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IEEE International Conference on Trust, Security and Privacy in computing and Communications (TrustCom)

作者： Meng Liu Priyadarsi Nanda Xuyun Zhang Chi Yang Shui Yu Jianxin Li School of Mechanical Electrical and Information Engineering Shandong University Weihai China School of Electrical and Data Engineering University of Technology Sydney Australia Department of Electrical and Computer Engineering University of Auckland New Zealand School of Computing and Information Technology University of Wollongong Australia School of Information Technology Deakin University Burwood Australia School of Computer Science and Software Engineering University of Western Australia Australia

Secure multiparty computation (SMC) is an important scheme in cryptography and can be applied in various real-life problems. The first SMC problem is the millionaires' problem which involves two-party secure computation. Because the efficiency of public key encryption scheme appears less than symmetric encryption scheme, most existing solutions based on public key cryptography to this problem is inefficient. Thus, a solution based on the symmetric encryption scheme has been proposed. Although it is claimed that this approach can be efficient and practical, we discover that there exist several severe security flaws in this solution. In this paper, we analyze the vulnerability of existing solutions, and propose a new scheme based on the Decisional Diffie-Hellman hypothesis (DDH). Our solution also uses two special encodings (0-encoding and 1-encoding) generated by our modified encoding method to reduce the computation cost of modular multiplications. Extensive experiments are conducted to evaluate the efficiency of our solution, and the experimental results show that our solution can be much more efficient and be approximately 8000 times faster than the solution based on symmetric encryption scheme for a 32-bit input and short-term security. Moreover, our solution is also more efficient than the state-of-the-art solution.

关键词： Encryption Protocols Encoding Public key Australia

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Formation Control of Multiple Dubins Airplane System with Geometric Approach

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Journal of Physics: Conference Series 2018年第1期1108卷

作者： Asmianto Hariyanto Miswanto Department of mathematics Faculty of Mathematics Computing and Data Science Institut Teknologi Sepuluh Nopember (ITS) Surabaya Indonesia Department of mathematics Airlangga University (UNAIR) Surabaya Indonesia

Formation Control is very important for multi agent systems (Swarm). This paper analyses control formation on the Dubins airplane that consists of three airplanes, where an airplane as the leader and two other airplanes move to follow leader airplane's track. First, Doing design of leader airplane's controls by using the method of tracking error dynamics. Controls on the leader follow the trajectory tracking that desired. Desired path is in the form of parametric functions. Second, geometric approaches method is used to design two other airplanes, so the move follows path of the airplane as the leader with a certain distance. Simulation result shows that airplane leader can be controlled to the desired path crosses with good results. Therefore, error has been defined as the distance between leader airplane's paths with the desired path while tracking also depends on the shape of path. The more difficult trajectory tracking of airplane also serves as a leader in passing through it. The result of the simulations also indicates that the value of the mean percentage error (MPE) of 26.93 percent. This suggests that the methods used in this study quite effective either used to control design leader or follower.

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Hierarchical and modularly-minimal vertex colorings

arXiv

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arXiv 2020年

作者： Valdivia, Dulce I. Geiß, Manuela Rosales, Maribel Hernández Stadler, Peter F. Hellmuth, Marc Km. 9.6 Libramiento Norte Carretera Irapuato-León Irapuato GTOMX-36821 Mexico Bioinformatics Group Department of Computer Science & Interdisciplinary Center for Bioinformatics Universität Leipzig Härtelstraße 16-18 LeipzigD-04107 Germany Software Competence Center Hagenberg GmbH Softwarepark 21 HagenbergA-4232 Austria CONACYT-Instituto de Matemáticas UNAM Juriquilla Blvd. Juriquilla 3001 Juriquilla Querétaro QRO76230 Mexico Halle-Jena-Leipzig Competence Center for Scalable Data Services and Solutions Dresden-Leipzig Leipzig Research Center for Civilization Diseases Centre for Biotechnology and Biomedicine at Leipzig University Universität Leipzig Max Planck Institute for Mathematics in the Sciences Inselstraße 22 LeipzigD-04103 Germany Institute for Theoretical Chemistry University of Vienna Währingerstrasse 17 WienA-1090 Austria Facultad de Ciencias Universidad National de Colombia Sede Bogotá Colombia Santa Fe Insitute 1399 Hyde Park Rd. Santa FeNM87501 United States School of Computing University of Leeds EC Stoner Building LeedsLS2 9JT United Kingdom

