March 2003 - Categories - categories.org.au

More Topos questions ala "Conceptual Mathematics"
by Galchin Vasili 11 Jun '03

11 Jun '03

Hello, 1) In the very last chapter (Session 33 "2: Toposes and logic" of "Conceptual Mathematics" where the authors cover topoi, they define '=>' for the internal Heyting algebra of Omega: "Another logical operation is 'implication', which is denoted '=>'. This is also a map Omega x Omega->Omega, defined as the classifying map of the subobject S 'hook' Omega x Omega determined by the all those <alpha, beta> in Omega x Omega such that alpha "subset of" beta." Starting from "subobject S 'hook" ......" I got totally lost. I am frustrated because I know this is crucial to understanding why Omega is an internal Heyting algebra, so any help would be appreciated. (I am assuming that alpha and beta are subojects of Omega???). 2) In the same Session 33 on pg 350 is a set "rules of logic". These are exactly the axioms for a Heyting algebra, yes? Regards, Bill Halchin

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Vietnamese Mathematician
by John Duskin 01 Apr '03

01 Apr '03

-- The mathematician from Hanoi recently honored by the French , Hoang Xuan Sinh, was a student of Grothendieck. Her thesis was on Gr-categories.

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Grothendieck's 1973 Buffalo Colloquium
by F W Lawvere 31 Mar '03

