{"@context":"https:\/\/schema.org\/","@type":"PublicationVolume","@id":"#volume601","volumeNumber":6111,"name":"Dagstuhl Seminar Proceedings, Volume 6111","dateCreated":"2006-10-09","datePublished":"2006-10-09","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"Periodical","@id":"#series119","name":"Dagstuhl Seminar Proceedings","issn":"1862-4405","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume601"},"hasPart":[{"@type":"ScholarlyArticle","@id":"#article1408","name":"06111 Abstracts Collection \u2013 Complexity of Boolean Functions","abstract":"From 12.03.06 to 17.03.06, the Dagstuhl Seminar 06111 ``Complexity of Boolean Functions'' was held in the International Conference and Research Center (IBFI),\r\nSchloss Dagstuhl.\r\nDuring the seminar, several participants presented their current\r\nresearch, and ongoing work and open problems were discussed. Abstracts of\r\nthe presentations given during the seminar as well as abstracts of\r\nseminar results and ideas are put together in this paper. The first section\r\ndescribes the seminar topics and goals in general.\r\nLinks to extended abstracts or full papers are provided, if available.","keywords":["Complexity of Boolean functions","Boolean circuits","binary decision diagrams","lower bound proof techniques","combinatorics of Boolean functions","communi algorithmic learning","cryptography","derandomization"],"author":[{"@type":"Person","name":"Krause, Matthias","givenName":"Matthias","familyName":"Krause"},{"@type":"Person","name":"Pudl\u00e1k, Pavel","givenName":"Pavel","familyName":"Pudl\u00e1k"},{"@type":"Person","name":"Reischuk, R\u00fcdiger","givenName":"R\u00fcdiger","familyName":"Reischuk"},{"@type":"Person","name":"van Melkebeek, Dieter","givenName":"Dieter","familyName":"van Melkebeek"}],"position":1,"pageStart":1,"pageEnd":24,"dateCreated":"2006-12-07","datePublished":"2006-12-07","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Krause, Matthias","givenName":"Matthias","familyName":"Krause"},{"@type":"Person","name":"Pudl\u00e1k, Pavel","givenName":"Pavel","familyName":"Pudl\u00e1k"},{"@type":"Person","name":"Reischuk, R\u00fcdiger","givenName":"R\u00fcdiger","familyName":"Reischuk"},{"@type":"Person","name":"van Melkebeek, Dieter","givenName":"Dieter","familyName":"van Melkebeek"}],"copyrightYear":"2006","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06111.1","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume601"},{"@type":"ScholarlyArticle","@id":"#article1409","name":"06111 Executive Summary \u2013 Complexity of Boolean Functions","abstract":"We briefly describe the state of the art concerning the complexity of discrete functions. \r\nComputational models and analytical techniques are summarized. \r\nAfter describing the formal organization of the Dagstuhl seminar \"Complexity of Boolean Functions\"\r\nheld in March 2006, we introduce the different topics that have been discussed there \r\nand mention some of the major achievements. \r\nThe summary closes with an outlook on the development of discrete computational complexity in the future.","keywords":["Boolean and quantum circuits","discrete problems","computational complexity","lower bounds","communication complexity","proof and query complexity","randomization","pseudo-randomness","derandomization","approximation","cryptography","computational learning"],"author":[{"@type":"Person","name":"Krause, Matthias","givenName":"Matthias","familyName":"Krause"},{"@type":"Person","name":"van Melkebeek, Dieter","givenName":"Dieter","familyName":"van Melkebeek"},{"@type":"Person","name":"Pudl\u00e1k, Pavel","givenName":"Pavel","familyName":"Pudl\u00e1k"},{"@type":"Person","name":"Reischuk, R\u00fcdiger","givenName":"R\u00fcdiger","familyName":"Reischuk"}],"position":2,"pageStart":1,"pageEnd":5,"dateCreated":"2006-12-08","datePublished":"2006-12-08","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Krause, Matthias","givenName":"Matthias","familyName":"Krause"},{"@type":"Person","name":"van Melkebeek, Dieter","givenName":"Dieter","familyName":"van Melkebeek"},{"@type":"Person","name":"Pudl\u00e1k, Pavel","givenName":"Pavel","familyName":"Pudl\u00e1k"},{"@type":"Person","name":"Reischuk, R\u00fcdiger","givenName":"R\u00fcdiger","familyName":"Reischuk"}],"copyrightYear":"2006","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06111.2","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume601"},{"@type":"ScholarlyArticle","@id":"#article1410","name":"A Generic Time Hierarchy for Semantic Models With One Bit of Advice","abstract":"We show that for any reasonable semantic model of computation and for any positive integer $a$ and rationals $1 leq c < d$, there exists a language computable in time $n^d$ with $a$ bits of advice but not in time $n^c$ with $a$ bits of advice. A semantic model is one for which there exists a computable enumeration that contains all machines in the model but may also contain others. We call such a model reasonable if it has an efficient universal machine that can be complemented