Cographs are exactly the hereditarily well-colored graphs, i.e., the graphs for which a greedy vertex coloring of every induced subgraph uses only the minimally necessary number of colors χ(G). We show that greedy colorings are a special case of the more general hierarchical vertex colorings, which recently were introduced in phylogenetic combinatorics. Replacing cotrees by modular decomposition trees generalizes the concept of hierarchical colorings to arbitrary graphs. We show that every graph has a modularly-minimal coloring σ satisfying |σ(M)| = χ(M) for every strong module M of G. This, in particular, shows that modularly-minimal colorings provide a useful device to design efficient coloring algorithms for certain hereditary graph classes. For cographs, the hierarchical colorings coincide with the modularly-minimal coloring. As a by-product, we obtain a simple linear-time algorithm to compute a modularly-minimal coloring of P4-sparse graphs. Copyright © 2020, The Authors. All rights reserved.

关键词： Coloring

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Optimal control of predator-prey mathematical model with infection and harvesting on prey

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Journal of Physics: Conference Series 2018年第1期974卷

作者： R. U. Diva Amalia Fatmawati Windarto Didik Khusnul Arif Department of Mathematics Faculty of Science and Technology Universitas Airlangga Surabaya 60115 Indonesia Department of Mathematics Faculty of Mathematics Computing and Data Science Institut Teknologi Sepuluh Nopember Surabaya 60111 INDONESIA.

This paper presents a predator-prey mathematical model with infection and harvesting on prey. The infection and harvesting only occur on the prey population and it assumed that the prey infection would not infect predator population. We analysed the mathematical model of predator-prey with infection and harvesting in prey. Optimal control, which is a prevention of the prey infection, also applied in the model and denoted as U. The purpose of the control is to increase the susceptible prey. The analytical result showed that the model has five equilibriums, namely the extinction equilibrium (E 0), the infection free and predator extinction equilibrium (E 1), the infection free equilibrium (E 2), the predator extinction equilibrium (E 3), and the coexistence equilibrium (E 4). The extinction equilibrium (E 0) is not stable. The infection free and predator extinction equilibrium (E 1), the infection free equilibrium (E 2), also the predator extinction equilibrium (E 3), are locally asymptotically stable with some certain conditions. The coexistence equilibrium (E 4) tends to be locally asymptotically stable. Afterwards, by using the Maximum Pontryagin Principle, we obtained the existence of optimal control U. From numerical simulation, we can conclude that the control could increase the population of susceptible prey and decrease the infected prey.

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Modified cuckoo search ased neural networks for forest types classification 2

Modified cuckoo search ased neural networks for forest types...

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2nd International Conference on Information Technology and Intelligent Transportation Systems, ITITS 2017

作者： Chatterjee, Sankhadeep Dey, Nilanjan Sen, Soumya Ashour, Amira S. Fong, Simon James Shi, Fuqian Department of Computer Science and Engineering University of Calcutta Kolkata India Department of Information Technology Techno India College of Technology Kolkata India A. K. Choudhury School of Information Technology University of Calcutta Kolkata West Bengal India Department of Electronics and Electrical Communications Engineering Faculty of Engineering Tanta University Egypt Department of Computer and Information Science Data Analytics and Collaborative Computing Laboratory University of Macau Taipa China College of Information and Engineering Wenzhou Medical University Wenzhou China

ISBN: (纸本)9781614997849

Pixel classification in land scape images is a challenging process especially in forest images due to the similar spectral features of pixels situated close to each other. Previously, meta-heuristic coupled artificial neural network (ANN) models have been used to classify the two-different species, namely Japanese Cedar, Japanese Cypress and one mixed forest class. Previous attempts have shown reasonable improvement in the classification process using genetic algorithm (GA) supported neural network over other traditional approaches. Consequently, in the current work, a modified Cuckoo Search (CS) supported Neural Network (NN-MCS) classifier is proposed. The lévy flight associated with cuckoo search has been modified using McCulloch's method of generating stable random numbers. The proposed approach is compared with GA-NN using single objective function and CS-NN (ANN trained with CS) classifiers in terms of confusion matrix based performance metrics. The results depicted the dominance of the suggested NN-MCS model compared to the CS-NN model to a greater extent. © 2017 The authors and IOS Press. All rights reserved.

关键词： Neural networks

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Nonlinearly-Activated Noise-Tolerant Zeroing Neural Network for Distributed Motion Planning of Multiple Robot Arms

Nonlinearly-Activated Noise-Tolerant Zeroing Neural Network ...