31 Mar '03

Thierry Coquand recently asked me > In your "Comments on the Development of Topos Theory" you refer > to a simpler alternative definition of "scheme" due to Grothendieck. > Is this definition available at some place?? Otherwise, it it possible > to describe shortly the main idea of this alternative definition?? Since several people have asked the same question over the years, I prepared the following summary which, I hope, will be of general interest: The 1973 Buffalo Colloquium talk by Alexander Grothendieck had as its main theme that the 1960 definition of scheme (which had required as a prerequisite the baggage of prime ideals and the spectral space, sheaves of local rings, coverings and patchings, etc.), should be abandoned AS the FUNDAMENTAL one and replaced by the simple idea of a good functor from rings to sets. The needed restrictions could be more intuitively and more geometrically stated directly in terms of the topos of such functors, and of course the ingredients from the "baggage" could be extracted when needed as auxiliary explanations of already existing objects, rather than being carried always as core elements of the very definition. Thus his definition is essentially well-known, and indeed is mentioned in such texts as Demazure-Gabriel, Waterhouse, and Eisenbud; but it is not carried through to the end, resulting in more complication, rather than less. I myself had learned the functorial point of view from Gabriel in 1966 at the Strasbourg-Heidelberg-Oberwolfach seminar and therefore I was particularly gratified when I heard Grothendieck so emphatically urging that it should replace the one previously expounded by Dieudonne' and himself. He repeated several times that points are not mere points, but carry Galois group actions. I regard this as a part of the content of his opinion (expressed to me in 1989) that the notion of topos was among his most important contributions. A more general expression of that content, I believe, is that a generalized "gros" topos can be a better approximation to geometric intuition than a category of topological spaces, so that the latter should be relegated to an auxiliary position rather than being routinely considered as "the" default notion of cohesive space. (This is independent of the use of localic toposes, a special kind of petit which represents only a minor modification of the traditional view and not even any modification in the algebraic geometry context due to coherence). It is perhaps a reluctance to accept this overthrow that explains the situation 30 years later, when Grothendieck's simplification is still not widely considered to be elementary and "basic". To recall some well-known ingredients, let A be the category of finitely-presented commutative algebras over k (or a larger category closed under the symmetric algebra functor, for some purposes). Then the underlying set functor R on A serves as the "line", and any system of polynomial equations with coefficients in k determines also a functor (sub space of Rn) in the well-known way; in fact, the idea of spec is simply identified with the Yoneda embedding of A^op. For example, R has a subfunctor U of invertible elements and another U' such that U'(A) = {f|f in A, 1/1-f in A}. The Grothendieck topology for which U and U' together cover R yields a subtopos Z known as the gros Zariski topos, which turns out to be the classifying topos for local k-algebras in any topos. This Z contains all algebraic schemes over k, but also function spaces Y^X and distribution spaces Hom(R^X,R) for all X,Y in Z. A basic open subspace of any space X is determined as the pullback U sub f of U under any map f: X-->R. One has obviously U sub f intersection U sub g = U sub fg and the intrinsic notion of epimorphism in Z gives a notion of covering. Thus for a space (functor) to have a finite open covering, each piece of which is representable, is a restrictive notion available when needed. A point of X is a map spec(L) --> X where L is a field extension of k.Thus the "points functor" on spaces goes not to the category of abstract sets but rather is just the restriction operation to the category of functors on fields only. This is part of what Grothendieck seems to have had in mind. A serious discontinuity is introduced by passing to the single underlying set traditionally considered, which is the inductive limit of the functor of fields. The fact that the latter process does not preserve products, and hence for example that an algebraic group "is not a group", was already for Cartier an indication that the traditional foundation had an unnatural ingredient, but before topos theory one tried to live with it (for example, I recall great geometers from the 1950s struggling to accept the new wisdom that +i and -i is one "point"). The acceptance of the view that, for non-algebraically-closed k, the appropriate base topos consists not of pure sets but rather of sheaves on just the simple objects in A, has in fact many simplifying conceptual and technical advantages; for example this base (in some sense due to Galois!) is at least qd in the sense of Johnstone, and even atomic Boolean in the sense of Barr. (Technically, to verify that the above limitation to "algebraic" A gives the usual results requires the use of a Birkhoff Nullstellensatz which guarantees that there are "enough" algebras which are finitely-generated as k-modules. The use of a larger A, insuring for example that spaces of distributions are often themselves representable, is quite possible, but the precise description of the kind of double structure which is then topos-theoretically classified needs to be worked out. Gaeta's notes of Grothendieck's lecture series at Buffalo point out that A is more closely suited than most categories to serve as a site for a geometric category, because it is what is now called "extensive" ) I believe that Grothendieck's point of view could be applied to real algebraic geometry as well, in several ways, including the following: Noting that within any topos the adjoint is available which assigns the ring R[-1] to any rig R, let us concentrate on the needed nature of positive quantities R. To include the advantages of differential calculus based on nilpotent elements, let us allow that the ideal of all elements having negatives can be non-trivial, and indeed include many infinitesimals, without disqualifying R from being "nonnegative". The ring generated by R might appear in a more geometric way as the fiber of R^T, where T is the representor for the tangent-bundle functor. The classifying topos for the theory of "real rigs", i.e., those for which 1/1+x is a given global operation, contains the classifying topos for "really local rigs" in the following sense (where "really" has the double meaning of (1) a strengthening of localness, but also (2) a concept appropriate to a real (as opposed to complex) environment): The subspace U of invertible elements in the generic algebra R has a classifying map R --> omega which of course as above preserves products; but the distributive lattice omega is in particular also a rig like R, so we can require that the classifying map be a rig homomorphism (i.e., also take + to "union"). (Of course, this elementary condition can be phrased in terms of subspaces of R and of R^2 without involving omega if desired.) The preservation of addition is a strengthening, possible for positive quantities, of the usual notion of localness (which on truth values was only an inequality). Does the right adjoint to ( )^T restrict to this really local rig classifier? ************************************************************ F. William Lawvere Mathematics Department, State University of New York 244 Mathematics Building, Buffalo, N.Y. 14260-2900 USA Tel. 716-645-6284 HOMEPAGE: http://www.acsu.buffalo.edu/~wlawvere ************************************************************

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NASSLLI 2003. Registration is open now.
by NASSLLI'03 Bloomington, Indiana 31 Mar '03

31 Mar '03

<apologies for multiple postings> Registration for NASSLLI 2003 is now open. For details, please visit http://www.indiana.edu/~nasslli/registration.html ------------------------------------------------------------------------- NASSLLI 2003 http://www.indiana.edu/~nasslli The main focus of NASSLLI is on the interface between linguistics, logic, and computation, broadly conceived, and on related fields. NASSLLI is a week-long summer school featuring courses on many topics of interest to students and researchers. Some of the course topics are introductory, while others are advanced courses that bring students to areas of active research. The instructors are leading researchers who like teaching in interdisciplinary settings. Three of the courses involve work in computer labs as well. Please join us for a week of learning! ----------------------------------------------------------------------------- Registration Registration does not include accommodations. We have arranged rooms in a renovated, air-conditioned dormitory at the rate of $37/night/person + 11% tax. These are single rooms with a bathroom shared between two rooms. You will need to pay for this when you are here with cash, check, MasterCard or Visa. To reserve one of these rooms please send an e-mail to nasslli(a)indiana.edu , detailing for which days you will need the room. In addition, our page on hotels lists some other housing options. http://www.indiana.edu/~nasslli/hotels.html -------------------------------------------------------------------------------- Register for NASSLLI alone Before May 1 After May 1 Full-time Student $135 $150 Academic $200 $225 Industrial $280 $315 -------------------------------------------------------------------------------- Register for MoL alone To register for MoL alone, without NASSLLI: $43. -------------------------------------------------------------------------------- Register for TARK alone To register for TARK alone, without NASSLLI: For students: $100 For others: $150 -------------------------------------------------------------------------------- Register for NASSLLI + TARK Before May 1 After May 1 Full-time Student $210 $225 Academic $325 $350 Industrial $405 $440