within the model in exponential time and if it is efficiently closed under deterministic transducers. Our result implies the first such hierarchy theorem for randomized machines with zero-sided error, quantum machines with one- or zero-sided error, unambiguous machines, symmetric alternation, Arthur-Merlin games of any signature, interactive proof protocols with one or multiple provers, etc.","keywords":["Time hierarchy","non-uniformity","one bit of advice","probabilistic algorithms"],"author":[{"@type":"Person","name":"van Melkebeek, Dieter","givenName":"Dieter","familyName":"van Melkebeek"},{"@type":"Person","name":"Pervyshev, Konstantin","givenName":"Konstantin","familyName":"Pervyshev"}],"position":3,"pageStart":1,"pageEnd":39,"dateCreated":"2006-11-20","datePublished":"2006-11-20","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"van Melkebeek, Dieter","givenName":"Dieter","familyName":"van Melkebeek"},{"@type":"Person","name":"Pervyshev, Konstantin","givenName":"Konstantin","familyName":"Pervyshev"}],"copyrightYear":"2006","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06111.3","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume601"},{"@type":"ScholarlyArticle","@id":"#article1411","name":"Approximability of Minimum AND-Circuits","abstract":"Given a set of monomials, the {sc Minimum AND-Circuit} problem asks for a circuit that computes these monomials using AND-gates of fan-in two and being of minimum size. \r\n\r\nWe prove that the problem is not polynomial time approximable within a factor of less than $1.0051$ unless $mathsf{P} = mathsf{NP}$, even if the monomials are restricted to be of degree at most three. For the latter case, we devise several efficient approximation algorithms, yielding an approximation ratio of $1.278$. For the general problem, we achieve an approximation ratio of $d-3\/2$, where $d$ is the degree of the largest monomial. \r\n\r\nIn addition, we prove that the problem is fixed parameter tractable with the number of monomials as parameter. Finally, we reveal connections between the {sc Minimum AND-Circuit} problem and several problems from different areas.","keywords":["Optimization problems","approximability","automated circuit design"],"author":[{"@type":"Person","name":"Arpe, Jan","givenName":"Jan","familyName":"Arpe"},{"@type":"Person","name":"Manthey, Bodo","givenName":"Bodo","familyName":"Manthey"}],"position":4,"pageStart":1,"pageEnd":21,"dateCreated":"2006-10-09","datePublished":"2006-10-09","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Arpe, Jan","givenName":"Jan","familyName":"Arpe"},{"@type":"Person","name":"Manthey, Bodo","givenName":"Bodo","familyName":"Manthey"}],"copyrightYear":"2006","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06111.4","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume601"},{"@type":"ScholarlyArticle","@id":"#article1412","name":"Bounds on the Fourier Coefficients of the Weighted Sum Function","abstract":"We estimate Fourier coefficients of a Boolean function\r\nwhich has recently been introduced in the study of read-once \r\nbranching programs. Our bound implies that this function \r\nhas an asymptotically ``flat'' Fourier spectrum and thus\r\nimplies several lower bounds of its various complexity \r\nmeasures.","keywords":["Fourier coefficients","congruences","average sensitivity","decision tree"],"author":{"@type":"Person","name":"Shparlinski, Igor E.","givenName":"Igor E.","familyName":"Shparlinski"},"position":5,"pageStart":1,"pageEnd":9,"dateCreated":"2006-11-20","datePublished":"2006-11-20","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":{"@type":"Person","name":"Shparlinski, Igor E.","givenName":"Igor E.","familyName":"Shparlinski"},"copyrightYear":"2006","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06111.5","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume601"},{"@type":"ScholarlyArticle","@id":"#article1413","name":"Computing Shortest Paths in Series-Parallel Graphs in Logarithmic Space","abstract":"Series-parallel graphs, which are built by repeatedly applying \r\n series or parallel composition operations to paths, play an\r\n important role in computer science as they model the flow of\r\n information in many types of programs. For directed series-parallel\r\n graphs, we study the problem of finding a shortest path between two\r\n given vertices. Our main result is that we can find such a path in\r\n logarithmic space, which shows that the distance problem for\r\n series-parallel graphs is L-complete. Previously, it was known\r\n that one can compute some path in logarithmic space; but for\r\n other graph types, like undirected graphs or tournament graphs,\r\n constructing some path between given vertices is possible in\r\n logarithmic space while constructing a shortest path is\r\n NL-complete.","keywords":["Series-parallel graphs","shortest