引用

International Joint Conference on Neural Networks

作者： Long Jin Shuai Li Xin Luo Ming-sheng Shang School of Information Science and Engineering Lanzhou University Department of Computing The Hong Kong Polytechnic University Chongqing Key Laboratory of Big Data and Intelligent Computing Chongqing Institute of Green and Intelligent Technology Chinese Academy of Sciences

ISBN: (纸本)9781509061839

This paper investigates the distributed motion planning of multiple robot arms with limited communications in the presence of noises. To do this, a nonlinearly-activated noise-tolerant zeroing neural network (NANTZNN) is designed and presented for the first time for solving the presented distributed scheme online. Theoretical analyses and simulation results show the effectiveness and accuracy of the presented distributed scheme with the aid of NANTZNN model.

关键词： robotic arm motion planning Distribute Noise Neural network Automatic incident detection Simulation results

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Euclid preparation TBD. Galaxy power spectrum modelling in real space

arXiv

引用

arXiv 2023年

作者： Pezzotta, A. Moretti, C. Zennaro, M. Dizgah, A. Moradinezhad Crocce, M. Sefusatti, E. Ferrero, I. Pardede, K. Eggemeier, A. Barreira, A. Angulo, R.E. Marinucci, M. Quevedo, B. Camacho de la Torre, S. Alkhanishvili, D. Biagetti, M. Breton, M.-A. Castorina, E. D’Amico, G. Desjacques, V. Guidi, M. Kärcher, M. Oddo, A. Ibanez, M. Pellejero Porciani, C. Pugno, A. Salvalaggio, J. Sarpa, E. Veropalumbo, A. Vlah, Z. Amara, A. Andreon, S. Auricchio, N. Baldi, M. Bardelli, S. Bender, R. Bodendorf, C. Bonino, D. Branchini, E. Brescia, M. Brinchmann, J. Camera, S. Capobianco, V. Carbone, C. Cardone, V.F. Carretero, J. Casas, S. Castander, F.J. Castellano, M. Cavuoti, S. Cimatti, A. Congedo, G. Conselice, C.J. Conversi, L. Copin, Y. Corcione, L. Courbin, F. Courtois, H.M. Da Silva, A. Degaudenzi, H. Di Giorgio, A.M. Dinis, J. Dupac, X. Dusini, S. Ealet, A. Farina, M. Farrens, S. Fosalba, P. Frailis, M. Franceschi, E. Galeotta, S. Gillis, B. Giocoli, C. Granett, B.R. Grazian, A. Grupp, F. Guzzo, L. Haugan, S.V.H. Hormuth, F. Hornstrup, A. Jahnke, K. Joachimi, B. Keihänen, E. Kermiche, S. Kiessling, A. Kilbinger, M. Kitching, T. Kubik, B. Kunz, M. Kurki-Suonio, H. Ligori, S. Lilje, P.B. Lindholm, V. Lloro, I. Maiorano, E. Mansutti, O. Marggraf, O. Markovic, K. Martinet, N. Marulli, F. Massey, R. Medinaceli, E. Mellier, Y. Meneghetti, M. Merlin, E. Meylan, G. Moresco, M. Moscardini, L. Munari, E. Niemi, S.-M. Padilla, C. Paltani, S. Pasian, F. Pedersen, K. Percival, W.J. Pettorino, V. Pires, S. Polenta, G. Pollack, J.E. Poncet, M. Popa, L.A. Pozzetti, L. Raison, F. Renzi, A. Rhodes, J. Riccio, G. Romelli, E. Roncarelli, M. Rossetti, E. Saglia, R. Sapone, D. Sartoris, B. Schneider, P. Schrabback, T. Secroun, A. Seidel, G. Seiffert, M. Serrano, S. Sirignano, C. Sirri, G. Stanco, L. Surace, C. Tallada-Crespí, P. Taylor, A.N. Tereno, I. Toledo-Moreo, R. Torradeflot, F. Tutusaus, I. Valentijn, E.A. Max Planck Institute for Extraterrestrial Physics Giessenbachstr. 1 Garching85748 Germany SISSA International School for Advanced Studies Via Bonomea 265 TS Trieste34136 Italy ICSC - Centro Nazionale di Ricerca in High Performance Computing Big Data e Quantum Computing Via Magnanelli 2 Bologna Italy Institute for Astronomy University of Edinburgh Royal Observatory Blackford Hill EdinburghEH9 3HJ United Kingdom INAF-Osservatorio Astronomico di Trieste Via G. B. Tiepolo 11 Trieste34143 Italy IFPU Institute for Fundamental Physics of the Universe via Beirut 2 Trieste34151 Italy Department of Physics Oxford University Keble Road OxfordOX1 3RH United Kingdom Université de Genève Département de Physique Théorique Centre for Astroparticle Physics 24 quai Ernest-Ansermet Genève 4CH-1211 Switzerland Campus UAB Carrer de Can Magrans s/n Barcelona08193 Spain Campus UAB Carrer de Can Magrans s/n Cerdanyola del Vallés Barcelona08193 Spain INFN Sezione di Trieste Via Valerio 2 TS Trieste34127 Italy Institute of Theoretical Astrophysics University of Oslo P.O. Box 1029 Blindern Oslo0315 Norway Strada Costiera 11 Trieste34151 Italy Universität Bonn Argelander-Institut für Astronomie Auf dem Hügel 71 Bonn53121 Germany Excellence Cluster ORIGINS Boltzmannstrasse e 2 Garching85748 Germany Ludwig-Maximilians-University Schellingstrasse 4 Munich80799 Germany Paseo Manuel de Lardizabal 4 Donostia-San Sebastián Guipuzkoa20018 Spain IKERBASQUE Basque Foundation for Science Bilbao48013 Spain Dipartimento di Scienze Matematiche Fisiche e Informatiche Università di Parma Viale delle Scienze 7/A Parma43124 Italy Technion Israel Institute of Technology Israel Carrer Gran Capitá 2-4 Barcelona08034 Spain Aix-Marseille Université CNRS CNES LAM Marseille France Area Science Park Località Padriciano 99 Trieste34149 Italy Laboratoire Univers et Théorie Observatoire de Paris Université PSL Université Paris Cité CNRS Meudon92190

