{"title":"Quantum Adversary (Upper) Bound","authors":"S. Kimmel","doi":"10.4086/cjtcs.2013.004","DOIUrl":"https://doi.org/10.4086/cjtcs.2013.004","url":null,"abstract":"We describe a method for upper bounding the quantum query complexity of certain boolean formula evaluation problems, using fundamental theorems about the general adversary bound. This nonconstructive method gives an upper bound on query complexity without producing an algorithm. For example, we describe an oracle problem that we prove (non-constructively) can be solved in O(1) queries, where the previous best quantum algorithm uses a polynomial number of queries. We then give an explicit O(1) query algorithm based on span programs, and show that for a special case of this problem, there exists a O(1) query algorithm that uses the quantum Haar transform. This special case is a potentially interesting problem in its own right, which we call the Haar Problem.","PeriodicalId":203487,"journal":{"name":"Chicago Journal of Theoretical Computer Science","volume":"291 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125494558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
V. Dujmovic, Joachim Gudmundsson, Pat Morin, T. Wolle
{"title":"Notes on Large Angle Crossing Graphs","authors":"V. Dujmovic, Joachim Gudmundsson, Pat Morin, T. Wolle","doi":"10.4086/cjtcs.2011.004","DOIUrl":"https://doi.org/10.4086/cjtcs.2011.004","url":null,"abstract":"A graph G is an a-angle crossing (aAC) graph if every pair of crossing edges in G intersect at an angle of at least a. The concept of right angle crossing (RAC) graphs (a=Pi/2) was recently introduced by Didimo et. al. It was shown that any RAC graph with n vertices has at most 4n-10 edges and that there are infinitely many values of n for which there exists a RAC graph with n vertices and 4n-10 edges. In this paper, we give upper and lower bounds for the number of edges in aAC graphs for all 0 < a < Pi/2.","PeriodicalId":203487,"journal":{"name":"Chicago Journal of Theoretical Computer Science","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115827313","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Query Complexity of Program Checking by Constant-Depth Circuits","authors":"V. Arvind, K. Subrahmanyam, N. V. Vinodchandran","doi":"10.1007/3-540-46632-0_13","DOIUrl":"https://doi.org/10.1007/3-540-46632-0_13","url":null,"abstract":"","PeriodicalId":203487,"journal":{"name":"Chicago Journal of Theoretical Computer Science","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117196886","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Planning by minimum consensus: Austrian co-operative federalism as a model for Europe?","authors":"A. Faludi","doi":"10.1080/09654319808720477","DOIUrl":"https://doi.org/10.1080/09654319808720477","url":null,"abstract":"Abstract Austria joined the European Union as late as 1995, so it may seem far‐fetched to present her as a model. However, Austria has a federal planning system. In the European Union, too, Member States have ceded powers to Brussels, so the European Union resembles federal planning systems. However, neither the Austrian federal government nor the European Union has a formal planning mandate, and so both have developed para‐constitutional planning institutions. Thus, in Austria there is the Austrian Conference on Spatial Planning where representatives of federal, state and local government co‐operate on a voluntary basis. In the European Union, also, planning co‐operation between Member States is voluntary. Part 1 puts the Conference on Spatial Planning within the context of Austria's evolving ‘co‐operative federal state’. Part 2 focuses on the Conference itself. Part 3 compares the Austrian arrangements with those for European planning. The conclusions draw lessons for European planning. The first is tha...","PeriodicalId":203487,"journal":{"name":"Chicago Journal of Theoretical Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127223214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Polynucleated regions in Northwest Europe","authors":"A. Faludi, F. Dieleman","doi":"10.1080/09654319808720468","DOIUrl":"https://doi.org/10.1080/09654319808720468","url":null,"abstract":"","PeriodicalId":203487,"journal":{"name":"Chicago Journal of Theoretical Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116137017","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Randstad, Rhine-Ruhr and Flemish diamond as one polynucleated macro-region?","authors":"F. Dieleman, A. Faludi","doi":"10.1111/1467-9663.00031","DOIUrl":"https://doi.org/10.1111/1467-9663.00031","url":null,"abstract":"","PeriodicalId":203487,"journal":{"name":"Chicago Journal of Theoretical Computer Science","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127660727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Asymptotically minimax estimation of a function with jumps","authors":"C. Oudshoorn","doi":"10.2307/3318530","DOIUrl":"https://doi.org/10.2307/3318530","url":null,"abstract":"Asymptotically minimax nonparametric estimation of a regression function observed in white Gaussian noise over a bounded interval is considered, with respect to a L2-loss function. The unknown function f is assumed to be m times differentiable except for an unknown although finite number of jumps, with piecewise mth derivative bounded in L2 norm. An estimator is constructed, attaining the same optimal risk bound, known as Pinsker's constant, as in the case of smooth functions (without jumps).","PeriodicalId":203487,"journal":{"name":"Chicago Journal of Theoretical Computer Science","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121848431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the countable generator theorem","authors":"M. Keane, J. Serafin","doi":"10.4064/fm-157-2-3-255-259","DOIUrl":"https://doi.org/10.4064/fm-157-2-3-255-259","url":null,"abstract":"Let T be a finite entropy, aperiodic automorphism of a nonatomic probability space. We give an elementary proof of the existence of a finite entropy, countable generating partition for T . In this short article we give a simple proof of Rokhlin’s countable generator theorem [Ro], originating from considerations in [Se] which use standard techniques in ergodic theory. We hope that these considerations will be useful for elementary expositions in the future. For other proofs see [Pa]. Let (X,A, μ) be a nonatomic probability space whose σ-algebra A is generated modulo μ by a countable collection {A1, A2, . . .} of elements of A. Let T be an aperiodic automorphism of (X,A, μ) with finite entropy. For the definitions and properties of entropy and generators used in the sequel, we refer the reader to Billingsley [Bill] and Walters [Wa]. Theorem. (X,A, μ, T ) has a countable generating partition of finite entropy. Our proof is based on the following lemma. Lemma. Let P be a finite partition of (X,A, μ, T ), A an element of A, and e > 0. Set P := P ∨ {A,Ac} and g := h− h, where h := h(T,P) and h := h(T, P) denote the respective mean entropies of the partitions P and P. Then there exists a finite partition Q of (X,A, μ, T ) such that (1) P Q, 1991 Mathematics Subject Classification: 28D05, 28D20.","PeriodicalId":203487,"journal":{"name":"Chicago Journal of Theoretical Computer Science","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122339406","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}