path","logspace"],"author":[{"@type":"Person","name":"Jakoby, Andreas","givenName":"Andreas","familyName":"Jakoby"},{"@type":"Person","name":"Tantau, Till","givenName":"Till","familyName":"Tantau"}],"position":6,"pageStart":1,"pageEnd":9,"dateCreated":"2006-11-30","datePublished":"2006-11-30","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Jakoby, Andreas","givenName":"Andreas","familyName":"Jakoby"},{"@type":"Person","name":"Tantau, Till","givenName":"Till","familyName":"Tantau"}],"copyrightYear":"2006","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06111.6","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume601"},{"@type":"ScholarlyArticle","@id":"#article1414","name":"Fault Jumping Attacks against Shrinking Generator","abstract":"In this paper we outline two new cryptoanalytic attacks against hardware implementation of the shrinking generator by Coppersmith et al., a classic design in low-cost, simple-design pseudorandom bitstream generator.\r\nThis is a report on work on progress, since implementation and careful adjusting \r\nthe attack strategy in order to optimize the atatck is still not completed.","keywords":["Pseudorandom generator","shrinking generator","fault cryptanalysis"],"author":[{"@type":"Person","name":"Gomulkiewicz, Marcin","givenName":"Marcin","familyName":"Gomulkiewicz"},{"@type":"Person","name":"Kutylowski, Miroslaw","givenName":"Miroslaw","familyName":"Kutylowski"},{"@type":"Person","name":"Wlaz, Pawel","givenName":"Pawel","familyName":"Wlaz"}],"position":7,"pageStart":1,"pageEnd":6,"dateCreated":"2006-11-20","datePublished":"2006-11-20","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Gomulkiewicz, Marcin","givenName":"Marcin","familyName":"Gomulkiewicz"},{"@type":"Person","name":"Kutylowski, Miroslaw","givenName":"Miroslaw","familyName":"Kutylowski"},{"@type":"Person","name":"Wlaz, Pawel","givenName":"Pawel","familyName":"Wlaz"}],"copyrightYear":"2006","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06111.7","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume601"},{"@type":"ScholarlyArticle","@id":"#article1415","name":"Graphs and Circuits: Some Further Remarks","abstract":"We consider the power of single level circuits in the context of\r\n graph complexity. We first prove that the single level conjecture\r\n fails for fanin-$2$ circuits over the basis ${oplus,land,1}$.\r\n This shows that the (surpisingly tight) phenomenon, established by\r\n Mirwald and Schnorr (1992) for quadratic functions, has no analogon\r\n for graphs. We then show that the single level conjecture fails for\r\n unbounded fanin circuits over ${lor,land,1}$. This partially\r\n answers the question of Pudl'ak, R\"odl and Savick'y (1986). We\r\n also prove that $Sigma_2\r\neq Pi_2$ in a restricted version of the\r\n hierarhy of communication complexity classes introduced by Babai,\r\n Frankl and Simon (1986). Further, we show that even depth-$2$\r\n circuits are surprisingly powerful: every bipartite $n\times n$\r\n graph of maximum degree $Delta$ can be represented by a monotone\r\n CNF with $O(Deltalog n)$ clauses. We also discuss a relation\r\n between graphs and $ACC$-circuits.","keywords":["Graph complexity","single level conjecture","Sylvester graphs","communication complexity","ACC-circuits"],"author":{"@type":"Person","name":"Jukna, Stasys","givenName":"Stasys","familyName":"Jukna"},"position":8,"pageStart":1,"pageEnd":16,"dateCreated":"2006-11-30","datePublished":"2006-11-30","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":{"@type":"Person","name":"Jukna, Stasys","givenName":"Stasys","familyName":"Jukna"},"copyrightYear":"2006","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06111.8","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume601"},{"@type":"ScholarlyArticle","@id":"#article1416","name":"Hadamard Tensors and Lower Bounds on Multiparty Communication Complexity","abstract":"We develop a new method for estimating the discrepancy\r\nof tensors associated with multiparty communication problems\r\nin the ``Number on the Forehead'' model of Chandra, Furst and Lipton.\r\nWe define an analogue of the Hadamard property of matrices\r\nfor tensors in multiple dimensions and show that any $k$-party communication\r\nproblem represented by a Hadamard tensor must have $Omega(n\/2^k)$\r\nmultiparty communication complexity.\r\nWe also exhibit constructions of Hadamard tensors,\r\ngiving $Omega(n\/2^k)$ lower bounds\r\non multiparty communication complexity\r\nfor a new class of explicitly defined Boolean functions.","keywords":["Multiparty communication complexity","lower bounds"],"author":[{"@type":"Person","name":"Ford, Jeff","givenName":"Jeff","familyName":"Ford"},{"@type":"Person","name":"G\u00e1l, Anna","givenName":"Anna","familyName":"G\u00e1l"}],"position":9,"pageStart":1,"pageEnd":20,"dateCreated":"2006-10-09","datePublished":"2006-10-09","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Ford, Jeff","givenName":"Jeff","familyName":"Ford"},{"@type":"Person","name":"G\u00e1l, Anna","givenName":"Anna","familyName":"G\u00e1l"}],"copyrightYear":"2006","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06111.9","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume601"},{"@type":"ScholarlyArticle","@id":"#article1417","name":"Incremental branching programs","abstract":"We propose a new model of restricted branching programs\r\nwhich we call {em incremental branching programs}. \r\nWe show that {em syntactic}\r\nincremental branching programs capture previously studied \r\nstructured models of computation for the problem GEN, namely marking\r\nmachines [Cook74].