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categorist makes good?
by Peter Freyd 29 Mar '03

29 Mar '03

Copyright 2003 Vietnam News Briefs Vietnam News Briefs March 28, 2003 LENGTH: 95 words HEADLINE: SOCIAL & CULTURAL ISSUES: FEMALE VIETNAMESE SCIENTISTS RECEIVE FRENCH ORDER BODY: The French Government has awarded the French Order of Academic Palms to two Vietnamese scientists, Le Hong Sam and Hoang Xuan Sinh, for their contributions to boosting cooperation in culture and science between the two nations. Ms Sam is a researcher on French literature and currently works for the National University of Social Sciences & Humanities in Hanoi. Ms Sinh, a mathematician, is the principal of the Thang Long Open University in Hanoi. The presentation ceremony was held at the French Embassy in Hanoi on March 25. ********************************************************************** Her papers, as adapted from MathSciNet: Hoang Xuan Sinh Gr-categories strictes. (French) Acta Math. Vietnam. 3 (1978), no. 2, 47--59. 18D10 (20J05 20L10) A Gr-category is a groupoid P which is a monoidal category with product and unit such that each object X of P has an inverse (X', t, p), where t:X'*X -> 1 and p:X*X' -> 1. It is called a strict Gr-category if it is a strict monoidal category and t and p are identities for every X. The main theorem of this paper states that every Gr-category is Gr-equivalent to a strict Gr-category...The proof of this theorem uses a result of the author's thesis at the University of Paris VII, 1975 which is that every Gr-category P is determined up to a Gr-equivalence by two groups...As an application of the results of this paper, the author proves Lemma 9.1 of S. Eilenberg and S. Mac Lane [Ann. of Math. (2) 48 (1947), 326--341; MR 9, 7] on the realization of a 3-cocycle as the obstruction of a problem of extension. Reviewed by J. L. Williams Hoang Xuan Sinh Categories de Picard restreintes. (French) [Restricted Picard categories] Acta Math. Vietnam. 7 (1982), no. 1, 117--122 (1983). 18E99 >>From the text: "A Picard category is a Gr-category equipped with a commutativity constraint compatible with its associativity constraint. A Picard category P is said to be restricted if its commutativity constraint c satisfies c_{x,x}= identity for all objects x. We represent every Picard category by a complex of chains and we deduce that the classification of restricted prefastened (`preepinglees') Picard categories of type (M,N) is trivial."

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CONCUR 2003 - Call for papers - Marseille, France
by Remi.Morin＠cmi.univ-mrs.fr 26 Mar '03