We investigate the accuracy of the perturbative galaxy bias expansion in view of the forthcoming analysis of the Euclid spectroscopic galaxy samples. We compare the performance of an Eulerian galaxy bias expansion, using state-of-art prescriptions from the effective field theory of large-scale structure (EFTofLSS), against a hybrid approach based on Lagrangian perturbation theory and high-resolution simulations. These models are benchmarked against comoving snapshots of the Flagship I N-body simulation at z = (0.9, 1.2, 1.5, 1.8), which have been populated with Hα galaxies leading to catalogues of millions of objects within a volume of about 58 h−3 Gpc3. Our analysis suggests that both models can be used to provide a robust inference of the parameters (h, ωc) in the redshift range under consideration, with comparable constraining power. We additionally determine the range of validity of the EFTofLSS model in terms of scale cuts and model degrees of freedom. From these tests, it emerges that the standard third-order Eulerian bias expansion can accurately describe the full shape of the real-space galaxy power spectrum up to the maximum wavenumber kmax = 0.45 hMpc−1, even with a measurement precision well below the percent level. In particular, this is true for a configuration with six free nuisance parameters, including local and non-local bias parameters, a matter counterterm, and a correction to the shot-noise contribution. Fixing either tidal bias parameters to physically-motivated relations still leads to unbiased cosmological constraints. We finally repeat our analysis assuming a volume that matches the expected footprint of Euclid, but without considering observational effects, as purity and completeness, showing that we can get consistent cosmological constraints over this range of scales and redshifts. © 2023, CC BY.

关键词： Galaxies

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Stable quantum memories with limited measurement

引用

Physical Review A 2018年第3期98卷 032322-032322页

作者： C. Daniel Freeman Mohan Sarovar C. M. Herdman K. B. Whaley Berkeley Quantum Information & Computation Center University of California Berkeley California 94720 USA Department of Physics University of California Berkeley California 94720 USA Extreme-scale Data Science and Analytics Sandia National Laboratories Livermore California 94550 USA Institute for Quantum Computing University of Waterloo Waterloo Ontario N2L 3G1 Canada Department of Chemistry University of Waterloo Waterloo Ontario N2L 3G1 Canada Department of Physics & Astronomy University of Waterloo Waterloo Ontario N2L 3G1 Canada Department of Chemistry University of California Berkeley California 94720 USA

We demonstrate the existence of a finite temperature threshold for a one-dimensional stabilizer code under an error correcting protocol that requires only a fraction of the syndrome measurements. Below the threshold temperature, encoded states have exponentially long lifetimes, as demonstrated by numerical and analytical arguments. We sketch how this algorithm generalizes to higher-dimensional stabilizer codes with stringlike excitations, such as the toric code.