\r\nand Poon's extension [Poon93] of jumping automata \r\non graphs [CookRackoff80].\r\n\r\nWe then prove\r\nexponential size lower bounds for our syntactic incremental model,\r\nand for some other restricted branching program models as well.\r\nWe further show that nondeterministic syntactic incremental \r\nbranching programs are\r\nprovably stronger than their deterministic counterpart when solving a\r\nnatural NL-complete GEN subproblem.\r\nIt remains open if syntactic incremental branching programs are as powerful\r\nas unrestricted branching programs for GEN problems.\r\n\r\nJoint work with Anna G\u00c3\u0192\u00c2\u00a1l and Michal Kouck\u00c3\u0192\u00c2\u00bd","keywords":["Complexity theory","branching programs","logarithmic space","marking machines"],"author":[{"@type":"Person","name":"G\u00e1l, Anna","givenName":"Anna","familyName":"G\u00e1l"},{"@type":"Person","name":"McKenzie, Pierre","givenName":"Pierre","familyName":"McKenzie"},{"@type":"Person","name":"Kouck\u00fd, Michal","givenName":"Michal","familyName":"Kouck\u00fd"}],"position":10,"pageStart":1,"pageEnd":20,"dateCreated":"2006-11-30","datePublished":"2006-11-30","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"G\u00e1l, Anna","givenName":"Anna","familyName":"G\u00e1l"},{"@type":"Person","name":"McKenzie, Pierre","givenName":"Pierre","familyName":"McKenzie"},{"@type":"Person","name":"Kouck\u00fd, Michal","givenName":"Michal","familyName":"Kouck\u00fd"}],"copyrightYear":"2006","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06111.10","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume601"},{"@type":"ScholarlyArticle","@id":"#article1418","name":"On Probabilistic Time versus Alternating Time","abstract":"Sipser and G\u00c3\u0192\u00c2\u00a1cs, and independently Lautemann, proved in '83 that probabilistic polynomial time is contained in the second level of the polynomial-time hierarchy, i.e. BPP is in Sigma_2 P. This is essentially the only non-trivial upper bound that we have on the power of probabilistic computation. More precisely, the Sipser-G\u00c3\u0192\u00c2\u00a1cs-Lautemann simulation shows that probabilistic time can be simulated deterministically, using two quantifiers, **with a quadratic blow-up in the running time**. That is, BPTime(t) is contained in Sigma_2 Time(t^2).\r\n\r\nIn this talk we discuss whether this quadratic blow-up in the running time is necessary. We show that the quadratic blow-up is indeed necessary for black-box simulations that use two quantifiers, such as those of Sipser, G\u00c3\u0192\u00c2\u00a1cs, and Lautemann. To obtain this result, we prove a new circuit lower bound for computing **approximate majority**, i.e. computing the majority of a given bit-string whose fraction of 1's is bounded away from 1\/2 (by a constant): We show that small depth-3 circuits for approximate majority must have bottom fan-in Omega(log n).\r\n\r\nOn the positive side, we obtain that probabilistic time can be simulated deterministically, using three quantifiers, in quasilinear time. That is, BPTime(t) is contained in Sigma_3 Time(t polylog t). Along the way, we show that approximate majority can be computed by uniform polynomial-size depth-3 circuits. This is a uniform version of a striking result by Ajtai that gives *non-uniform* polynomial-size depth-3 circuits for approximate majority.\r\n\r\nIf time permits, we will discuss some applications of our results to proving lower bounds on randomized Turing machines.","keywords":["Probabilistic time","alternating time","polynomial-time hierarchy","approximate majority","constant-depth circuit"],"author":{"@type":"Person","name":"Viola, Emanuele","givenName":"Emanuele","familyName":"Viola"},"position":11,"pageStart":1,"pageEnd":0,"dateCreated":"2006-11-30","datePublished":"2006-11-30","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":{"@type":"Person","name":"Viola, Emanuele","givenName":"Emanuele","familyName":"Viola"},"copyrightYear":"2006","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06111.11","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume601"},{"@type":"ScholarlyArticle","@id":"#article1419","name":"On the Complexity of Numerical Analysis","abstract":"We study two quite different approaches to understanding the complexity of fundamental problems in numerical analysis. We show that both hinge on the question of understanding the complexity of the following problem, which we call PosSlp: Given a division-free straight-line program producing an integer N, decide whether N>0. We show that OrdSlp lies in the counting hierarchy, and combining