and characteristics and the significance and existing problems of using software for teaching are discussed in this paper in order to promote the reform of the curriculum system of  ...  This paper mainly introduces the application of some popular calculation software or application software in the teaching of chemical engineering principle curriculum design.  ...  Open Access Library Journal combination of teaching and practice, but also for teachers to guide the design work has brought convenience.  ... 
doi:10.4236/oalib.1105295 fatcat:qq3kb4huqfgepiqwkvnimxmx6e

Page 7064 of Mathematical Reviews Vol. , Issue 2003i [page]

2003 Mathematical Reviews  
The first one is the DTOL w-sequence equivalence problem. The decidability status of this problem remains open. We also introduce two closely related variants.  ...  (English summary) Computability and complexity in analysis (Castle Dagstuhl, 1999). Theoret. Comput. Sci. 284 (2002), no. 2, 455—466.  ... 

Scheme-theoretic Approach to Computational Complexity II. The Separation of P and NP over ℂ, ℝ, and ℤ [article]

Ali Çivril
2022 arXiv   pre-print
This separates P and NP over these fields/rings in the BCSS model of computation.  ...  We show that the problem of determining the feasibility of quadratic systems over ℂ, ℝ, and ℤ requires exponential time.  ...  The purpose of this paper is to show that the theory presented in the first paper of the series [3] naturally extends to these cases, answering the open questions raised in [1] .  ... 
arXiv:2107.07387v9 fatcat:s6lr3ucalvgpresf2dhngnlv4m

Computability and the morphological complexity of some dynamics on continuous domains

Mathieu Hoyrup, Arda Kolçak, Giuseppe Longo
2008 Theoretical Computer Science  
Crucial dynamical properties are transferred to it, while allowing an investigation of stability and chaoticity, in terms of computability, in particular in the presence of singularities.  ...  We will survey some results which display the connections between the geometric complexity of the dynamics and computability issues, as well as new relations between dynamic predictability and effective  ...  If we look at this problem in domain theoretical terms, we have a dynamical system on the domain of intervals II.  ... 
doi:10.1016/j.tcs.2008.01.048 fatcat:pbesijwghngjzioblranl242ty

On the amplitude of intervals of natural numbers whose every element has a common prime divisor with at least an extremity

Patrick Cégielski, François Heroult, Denis Richard
2003 Theoretical Computer Science  
The computation of the ÿrst d leads to rise a lot of open problems.  ...  An interval [a; a + d] of natural numbers veriÿes the property of no coprimeness if and only if every element a + 1; a + 2; : : : ; a + d − 1 has a common prime divisor with extremity a or a + d.  ...  Open problem 5 (Complexity of AmplitudeNoCoprime). To which complexity classes does AmplitudeNoCoprime belong? Open problem 6. Find a lower bound for AmplitudeNoCoprime.  ... 
doi:10.1016/s0304-3975(02)00444-9 fatcat:do2x2t6iknchja4uoyqkeppf6a

Isoscattering strings of concatenating graphs and networks

Michał Ławniczak, Adam Sawicki, Małgorzata Białous, Leszek Sirko
2021 Scientific Reports  
of open complex graphs and networks with many external leads are uniquely connected to their shapes.  ...  , originally posed in the case of isospectral dissipationless systems, to the case of infinite strings of open graphs and networks.  ...  Acknowledgements This work was supported in part by the National Science Centre, Poland, Grant No. UMO-2016/23/B/ST2/03979.  ... 
doi:10.1038/s41598-020-80950-6 pmid:33452312 fatcat:t4uyqdgusncvzbxtpyiwv6b7ve

Page 466 of Mathematical Reviews Vol. , Issue 88a [page]

1988 Mathematical Reviews  
(I-CNR-CY) Computational complexity: the problem of approximation. Algebra, combinatorics and logic in computer science, Vol. I, II (Gyor, 1983), 51-62, Collog. Math. Soc.  ...  Summary: “A definition of computability and complexity of real functions and real numbers is given which is open to methods of recursive function theory as well as to methods of numerical analy- sis.  ... 

Complex Problem Solving and Its Position in the Wider Realm of the Human Intellect

Samuel Greiff, Ronny Scherer
2018 Journal of Intelligence  
We cannot solve our problems with the same thinking we used when we created them.[...].  ...  ., the number of relations among variables) and the situational demands in CPS scenarios (e.g., individual vs. collaborative problem solving) contribute to complexity.  ...  In other words, problems that are considered complex today might not be considered complex tomorrow.  ... 
doi:10.3390/jintelligence6010005 pmid:31162432 pmcid:PMC6480745 fatcat:pvmowdnvojffxephudym3zgy6u

Game theoretic controller synthesis for multi-robot motion planning Part I: Trajectory based algorithms

Minghui Zhu, Michael Otte, Pratik Chaudhari, Emilio Frazzoli
2014 2014 IEEE International Conference on Robotics and Automation (ICRA)  
case, the computational complexity and communication cost are linear in the robot number.  ...  The problems are formulated as an open-loop non-cooperative differential game. A distributed anytime algorithm is proposed to compute a Nash equilibrium of the game.  ...  The problems are formulated as an open-loop non-cooperative differential game.  ... 
doi:10.1109/icra.2014.6907072 dblp:conf/icra/ZhuOCF14 fatcat:dvylaqdyyrhyzl2wpgpzwyip74

Looking for a Needle in a Haystack: How to Search for Bottom‐up Social Innovations that Solve Complex Humanitarian Problems

Daniel J. Kruse, Moritz Goeldner, Katrin Eling, Cornelius Herstatt
2019 The Journal of product innovation management  
Since humanitarian problems are complex problems, with the relevant knowledge being hidden, organizational search theory advocates the application of bottom-up and theory-guided search processes to identify  ...  Unfortunately, there has been no theoretical attention to understanding which approaches apply in this context.  ...  Our study makes a number of important theoretical contributions to the open innovation literature generally, and specifically to the topic of open innovation in the social innovation domain.  ... 
doi:10.1111/jpim.12507 fatcat:ctmmehcqfnat7fvijaz2h6itoi
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