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Complexity of computation

Gian-Carlo Rota
<span title="">1977</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/37jjomjmvfhrzf3di2gjnrrfuu" style="color: black;">Advances in Mathematics</a> </i> &nbsp;
But, alas, so complex! s. A. ALBEVERIO AKD R. J. HeEGH-KktOmr, Muthematicol Theory of Feymum Paths Intc,r& Springer, 1976, 139 pp.  ...  cs of Theo&s, Springer, 1976, 284 pp. High-class philosophy of science, with stress on physics.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0001-8708(77)90111-6">doi:10.1016/0001-8708(77)90111-6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xdneglllinddtbddttfkgrzzvq">fatcat:xdneglllinddtbddttfkgrzzvq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170924183446/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/1a0/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS8wMDAxODcwODc3OTAxMTE2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/a9/c9/a9c9d4dd72e78858d4abf4993844bebda58f4b73.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0001-8708(77)90111-6"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Complexity of computations

Michael O. Rabin
<span title="1977-09-01">1977</span> <i title="Association for Computing Machinery (ACM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/i6iajiiyxvgz3ob6jwcn2pufni" style="color: black;">Communications of the ACM</a> </i> &nbsp;
The framework for research in the theory of complexity of computations is described, emphasizing the interrelation between seemingly diverse problems and methods.  ...  and dimension: the first applies computer science to mathematics, and the second applies mathematics to computer science.  ...  Introduction The theory of complexity of computations addresses itself to the quantitative aspects of the solutions of computational problems.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/359810.359816">doi:10.1145/359810.359816</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jlj6n4wzlbgd7aq524lsmx2i5u">fatcat:jlj6n4wzlbgd7aq524lsmx2i5u</a> </span>
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Computational Complexity of Segmentation [article]

Federico Adolfi, Todd Wareham, Iris van Rooij
<span title="2022-05-11">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We undertake here computational-level modeling and complexity analyses of segmentation - a widely hypothesized subcomputation that plays a requisite role in explanations of capacities across domains -  ...  The specification of cognitive system capacities is often shaped by unexamined intuitive assumptions about the search space and complexity of a subcomputation.  ...  that helped improve the manuscript, and Ronald de Haan for comments on future directions of this work.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2201.13106v4">arXiv:2201.13106v4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dmwdohyln5esxmu3mxs7hf6tsm">fatcat:dmwdohyln5esxmu3mxs7hf6tsm</a> </span>
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Complexity of computer algorithms

Ronald J. Leach
<span title="">1987</span> <i title="Rocky Mountain Mathematics Consortium"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/77ppzerlsvfczgvezw53uqeqni" style="color: black;">Rocky Mountain Journal of Mathematics</a> </i> &nbsp;
We will be considering the complexity of algorithms as being defined relatively : algorithm A is more complex than algorithm B if the time to run program A is longer than that of program B.  ...  Complexity measures and von-Neumann machines. 1.1 Algorithms. An algorithm is a definite procedure for solving a problem in a finite number of steps.  ...  Many thanks also to Sam Lomonaco and Brooke Stephens for criticizing an earlier version of this paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1216/rmj-1987-17-1-167">doi:10.1216/rmj-1987-17-1-167</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/f22nifht7vbejjce7brdpxjggm">fatcat:f22nifht7vbejjce7brdpxjggm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220127134357/https://projecteuclid.org/journals/rocky-mountain-journal-of-mathematics/volume-17/issue-1/Complexity-of-computer-algorithms/10.1216/RMJ-1987-17-1-167.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/f9/da/f9daaf98c42348ca2cf4793d03baa6d929b84f11.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1216/rmj-1987-17-1-167"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Computational Complexity of Functions [article]

Leonid A. Levin
<span title="2014-11-11">2014</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
I translated only the part with the statement of the results. Instead of the proof part I appended a later (1979, unpublished) proof sketch of a slightly tighter version.  ...  The extension has no (even logarithmic) restrictions on complexity and no overhead (beyond an additive constant).  ...  Every function F is associated with a class of algorithms that compute it and with the class of their space complexities M F .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1411.3010v1">arXiv:1411.3010v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2fwb7hjljveuhbugdmubv7seu4">fatcat:2fwb7hjljveuhbugdmubv7seu4</a> </span>
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Computational complexity of functions