our results with work of Tiwari, we show that the Euclidean Traveling Salesman Problem lies in the counting hierarchy \u2013 the previous best upper bound for this important problem (in terms of classical complexity classes) being PSPACE.","keywords":["Blum-Shub-Smale Model","Euclidean Traveling Salesman Problem","Counting Hierarchy"],"author":[{"@type":"Person","name":"Allender, Eric","givenName":"Eric","familyName":"Allender"},{"@type":"Person","name":"B\u00fcrgisser, Peter","givenName":"Peter","familyName":"B\u00fcrgisser"},{"@type":"Person","name":"Kjeldgaard-Pedersen, Johan","givenName":"Johan","familyName":"Kjeldgaard-Pedersen"},{"@type":"Person","name":"Miltersen, Peter Bro","givenName":"Peter Bro","familyName":"Miltersen"}],"position":12,"pageStart":1,"pageEnd":9,"dateCreated":"2006-11-20","datePublished":"2006-11-20","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Allender, Eric","givenName":"Eric","familyName":"Allender"},{"@type":"Person","name":"B\u00fcrgisser, Peter","givenName":"Peter","familyName":"B\u00fcrgisser"},{"@type":"Person","name":"Kjeldgaard-Pedersen, Johan","givenName":"Johan","familyName":"Kjeldgaard-Pedersen"},{"@type":"Person","name":"Miltersen, Peter Bro","givenName":"Peter Bro","familyName":"Miltersen"}],"copyrightYear":"2006","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06111.12","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume601"},{"@type":"ScholarlyArticle","@id":"#article1420","name":"On the Teachability of Randomized Learners","abstract":"The present paper introduces a new model for teaching {em randomized learners}.\r\nOur new model, though based on the classical teaching dimension model,\r\nallows to study the influence of various parameters such as the\r\nlearner's memory size, its ability to provide or to not provide feedback,\r\nand the influence of the order in which examples are presented.\r\nFurthermore, within the new model it is possible to investigate \r\nnew aspects of teaching like teaching from positive data only or \r\nteaching with inconsistent teachers. \r\n\r\nFurthermore, we provide characterization theorems for teachability from \r\npositive data for both ordinary teachers and inconsistent teachers with and\r\nwithout feedback.","keywords":["Algorithmic Teaching","Complexity of teaching"],"author":[{"@type":"Person","name":"Balbach, Frank J.","givenName":"Frank J.","familyName":"Balbach"},{"@type":"Person","name":"Zeugmann, Thomas","givenName":"Thomas","familyName":"Zeugmann"}],"position":13,"pageStart":1,"pageEnd":20,"dateCreated":"2006-11-30","datePublished":"2006-11-30","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Balbach, Frank J.","givenName":"Frank J.","familyName":"Balbach"},{"@type":"Person","name":"Zeugmann, Thomas","givenName":"Thomas","familyName":"Zeugmann"}],"copyrightYear":"2006","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06111.13","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume601"},{"@type":"ScholarlyArticle","@id":"#article1421","name":"Quantum Network Coding","abstract":"Since quantum information is continuous, its handling is sometimes\r\nsurprisingly harder than the classical counterpart. A typical\r\nexample is cloning; making a copy of digital information is\r\nstraightforward but it is not possible exactly for quantum\r\ninformation. The question in this paper is whether or not {em\r\nquantum} network coding is possible. Its classical counterpart is\r\nanother good example to show that digital information flow can be done\r\nmuch more efficiently than conventional (say, liquid) flow.\r\n\r\nOur answer to the question is similar to the case of cloning, namely,\r\nit is shown that quantum network coding is possible if approximation\r\nis allowed, by using a simple network model called Butterfly. In this\r\nnetwork, there are two flow paths, $s_1$ to $t_1$ and $s_2$ to $t_2$,\r\nwhich shares a single bottleneck channel of capacity one. In the\r\nclassical case, we can send two bits simultaneously, one for each\r\npath, in spite of the bottleneck. Our results for quantum network\r\ncoding include: (i) We can send any quantum state $|psi_1\r\nangle$\r\nfrom $s_1$ to $t_1$ and $|psi_2\r\nangle$ from $s_2$ to $t_2$\r\nsimultaneously with a fidelity strictly greater than $1\/2$. (ii) If\r\none of $|psi_1\r\nangle$ and $|psi_2\r\nangle$ is classical, then the\r\nfidelity can be improved to $2\/3$. (iii) Similar improvement is also\r\npossible if $|psi_1\r\nangle$ and $|psi_2\r\nangle$ are restricted to\r\nonly a finite number of (previously known) states. (iv) Several\r\nimpossibility results including the general upper bound of the fidelity\r\nare also given.","keywords":["Network coding","quantum computation","quantum