关键词： Quantum error correction Quantum memories

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Euclid preparation. Sensitivity to neutrino parameters

arXiv

引用

arXiv 2024年

作者： Archidiacono, M. Lesgourgues, J. Casas, S. Pamuk, S. Schöneberg, N. Sakr, Z. Parimbelli, G. Schneider, A. Hervas Peters, F. Pace, F. Sabarish, V.M. Costanzi, M. Camera, S. Carbone, C. Clesse, S. Frusciante, N. Fumagalli, A. Monaco, P. Scott, D. Viel, M. Amara, A. Andreon, S. Auricchio, N. Baldi, M. Bardelli, S. Bodendorf, C. Bonino, D. Branchini, E. Brescia, M. Brinchmann, J. Capobianco, V. Cardone, V.F. Carretero, J. Castellano, M. Cavuoti, S. Cimatti, A. Congedo, G. Conselice, C.J. Conversi, L. Copin, Y. Courbin, F. Courtois, H.M. Da Silva, A. Degaudenzi, H. Douspis, M. Dubath, F. Duncan, C.A.J. Dupac, X. Dusini, S. Ealet, A. Farina, M. Farrens, S. Ferriol, S. Frailis, M. Franceschi, E. Galeotta, S. Gillis, B. Giocoli, C. Grazian, A. Grupp, F. Guzzo, L. Haugan, S.V.H. Hoekstra, H. Hormuth, F. Hornstrup, A. Jahnke, K. Joachimi, B. Keihänen, E. Kermiche, S. Kiessling, A. Kilbinger, M. Kitching, T. Kubik, B. Kunz, M. Kurki-Suonio, H. Ligori, S. Lilje, P.B. Lindholm, V. Lloro, I. Maino, D. Maiorano, E. Mansutti, O. Marggraf, O. Markovic, K. Martinet, N. Marulli, F. Massey, R. Maurogordato, S. McCracken, H.J. Medinaceli, E. Mei, S. Mellier, Y. Meneghetti, M. Merlin, E. Meylan, G. Moresco, M. Moscardini, L. Munari, E. Niemi, S.-M. Nightingale, J.W. Padilla, C. Paltani, S. Pasian, F. Pedersen, K. Percival, W.J. Pettorino, V. Pires, S. Polenta, G. Poncet, M. Popa, L.A. Pozzetti, L. Raison, F. Rebolo, R. Renzi, A. Rhodes, J. Riccio, G. Romelli, E. Roncarelli, M. Saglia, R. Sapone, D. Sartoris, B. Scaramella, R. Schirmer, M. Schneider, P. Schrabback, T. Secroun, A. Seidel, G. Serrano, S. Sirignano, C. Sirri, G. Stanco, L. Tallada-Crespí, P. Taylor, A.N. Tereno, I. Toledo-Moreo, R. Torradeflot, F. Tutusaus, I. Valenziano, L. Vassallo, T. Veropalumbo, A. Wang, Y. Weller, J. Zamorani, G. Zoubian, J. Zucca, E. Biviano, A. Boucaud, A. Bozzo, E. Burigana, C. Calabrese, M. Dipartimento di Fisica "Aldo Pontremoli" Università degli Studi di Milano Via Celoria 16 Milano20133 Italy INFN-Sezione di Milano Via Celoria 16 Milano20133 Italy RWTH Aachen University Aachen52056 Germany Martí i Franquès 1 Barcelona08028 Spain Institut für Theoretische Physik University of Heidelberg Philosophenweg 16 Heidelberg69120 Germany Université de Toulouse CNRS UPS CNES 14 Av. Edouard Belin Toulouse31400 France Université St Joseph Faculty of Sciences Beirut Lebanon Campus UAB Carrer de Can Magrans s/n Barcelona08193 Spain Dipartimento di Fisica Università degli studi di Genova INFN-Sezione di Genova via Dodecaneso 33 Genova16146 Italy SISSA International School for Advanced Studies Via Bonomea 265 TS Trieste34136 Italy Department of Astrophysics University of Zurich Winterthurerstrasse 190 Zurich8057 Switzerland AIM CEA CNRS Université Paris-Saclay Université de Paris Gif-sur-Yvette91191 France Dipartimento di Fisica Università degli Studi di Torino Via P. Giuria 1 Torino10125 Italy INFN-Sezione di Torino Via P. Giuria 1 Torino10125 Italy INAF-Osservatorio Astrofisico di Torino Via Osservatorio 20 TO Pino Torinese10025 Italy Hamburger Sternwarte University of Hamburg Gojenbergsweg 112 Hamburg21029 Germany Dipartimento di Fisica Sezione di Astronomia Università di Trieste Via Tiepolo 11 Trieste34131 Italy INAF-Osservatorio Astronomico di Trieste Via G. B. Tiepolo 11 Trieste34143 Italy IFPU Institute for Fundamental Physics of the Universe via Beirut 2 Trieste34151 Italy INAF-IASF Milano Via Alfonso Corti 12 Milano20133 Italy Service de Physique Théorique CP225 Boulevard du Triophe Bruxelles1050 Belgium Department of Physics "E. Pancini" University Federico II Via Cinthia 6 Napoli80126 Italy Ludwig-Maximilians-University Schellingstrasse 4 Munich80799 Germany INFN Sezione di Trieste Via Valerio 2 TS Trieste34127 Italy Department of Physics and Astronomy University of British Colu