Leonid A. Levin
<span title="">1996</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
Every function F is associated with a class of algorithms that compute it and with the class of their space complexities M,v.  ...  decreasing sequence of functions p, there exists a function, computable with such and only such space complexities that exceed some of the pi's, The Compression and Speed-up Theorems are special  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0304-3975(95)00163-8">doi:10.1016/0304-3975(95)00163-8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/26fnbywdi5d7fjba3jxa3xtnc4">fatcat:26fnbywdi5d7fjba3jxa3xtnc4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190313063511/https://core.ac.uk/download/pdf/82685010.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/45/ec/45ecc9ec5ba035c83a7cbb85b2247e0b739b8053.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0304-3975(95)00163-8"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Degrees of computational complexity

H.B. Enderton
<span title="">1972</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/p6ovb2qpkfenhmb7mcksobrcxq" style="color: black;">Journal of computer and system sciences (Print)</a> </i> &nbsp;
We consider a measure ~b of computational complexity.  ...  In this paper we give a simple proof of a result of McCreight: An arbitrary countable partial ordering can be embedded in this ordering of degrees of complexity.  ...  Consider the case of x in z{j. By (8) S(x, r X(x, ~)(x), S(x, 4~,(x), C/x)))) ~< S(x, g,~,(x), 4~,(x)).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0022-0000(72)80010-2">doi:10.1016/s0022-0000(72)80010-2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/sadikjexubdm7pdljzhfnuzdry">fatcat:sadikjexubdm7pdljzhfnuzdry</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170929072257/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/761/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS9zMDAyMjAwMDA3MjgwMDEwMg%3D%3D.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/3b/a0/3ba0ef2e4f3cad0eb3cfa82fac5a5cbd2d7090be.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0022-0000(72)80010-2"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

On the Computational Complexity of Conservative Computing [chapter]

Giancarlo Mauri, Alberto Leporati
<span title="">2003</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Workshop MIUR/COFIN -September 19-21, Ravello (SA) -p. 23 Complexity of ConsComp Theorem: ConsComp is NP-complete. Proof. Reduction from Partition (details on the paper).  ...  the function computed by an (n, m, d)-gate • S in = x 1 , x 2 , . . . , x k be a sequence of elements of L n d • S out = G(x 1 ), G(x 2 ), . . . , G(x k ) be the corresponding elements of L m d computed  ...  ) < 2M ≤ 2 · opt(I) Conclusions We have: • proposed the first steps towards a theory of conservative computations • introduced a new NP-complete decision problem (ConsComp) and a new NP-hard optimization  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-45138-9_5">doi:10.1007/978-3-540-45138-9_5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qg5jpvj7ird3pfidwhzzac2cwm">fatcat:qg5jpvj7ird3pfidwhzzac2cwm</a> </span>
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Computability and Complexity of Unconventional Computing Devices [article]

Hajo Broersma, Susan Stepney, Goran Wendin
<span title="2017-03-23">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We discover that all these claims rely on the provision of one or more unphysical resources.  ...  We discuss some claims that certain UCOMP devices can perform hypercomputation (compute Turing-uncomputable functions) or perform super-Turing computation (solve NP-complete problems in polynomial time  ...  Identification of the least complex algorithm for problems is at the heart of the theory of computational complexity.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1702.02980v2">arXiv:1702.02980v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pikmc4gtuncztofsjw6as7vetu">fatcat:pikmc4gtuncztofsjw6as7vetu</a> </span>
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Mechanical Computing: The Computational Complexity of Physical Devices [chapter]

John H. Reif
<span title="">2015</span> <i title="Springer Berlin Heidelberg"> Encyclopedia of Complexity and Systems Science </i> &nbsp;
Computational Complexity Classes Computational complexity (see [2] ) is the amount of computational resources required to solve a given computational problem.  ...  The Computational Complexity of Motion Planning and Simulation of Mechanical Devices Complexity of Motion Planning for Mechanical Devices with Articulated Joints The first known computational complexity  ...  (Note that both analog and digital computers uses some kind of physical quantity to represent values that are stored and computed, so the use of physical encoding of computational values is not necessarily  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-27737-5_325-3">doi:10.1007/978-3-642-27737-5_325-3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5rha5nqjlzao3crnsi7hot4vfa">fatcat:5rha5nqjlzao3crnsi7hot4vfa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170201151242/https://users.cs.duke.edu/~reif/paper/MechComp/MechCompUpdate/MechCompUpdate.pub.web.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ee/2f/ee2f34d643e49b2af3f41610c8f2de48648c83b2.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-27737-5_325-3"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Mechanical Computing: The Computational Complexity of Physical Devices [chapter]