information"],"author":[{"@type":"Person","name":"Hayashi, Masahito","givenName":"Masahito","familyName":"Hayashi"},{"@type":"Person","name":"Iwama, Kazuo","givenName":"Kazuo","familyName":"Iwama"},{"@type":"Person","name":"Nishimura, Harumichi","givenName":"Harumichi","familyName":"Nishimura"},{"@type":"Person","name":"Raymond, Rudy","givenName":"Rudy","familyName":"Raymond"},{"@type":"Person","name":"Yamashita, Shigeru","givenName":"Shigeru","familyName":"Yamashita"}],"position":14,"pageStart":1,"pageEnd":17,"dateCreated":"2006-10-09","datePublished":"2006-10-09","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Hayashi, Masahito","givenName":"Masahito","familyName":"Hayashi"},{"@type":"Person","name":"Iwama, Kazuo","givenName":"Kazuo","familyName":"Iwama"},{"@type":"Person","name":"Nishimura, Harumichi","givenName":"Harumichi","familyName":"Nishimura"},{"@type":"Person","name":"Raymond, Rudy","givenName":"Rudy","familyName":"Raymond"},{"@type":"Person","name":"Yamashita, Shigeru","givenName":"Shigeru","familyName":"Yamashita"}],"copyrightYear":"2006","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06111.14","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume601"},{"@type":"ScholarlyArticle","@id":"#article1422","name":"Quantum vs. Classical Read-Once Branching Programs","abstract":"A simple, explicit boolean function on 2n input bits is presented that is \r\ncomputable by errorfree quantum read-once branching programs of size \r\nO(n^3), while each classical randomized read-once branching program \r\nand each quantum OBDD for this function with bounded two-sided error \r\nrequires size 2^{omega(n)}.","keywords":["Quantum branching program","randomized branching program","read-once"],"author":{"@type":"Person","name":"Sauerhoff, Martin","givenName":"Martin","familyName":"Sauerhoff"},"position":15,"pageStart":1,"pageEnd":13,"dateCreated":"2006-11-20","datePublished":"2006-11-20","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":{"@type":"Person","name":"Sauerhoff, Martin","givenName":"Martin","familyName":"Sauerhoff"},"copyrightYear":"2006","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06111.15","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume601"},{"@type":"ScholarlyArticle","@id":"#article1423","name":"Secure Linear Algebra Using Linearly Recurrent Sequences","abstract":"In this work we present secure two-party protocols for\r\nvarious core problems in linear algebra.\r\nOur main building block is a protocol to obliviously decide singularity\r\nof an encrypted matrix:\r\nBob holds an $n \times n$ matrix $M$, encrypted with Alice's secret\r\nkey, and wants to learn whether\r\nthe matrix is singular or not (and nothing beyond that).\r\nWe give an interactive protocol between Alice and Bob that solves the\r\nabove problem\r\nwith optimal communication complexity while at the same time achieving\r\nlow round complexity.\r\nMore precisely, the number of communication rounds in our protocol\r\nis $polylog(n)$ and\r\nthe overall communication is roughly $O(n^2)$ (note that the input size is $n^2$).\r\nAt the core of our protocol we exploit some nice mathematical\r\nproperties of linearly recurrent sequences and their\r\nrelation to the characteristic polynomial of the matrix $M$, following [Wiedemann, 1986].\r\nWith our new techniques we are able to improve the round complexity of\r\nthe communication efficient solution of [Nissim and Weinreb, 2006] from $n^{0.275}$ to $polylog(n)$.\r\n\r\nBased on our singularity protocol we further\r\nextend our result to the problems of securely computing the rank of an\r\nencrypted matrix and solving systems of linear equations.","keywords":["Secure Linear Algebra","Linearly Recurrent Sequences","Wiedemann's Algorithm"],"author":[{"@type":"Person","name":"Kiltz, Eike","givenName":"Eike","familyName":"Kiltz"},{"@type":"Person","name":"Weinreb, Enav","givenName":"Enav","familyName":"Weinreb"}],"position":16,"pageStart":1,"pageEnd":19,"dateCreated":"2006-11-20","datePublished":"2006-11-20","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Kiltz, Eike","givenName":"Eike","familyName":"Kiltz"},{"@type":"Person","name":"Weinreb, Enav","givenName":"Enav","familyName":"Weinreb"}],"copyrightYear":"2006","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06111.16","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume601"},{"@type":"ScholarlyArticle","@id":"#article1424","name":"The Cell Probe Complexity of Succinct Data Structures","abstract":"In the cell probe model with word size 1 (the bit probe model), a\r\nstatic data structure problem is given by a map \r\n$f: {0,1}^n \times {0,1}^m \r\nightarrow {0,1}$,\r\nwhere ${0,1}^n$ is a set of possible data to be stored, \r\n${0,1}^m$ is a set of possible queries (for natural problems, we\r\nhave $m ll n$) and $f(x,y)$ is \r\nthe answer to question $y$ about data $x$.\r\n\r\nA solution is given by a \r\nrepresentation $phi: {0,1}^n \r\nightarrow {0,1}^s$ and a query algorithm\r\n$q$ so that $q(phi(x), y) = f(x,y)$. The time $t$ of the query algorithm\r\nis the number of bits it reads in $phi(x)$.\r\n\r\nIn this paper, we consider the case of {em succinct} representations\r\nwhere $s = n + r$ for some {em redundancy} $r ll n$.