26 Mar '03

We apologize if you receive multiple copies of this message. ********************************************************** ********************************************************** *** *** *** CONCUR 2003 *** *** *** *** September, 3-5, 2003 *** *** Marseille, France *** *** *** *** CALL FOR PAPERS *** *** *** ********************************************************** ********************************************************** CONCUR 2003, the 14th international conference on concurrency theory, is organized by the Laboratoire d'Informatique Fondamentale de Marseille (LIF). The purpose of the CONCUR conferences is to bring together researchers, developers and students in order to advance the theory of concurrency, and promote its applications. Interest in this topic is continuously growing, as a consequence of the importance and ubiquity of concurrent systems and their applications, and of the scientific relevance of their foundations. Submissions are solicited in all areas of semantics, logics and verification techniques for concurrent systems. Principal topics include (but are not limited to): - Basic models and logics of concurrent and distributed computation (such as process algebras, Petri nets, domain theoretic or game theoretic models, modal and temporal logics). - Specialized or enriched models (such as circuits, synchronous systems, real time and hybrid systems, stochastic systems, data bases, mobile and migrating systems, parametric protocols, security protocols). - Related verification techniques and tools (such as state-space exploration, model-checking, synthesis, abstraction, automated deduction, testing). - Related programming models (such as distributed, constraints or object oriented, graph rewriting, as well as associated type systems, static analyses, abstract machines, and environments). Authors are invited to submit an extended abstract not exceeding 15 pages electronically via the web submission form at the conference's web site. Submissions will be evaluated by the program committee for inclusion in the proceedings, which will be published by Springer-Verlag in the Lecture Notes in Computer Science series. Papers must contain original contributions, be clearly written, and include appropriate reference to and comparison with related work. Simultaneous submissions to other conferences are not allowed. Important dates Submission: April 4, 2003 --> There will be no deadline extension. Notification: May 26, 2003 Final version: June 10, 2003 Workshops: September 2,6, and 7, 2003 Program committee Roberto Amadio, chair (Marseille) Denis Lugiez, co-chair (Marseille) David Basin (Zurich) Madhavan Mukund (Chennai) Julian Bradfield (Edinburgh) Doron Peled (Austin) Witold Charatonik (Wroclaw) Jean-François Raskin (Brussels) Alessandro Cimatti (Trento) Roberto Segala (Verona) Philippa Gardner (London) Eugene Stark (Stony-Brook) Patrice Godefroid (Murray-Hill) Peter Van Roy (Louvain-la-Neuve) Holger Hermanns (Twente) Thomas Wilke (Kiel) Naoki Kobayashi (Tokyo) Glynn Winskel (Cambridge) Kim Larsen (Aalborg) Invited speakers Albert Benveniste (Rennes) Nancy Lynch (Boston) Luca De Alfaro (Santa-Cruz) Andre Scedrov (Philadelphia) More informations available at the conference's web site http://concur03.univ-mrs.fr

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Peripatetic Seminar on Sheaves and Logic
by Benno van den Berg 24 Mar '03

24 Mar '03

Dear all, A PSSL will be organized by the University of Utrecht (in the Netherlands) in the weekend of the 28th and 29th of June. I will launch a webpage where the necessary information can be found. You will be informed as soon as it is finished. With best regards, Benno -- Benno van den Berg - Mathematisch Instituut, UU vdberg(a)math.uu.nl - P.O.box 80.010, 3508 TA Utrecht, NL

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Prime Ideal Theorem implies Excluded Middle?
by C.F.Townsend 23 Mar '03

23 Mar '03

Dear all, does anyone know a reference for the question: Prime Ideal Theorem implies the Excluded Middle ? Certainly, Axiom of Choice implies Excluded Middle, but I have convinced myself that the weaker statement is true and would be grateful for any pointers. Regards, Christopher Townsend PS there are definitely formulations of the PIT that do not use negation. E.g. it is equivalent to the statement that for every Boolean alg. B if x in B has the property that f(x)=0 for every Boolean alg. homomorphism f:B->Omega, then x=0.

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Alexandrov topology and Scott topology
by Galchin Vasili 20 Mar '03

20 Mar '03

Hello, A common example of a Heyting Algebra is one defined on an arbitrary topology. In the cases of an Alexandrov topology and a Scott topology, are either of these Boolean Algebras (special case of a HA) or purely Heyting Algebras? Regards, Bill Halchin

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list accepted papers for ICALP 2003
by icalp2003＠TUE.nl 19 Mar '03