John H. Reif
<span title="">2017</span> <i title="Springer Berlin Heidelberg"> Encyclopedia of Complexity and Systems Science </i> &nbsp;
Computable: Capable of being worked out by calculation, especially using a computer.  ...  Bibliography Glossary Mechanism: a machine or part of a machine that performs a particular task computation: the use of a computer for calculation.  ...  Computational Complexity Classes. Computational complexity (see [2] ) is the amount of computational resources required to solve a given computational problem.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-27737-5_325-4">doi:10.1007/978-3-642-27737-5_325-4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gwhg74q6sfas3ijoldk2ipuc4i">fatcat:gwhg74q6sfas3ijoldk2ipuc4i</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170201151238/https://users.cs.duke.edu/~reif/paper/MechComp/MechComp2009/MechComp2009.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/01/ee/01ee0aef00a047de51012d0a4d44c60edd4d0195.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-27737-5_325-4"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Mechanical Computing: The Computational Complexity of Physical Devices [chapter]

John H. Reif
<span title="">2009</span> <i title="Springer New York"> Encyclopedia of Complexity and Systems Science </i> &nbsp;
The Computational Complexity of Motion Planning and Simulation of Mechanical Devices Complexity of Motion Planning for Mechanical Devices with Articulated Joints The first known computational complexity  ...  There are a number of notable complexity classes: P is the complexity class associated with efficient computations, and is formally defined to be the set of problems solved by Turing machine computations  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-0-387-30440-3_325">doi:10.1007/978-0-387-30440-3_325</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/q7bxj4x5ina4jbj762k55rjgbq">fatcat:q7bxj4x5ina4jbj762k55rjgbq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170201151238/https://users.cs.duke.edu/~reif/paper/MechComp/MechComp2009/MechComp2009.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/01/ee/01ee0aef00a047de51012d0a4d44c60edd4d0195.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-0-387-30440-3_325"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Complexity and mission computability of adaptive computing systems [article]

Venkat R. Dasari, Mee Seong Im, Billy Geerhart
<span title="2018-08-29">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We define a subclass of deterministic polynomial time complexity class called mission class, as many polynomial problems are not computable in mission time.  ...  There is a subset of computational problems that are computable in polynomial time for which an existing algorithm may not complete due to a lack of high performance technology on a mission field.  ...  One gauge of efficiency is based on the computational complexity of an algorithm which is generally expressed in terms of time complexity that describes how long it takes for an algorithm to compute an  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1808.09586v1">arXiv:1808.09586v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cubu5owxs5etpeoo2p7zyq3azm">fatcat:cubu5owxs5etpeoo2p7zyq3azm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200830065750/https://arxiv.org/pdf/1808.09586v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/cd/55/cd5545acd924803e637e64594a8d92cbf835dea6.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1808.09586v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Mechanical Computing: The Computational Complexity of Physical Devices [chapter]

John H. Reif
<span title="">2012</span> <i title="Springer New York"> Computational Complexity </i> &nbsp;
The Computational Complexity of Motion Planning and Simulation of Mechanical Devices Complexity of Motion Planning for Mechanical Devices with Articulated Joints The first known computational complexity  ...  There are a number of notable complexity classes: P is the complexity class associated with efficient computations, and is formally defined to be the set of problems solved by Turing machine computations  ... 
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Computational Depth Complexity of Measurement-Based Quantum Computation [chapter]

Dan Browne, Elham Kashefi, Simon Perdrix
<span title="">2011</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
It demonstrates that the one-way model is not only one of the most promising models of physical realisation, but also a very powerful model of quantum computation.  ...  We prove that one-way quantum computations have the same computational power as quantum circuits with unbounded fan-out.  ...  We consider the classes of complexity QNC and QNC k for quantum circuits [MN98]: QNC(d(n)) contains decision problems computed exactly by uniform families of quantum circuits of input size n, depth O(d  ... 
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