\r\nFor \r\na boolean version of the problem of polynomial\r\nevaluation with preprocessing of coefficients, we show a lower bound on \r\nthe redundancy-query time tradeoff of the form \r\n[ (r+1) t geq Omega(n\/log n).] \r\nIn particular, for very small \r\nredundancies $r$, we get an almost optimal lower bound stating that the \r\nquery algorithm has to inspect almost the entire data structure\r\n(up to a logarithmic factor).\r\nWe show similar lower bounds for problems satisfying a certain\r\ncombinatorial property of a coding theoretic flavor. \r\nPreviously, no $omega(m)$ lower bounds were known on $t$ \r\nin the general model for explicit functions, even for very small\r\nredundancies.\r\n\r\nBy restricting our attention to {em systematic} or {em index}\r\nstructures $phi$ satisfying $phi(x) = x cdot phi^*(x)$ for some\r\nmap $phi^*$ (where $cdot$ denotes concatenation) we show\r\nsimilar lower bounds on the redundancy-query time tradeoff \r\nfor the natural data structuring problems of Prefix Sum\r\nand Substring Search.","keywords":["Cell probe model","data structures","lower bounds","time-space tradeoffs"],"author":[{"@type":"Person","name":"G\u00e1l, Anna","givenName":"Anna","familyName":"G\u00e1l"},{"@type":"Person","name":"Miltersen, Peter Bro","givenName":"Peter Bro","familyName":"Miltersen"}],"position":17,"pageStart":1,"pageEnd":13,"dateCreated":"2006-10-09","datePublished":"2006-10-09","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"G\u00e1l, Anna","givenName":"Anna","familyName":"G\u00e1l"},{"@type":"Person","name":"Miltersen, Peter Bro","givenName":"Peter Bro","familyName":"Miltersen"}],"copyrightYear":"2006","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06111.17","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume601"},{"@type":"ScholarlyArticle","@id":"#article1425","name":"The complexity of Boolean functions from cryptographic viewpoint","abstract":"Cryptographic Boolean functions must be complex to satisfy Shannon's principle of confusion. But the cryptographic viewpoint on complexity is not the same as in circuit complexity. \r\nThe two main criteria evaluating the cryptographic complexity of Boolean functions on $F_2^n$ are the nonlinearity (and more generally the $r$-th order nonlinearity, for every positive $r< n$) and the algebraic degree. Two other criteria have also been considered: the algebraic thickness and the non-normality. After recalling the definitions of these criteria and why, asymptotically, almost all Boolean functions are deeply non-normal and have high algebraic degrees, high ($r$-th order) nonlinearities and high algebraic thicknesses, we study the relationship between the $r$-th order nonlinearity and a recent cryptographic criterion called the algebraic immunity. This relationship strengthens the reasons why the algebraic immunity can be considered as a further cryptographic complexity criterion.","keywords":["Boolean function","nonlinearity","Reed-Muller code"],"author":{"@type":"Person","name":"Carlet, Claude","givenName":"Claude","familyName":"Carlet"},"position":18,"pageStart":1,"pageEnd":15,"dateCreated":"2006-10-09","datePublished":"2006-10-09","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":{"@type":"Person","name":"Carlet, Claude","givenName":"Claude","familyName":"Carlet"},"copyrightYear":"2006","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06111.18","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume601"},{"@type":"ScholarlyArticle","@id":"#article1426","name":"The optimal sequence compression","abstract":"This paper presents the optimal compression for sequences with\r\nundefined values. \r\n\r\nLet we have $(N-m)$ undefined and $m$ defined positions in the\r\nboolean sequence $vv V$ of length $N$. The sequence code length\r\ncan't be less then $m$ in general case, otherwise at least two\r\nsequences will have the same code.\r\n\r\nWe present the coding algorithm which generates codes of almost $m$\r\nlength, i.e. almost equal to the lower bound.\r\n\r\nThe paper presents the decoding circuit too. The circuit has low\r\ncomplexity which depends from the inverse density of defined values\r\n$D(vv V) = frac{N}{m}$.\r\n\r\nThe decoding circuit includes RAM and random logic. It performs\r\nsequential decoding. The total RAM size is proportional to the\r\n$$logleft(D(vv V)\r\night) ,$$\r\nthe number of random logic cells is proportional to\r\n$$log logleft(D(vv V)\r\night) * left(log log logleft(D(vv V)\r\night)\r\night)^2 .