19 Mar '03

=09charset=3D"iso-8859-1" Sender: cat-dist(a)mta.ca Precedence: bulk ------------------------------------------------------------------------- We apologize for the reception of multiple copies of this message. ---------------------------------------------------------------------------= - ---------------------------- =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D List of papers accepted for ICALP'2003, Track A and Track B Eindhoven, The Netherlands, June 30 - July 4, 2003 http://www.win.tue.nl/icalp2003/ =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D Vincent Blondel, Paul Van Dooren Similarity matrices for pairs of graphs Arnold Schoenhage Adaptive raising strategies optimizing relative efficiency Sergei Bespamyatnikh, Michael Segal Dynamic algorithms for approximating interdistances Amos Korman, David Peleg Labeling schemes for dynamic tree networks Geraud Senizergues The equivalence problem for t-turn DPDA is co-NP John Hitchcock, Jack Lutz, Elvira Mayordomo Scaled dimension and nonuniform complexity Yossi Matias, Ely Porat Efficient pebbling for list traversal synopses Alexander Ageev, Yinyu Ye, Jiawei Zhang Improved combinatorial approximation algorithms for the k-level facility location problem Markus Blaeser An improved approximation algorithm for the asymmetric TSP with strengthene= d triangle inequality Susanne Albers, Rob van Stee A study of integrated document and connection caching Amihood Amir, Yonatan Aumann, Richard Cole, Moshe Lewenstein, Ely Porat Function matching: algorithms, applications, and a lower bound Eyal Even-Dar, Alex Kesselman, Yishay Mansour Convergence time to Nash equilibria Amin Coja-Oghlan, Cristopher Moore, Vishal Sanwalani MAX k-CUT and approximating the chromatic number of random graphs Jiri Fiala, Daniel Paulusma The computational complexity of the role assignment problem Vipul Bansal, Aseem Agrawal, Varun Malhotra Stable marriages with multiple partners: efficient search for an optimal solution Juraj Hromkovic, Georg Schnitger Pushdown automata and multicounter machines, a comparison of computation mode Jens Jaegerskuepper Analysis of a simple evolutionary algorithm for minimization in Euclidean spaces Noam Berger, Bela Bollobas, Christian Borgs, Jennifer Chayes, Oliver Riorda= n Degree distribution of the FKP network model Luisa Gargano, Mikael Hammar There are spanning spiders in dense graphs (and we know how to find them) Annalisa De Bonis, Leszek Gasieniec, Ugo Vaccaro Generalized framework for selectors with applications in optimal group testing Michael Elkin, Guy Kortsarz Approximation algorithm for the directed telephone multicast problem Sanjeev Arora, Kevin Chang Approximation schemes for degree-restricted MST and red-blue separation problem Surender Baswana, Sandeep Sen A simple linear time algorithm for computing a (2k-1)-Spanner of O(n^{1+1/k}) size in weighted graphs Chandra Chekuri, Marcelo Mydlarz, Bruce Shepherd Multicommodity demand flow in a tree Randeep Bhatia, Julia Chuzhoy, Ari Freund, Joseph Naor Algorithmic aspects of bandwidth trading Chandra Chekuri, Sudipto Guha, Joseph Naor Approximating Steiner k-cuts Endre Boros, Khaled Elbassioni, Vladimir Gurvich, Leonid Khachiyan, Kazuhis= a Makino An intersection inequality for discrete distributions and related generatio= n problems Erik Demaine, Fedor Fomin, MohammadTaghi Hajiaghayi, Dimitrios Thilikos Fixed-parameter algorithms for the (k,r)-center in planar graphs and map graphs Gianni Franceschini, Roberto Grossi Optimal cache-oblivious implicit dictionaries Anna Gal, Peter Bro Miltersen The cell probe complexity of succinct data structures, Alex Hall, Steffen Hippler, Martin Skutella Multicommodity flows over time: efficient algorithms and complexity Rene Sitters, Leen Stougie, Willem Paepe A competitive algorithm for the general 2-server problem Luis Antunes, Lance Fortnow Sophistication revisited Peter Hoyer, Michele Mosca, Ronald de Wolf Quantum search on bounded-error inputs Dimitris Fotakis On the competitive ratio for online facility location Satoshi Ikeda, Izumi Izumi Kubo, Norihiro Okumoto, Masafumi Yamashita Impact of local topological information on random walks on finite graphs Pilu Crescenzi, Giorgio Gambosi, Gaia Nicosia, Paolo Penna, Walter Unger On-line load balancing made simple: greedy strikes back Seffi Naor, Hadas Shachnai, Tami Tamir Real-time scheduling with a budget Mark Cieliebak, Paola Flocchini, Giuseppe Prencipe, Nicola Santoro