Context. The Euclid mission of the European Space Agency will deliver weak gravitational lensing and galaxy clustering surveys that can be used to constrain the standard cosmological model and extensions thereof. Aims. We present forecasts from the combination of the Euclid photometric galaxy surveys (weak lensing, galaxy clustering and their cross-correlation) and its spectroscopic redshift survey on the sensitivity to cosmological parameters including the summed neutrino mass ∑ mν and the effective number of relativistic species Neff in the standard ΛCDM scenario and in a scenario with dynamical dark energy (w0waCDM). Methods. We compare the accuracy of different algorithms predicting the nonlinear matter power spectrum for such models. We then validate several pipelines for Fisher matrix and Markov Chain Monte Carlo (MCMC) forecasts, using different theory codes, algorithms for numerical derivatives, and assumptions concerning the non-linear cut-off scale. Results. The Euclid primary probes alone will reach a sensitivity of σ(∑ mν = 60 meV) = 56 meV in the ΛCDM+∑ mν model, whereas the combination with cosmic microwave background (CMB) data from Planck is expected to achieve σ(∑ mν) = 23 meV and raise the evidence for a non-zero neutrino mass to at least the 2.6 σ level. This can be pushed to a 4 σ detection if future CMB data from LiteBIRD and CMB Stage-IV are included. In combination with Planck, Euclid will also deliver tight constraints on ∆Neff ν+Neff model, or ∆Neff eff remains stable, while that to ∑ mν degrades at most by a factor two. Conclusions. This work illustrates the complementarity between the Euclid spectroscopic and imaging/photometric surveys and between Euclid and CMB constraints. Euclid will have a great potential for measuring the neutrino mass and excluding well-motivated scenarios with additional relativistic particles. Copyright © 2024, The Authors. All rights reserved.

关键词： Galaxies

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A structured view on weighted counting with relations to counting, quantum computation and applications

arXiv

引用

arXiv 2017年

作者： de Campos, Cassio P. Stamoulis, Georgios Weyland, Dennis Queen’s University Belfast United Kingdom Department of Information and Computing Sciences Utrecht University Netherlands Department of Data Science & Knowledge Engineering Maastricht University Netherlands Google Zürich Switzerland

Weighted counting problems are a natural generalization of counting problems where a weight is associated with every computational path of polynomial-time non-deterministic Turing machines and the goal is to compute the sum of the weights of all paths (instead of just computing the number of accepting paths). Useful closure properties and plenty of applications make weighted counting problems interesting. The general definition of these problems captures even undecidable problems, but it turns out that obtaining an exponentially small additive approximation is just as hard as solving conventional counting problems. In many cases such an approximation is sufficient and working with weighted counting problems tends to be very convenient. We present a structured view on weighted counting by defining classes that depend on the range of the function that assigns weights to paths and by showing the relationships between these different classes. These classes constitute generalizations of the usual counting problems. Weighted counting allows us to easily cast a number of famous results of computational complexity in its terms, especially regarding counting and quantum computation. Moreover, these classes are flexible enough and capture the complexity of various problems in fields such as probabilistic graphical models and stochastic combinatorial optimization. Using the weighted counting terminology and our results, we are able to simplify and answer some open questions in those fields. Copyright © 2017, The Authors. All rights reserved.

关键词： Turing machines

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