$$\r\nSo the decoding circuit will be small enough even for the very low\r\ndensity sequences. The decoder complexity doesn't depend of the\r\nsequence length at all.","keywords":["Compression","partial boolean function"],"author":{"@type":"Person","name":"Andreev, Alexander E.","givenName":"Alexander E.","familyName":"Andreev"},"position":19,"pageStart":1,"pageEnd":11,"dateCreated":"2006-10-09","datePublished":"2006-10-09","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":{"@type":"Person","name":"Andreev, Alexander E.","givenName":"Alexander E.","familyName":"Andreev"},"copyrightYear":"2006","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06111.19","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume601"},{"@type":"ScholarlyArticle","@id":"#article1427","name":"Time-Space Lower Bounds for the Polynomial-Time Hierarchy on Randomized Machines","abstract":"In this talk, we establish lower bounds for the running time of randomized\r\nmachines with two-sided error which use a small amount of workspace to\r\nsolve complete problems in the polynomial-time hierarchy. In particular,\r\nwe show that for integers $l > 1$, a randomized machine with two-sided error\r\nusing subpolynomial space requires time $n^{l - o(1)}$ to solve QSATl, where\r\nQSATl denotes the problem of deciding the validity of a Boolean first-order\r\nformula with at most $l-1$ quantifier alternations. This represents the first\r\ntime-space lower bounds for complete problems in the polynomial-time\r\nhierarchy on randomized machines with two-sided error.\r\n\r\nCorresponding to $l = 1$, we show that a randomized machine with one-sided\r\nerror using subpolynomial space requires time $n^{1.759}$ to decide the set\r\nof Boolean tautologies. As a corollary, this gives the same lower bound for\r\nsatisfiability on deterministic machines, improving on the previously best\r\nknown such result.","keywords":["Time-space lower bounds","lower bounds","randomness","polynomial-time hierarchy"],"author":[{"@type":"Person","name":"Diehl, Scott","givenName":"Scott","familyName":"Diehl"},{"@type":"Person","name":"van Melkebeek, Dieter","givenName":"Dieter","familyName":"van Melkebeek"}],"position":20,"pageStart":1,"pageEnd":33,"dateCreated":"2006-10-09","datePublished":"2006-10-09","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Diehl, Scott","givenName":"Scott","familyName":"Diehl"},{"@type":"Person","name":"van Melkebeek, Dieter","givenName":"Dieter","familyName":"van Melkebeek"}],"copyrightYear":"2006","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06111.20","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume601"},{"@type":"ScholarlyArticle","@id":"#article1428","name":"Using Quantum Oblivious Transfer to Cheat Sensitive Quantum Bit Commitment","abstract":"We define $(varepsilon,delta)$-secure quantum computations \r\nbetween two parties that can play dishonestly to maximise \r\nadvantage $delta$, however keeping small the probability \r\n$varepsilon$ that the computation fails in evaluating correct value. \r\nWe present a simple quantum protocol for computing \r\none-out-of-two oblivious transfer that is \r\n$(O(sqrt{varepsilon}),varepsilon)$-secure.\r\nUsing the protocol as a black box we construct a scheme for\r\ncheat sensitive quantum bit commitment which guarantee that \r\na mistrustful party has a nonzero probability of detecting a \r\ncheating.","keywords":["Two-Party Computations","Quantum Protocols","Bit Commitment","Oblivious Transfer."],"author":[{"@type":"Person","name":"Jakoby, Andreas","givenName":"Andreas","familyName":"Jakoby"},{"@type":"Person","name":"Liskiewicz, Maciej","givenName":"Maciej","familyName":"Liskiewicz"},{"@type":"Person","name":"Madry, Aleksander","givenName":"Aleksander","familyName":"Madry"}],"position":21,"pageStart":1,"pageEnd":12,"dateCreated":"2006-11-30","datePublished":"2006-11-30","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Jakoby, Andreas","givenName":"Andreas","familyName":"Jakoby"},{"@type":"Person","name":"Liskiewicz, Maciej","givenName":"Maciej","familyName":"Liskiewicz"},{"@type":"Person","name":"Madry, Aleksander","givenName":"Aleksander","familyName":"Madry"}],"copyrightYear":"2006","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06111.21","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume601"},{"@type":"ScholarlyArticle","@id":"#article1429","name":"Very Large Cliques are Easy to Detect","abstract":"It is known that, for every constant $kgeq 3$, the presence of a\r\n $k$-clique (a complete subgraph on $k$ vertices) in an $n$-vertex\r\n graph cannot be detected by a monotone boolean circuit using fewer\r\n than $Omega((n\/log n)^k)$ gates. We show that, for every constant\r\n $k$, the presence of an $(n-k)$-clique in an $n$-vertex graph can be\r\n detected by a monotone circuit using only $O(n^2log n)$ gates.\r\n Moreover, if we allow unbounded fanin, then $O(log n)$ gates are\r\n enough.","keywords":["Clique function","monotone circuits","perfect hashing"],"author":[{"@type":"Person","name":"Andreev, Alexander E.","givenName":"Alexander E.","familyName":"Andreev"},{"@type":"Person","name":"Jukna, Stasys","givenName":"Stasys","familyName":"Jukna"}],"position":22,"pageStart":1,"pageEnd":7,"dateCreated":"2006-11-20","datePublished":"2006-11-20","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Andreev, Alexander E.","givenName":"Alexander E.","familyName":"Andreev"},{"@type":"Person","name":"Jukna, Stasys","givenName":"Stasys","familyName":"Jukna"}],"copyrightYear":"2006","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06111.22","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume601"}]}