Solving the robots gathering problem Rainer Feldmann, Martin Gairing, Thomas Luecking, Burkhard Monien, Manuel Rode Nashification and the coordination ratio for a selfish routing game Brian Dean, Michel Goemans Improved approximation algorithms for minimum-space advertisement schedulin= g Baruch Awerbuch, Andre Brinkmann, Christian Scheideler Anycasting in adversarial systems: routing and admission control Jianer Chen, Iyad Kanj, Ljubomir Perkovic, Eric Sedgwick, Ge Xia Genus characterizes the complexity of graph problems: some tight results Markus Holzer, Martin Kutrib Flip-pushdown automata: k+1 pushdown reversals are better than k Manuel Bodirsky, Clemens Gr=F6pl, Mihyun Kang Generating labeled planar graphs uniformly at random Rajiv Gandhi, Eran Halperin, Samir Khuller, Guy Kortsarz, Aravind Srinivasa= n An improved approximation algorithm for vertex cover with hard capacities Dominique Poulalhon, Gilles Schaeffer Optimal coding and sampling of triangulations Ian Munro, Rajeev Raman, Venkatesh Raman, Srinivasa Rao Satti Succinct representations of permutations Rahul Jain, Jaikumar Radhakrishnan, Pranab Sen A direct sum theorem in communication complexity via message compression Rajeev Raman, Srinivasa Rao Succinct dynamic dictionaries and trees Daniel Bleichenbacher, Aggelos Kiayias, Moti Yung Decoding of interleaved Reed Solomon codes over noisy data, Juha K=E4rkk=E4inen, Peter Sanders Simple linear work suffix array construction Manfred Droste, Dietrich Kuske Skew and infinitary formal power series Ernst-Erich Doberkat Semi-pullbacks and bisimulations in categories of stochastic relations Stefan Blom, Wan Fokkink, Sumit Nain On the axiomatizability of ready traces, ready simulation and failure trace= s Juraj Hromkovic, Georg Schnitger Nondeterminisn versus determinism for two-way finite automata: generalizations of Sipser's separation Daniele Gorla, Rosario Pugliese Resource access and mobility control with dynamic privileges acquisition Jan Johannsen, Martin Lange CTL+ is complete for double exponential time Davide Ancona, Sonia Fagorzi, Eugenio Moggi, Elena Zucca Mixin modules and computational effects Thierry Cachat Higher order pushdown automata, the Caucal hierarchy of graphs and parity games Gaoyan Xie, Zhe Dang, Oscar Ibarra A solvable class of quadratic Diophantine equations with applications to verification of infinite state systems Alexander Okhotin Decision problems for language equations with Boolean operations Roberto Bruni, Jose Meseguer Generalized rewrite theories Salvatore La Torre, Margherita Napoli, Mimmo Parente, Gennaro Parlato Hierarchical and recursive state machines with context-dependent properties Cindy Eisner, Dana Fisman, John Havlicek, Anthony McIsaac, David Van Campenhout The definition of a temporal clock operator Nadia Busi, Maurizio Gabbrielli, Gianluigi Zavattaro Replication vs. recursive definitions in channel based calculi Richard Mayr Undecidability of weak bisimulation equivalence for 1-counter processes Felix Klaedtke, Harald Ruess Monadic second-order logics with cardinalities Orna Kupferman, Moshe Vardi Pi_2 intersected Sigma_2 equals AFMC Alexander Rabinovich Quantitative analysis of probabilistic lossy channel systems Massimo Merro, Francesco Zappa Nardelli Bisimulation proof methods for mobile ambients Tatiana Rybina, Andrei Voronkov Upper bounds for a theory of queues Zena Ariola, Hugo Herbelin Minimal classical logic and control operators Arnaud Carayol, Thomas Colcombet On equivalent representations of infinite structures Philippe Schnoebelen Oracle circuits for branching-time model checking Luca de Alfaro, Thomas A. Henzinger, Rupak Majumdar Discounting the future in systems theory Thomas Henzinger, Ranjit Jhala, Rupak Majumdar Counterexample guided control Jo Hannay Axiomatic criteria for quotients and subobjects for higher-order data types Francois Denis, Yann Esposito Residual languages and probabilistic automata Francisco Gutierrez, Blas Ruiz Expansion postponement via cut elimination in sequent calculi for pure type systems Michele Bugliesi, Silvia Crafa, Amela Prelic, Vladimiro Sassone Secrecy in untrusted networks Luca de Alfaro, Marco Faella Information flow in concurrent games Marielle Stoelinga , Frits Vaandrager A testing scenario for probabilistic automata Arkadev Chattopadhyay, Denis Therien Locally commutative categories =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D

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