41. Process Algebra: Open Problems And Future Directions This web page lists some open problems in process algebra communicated, The process algebra (PA) related open problem I am interested in is that of the http://www.cs.auc.dk/~luca/BICI/open-problems.html

Process Algebra: Open Problems and Future Directions July 21-25, 2003 University of Bologna Residential Center Bertinoro Forl¬ ), Italy Some Open Problems in Process Algebra This web page lists some open problems in process algebra communicated, at least initially, by the participants at the workshop Process Algebra: Open Problems and Future Directions We intend to maintain this page as up to date as possible, in the hope that it will be a useful resource for the practising process algebraist and concurrency theorist. To this end, we invite all of the members of the process algebra community to help us by sending the maintainer of this page suggestions for new problems to be posted here, and pointers to their solutions. Some further open problems are mentioned in the note Some of My Favourite Results in Classic Process Algebra by Luca Aceto , and on the slides of the talks delivered at the workshop. Problems Posted by Luca Aceto Does bisimulation equivalence admit a finite equational axiomatization over the language obtained by adding Hennessy's auxiliary operator from to CCS?

42. Interval Computations Presents a guide to Interval Arithmetic research featuring open problems, applications, generalizations, bibliography, researchers' sites, ftp site, and mailing list. http://www.cs.utep.edu/interval-comp/

Interval Computations: Introduction and Technical issues Interval Computations: Introduction ( PostScript dvi see also the following page B. Hayes, A Lucid Interval ... American Scientist , 2003, Vol. 91, No. 6, pp. 484-488 provides an intro based on round-off errors. Frequently Asked Questions (FAQ) Roundings Necessary for Interval Computations see also the following page Generalizations of Interval Arithmetic and their Applications ... Interval Notations (original suggestion, reaction) Early Papers on Interval Computations, by R. E. Moore and by Others Open Problems Software and Languages Languages for Interval Computations Interval and Related Software Interval Arithmetic in the Forte Fortran 95 Compiler see also More Information about Interval Computations Books and Courses on Interval Computations Bibliographies on Interval and Related Methods Interval Ftp Site and Interval Mailing Lists The Interval Computations Community Homepages of Interval Computations Research Centers and Special Interest Groups Personalia: Homepages of Interval Computations Researchers Reliable Computing (formerly ... an International Journal, and other journals of interest to the interval computations community Conferences: Forthcoming and Previous Honors Received by Interval Researchers Important Web Sites of Interest to the Interval Computations Community Applications Applications of Interval Computations (see also GlobSol - software for global solutions Generalizations of Interval Arithmetic and their Applications Intervals and Probability US-Based Website,

43. Computability Theory Directory of researchers working in computability theory, and list of open problems. http://www.nd.edu/~cholak/computability/computability.html

Computability Theory Bibliographic Database for Computability Theory Open Questions in Recursion Theory: LaTeX or pdf Open Problems in Mathematical Logic Other Useful Sites: Association for Symbolic Logic People who work (or have worked) in Computability Theory: Klaus Ambos-Spies George Barmpalias Valeriy Bulitko Sam Buss ... Sy Friedman Edward R. Griffor Valentina Harizanov Leo Harrington Denis R. Hirschfeldt Jeff Hirst ... Steffen Lempp Manuel Lerman Andy Lewis Iraj Kalantari Jan Kraijeck Matrin Kummer David Marker Anil Nerode Yiannis Moschovakis Andre Nies ... Stan Wainer Dongping Yang Mike Yates People whose work had great impact on the field: Charles Babbage Alonzo Church Robin Gandy Reuben Goodstein ... Computability Theory E-mailing List Research Announcements Recursive Function Theory Newsletter Meetings (see the Association for Symbolic Logic for ASL meetings) New Computational Paradigms, Amsterdam. Research Grants Computability in Europe (CiE). Graduate School in Computability Theory The University of Connecticut Math Department Univeristy of Notre Dame Job Announcements As with most web pages, this page is a continuously evolving resource. It will only develop into a useful resource for computability theorists if they help by adding information related to computability theory to the web and this page. Therefore computability theorists are encouraged to add information and links to this page. There are two ways of achieving this. The preferred method is to add the information to the web yourself and

44. Problems In Graph Theory And Combinatorics" open problems are listed along with what is known about them, Other directoriesof open problems pages can be found as follows Graph Theory, http://www.math.uiuc.edu/~west/openp/

Open Problems - Graph Theory and Combinatorics collected and maintained by Douglas B. West Number of problem pages now posted: 38 This site is a resource for research in graph theory and combinatorics. Open problems are listed along with what is known about them, updated as time permits. Individual pages contain such material as title, originator, date, statement of problem, background, partial results, comments, references. Also available is a Glossary of Terms Most pages in this directory have not yet been created; so far this is mostly a list of some well-known problems for which more detailed pages will be written later. Its accessibility at this early stage is a plea for contributed material to accelerate its development. The organization of topics roughly follows the four volumes of The Art of Combinatorics under development by D.B. West. Thus the four main headings are Extremal Graph Theory Structure of Graphs Order and Optimization , and Arrangements and Methods Alternatively, below is a direct search, courtesy of Google. On this page, the search will only take you right here, but it will also find problem pages under this that contain your search term. Contributions!

45. Algorithmic Information Theory open problems and links to software. http://www.cs.auckland.ac.nz/CDMTCS/docs/ait.html

A LGORITHMIC I NFORMATION T HEORY Algorithmic information theory ( AIT ) is the result of putting Shannon's information theory and Turing's computability theory into a cocktail shaker and shaking vigorously. The basic idea is to measure the complexity of an object by the size in bits of the smallest program for computing it. ( G. J. Chaitin A NNIVERSARIES G. J. Chaitin. On the length of programs for computing finite binary sequences, J. Assoc. Comput. Mach. A. M. Turing. On computable numbers, with an application to the Entscheidungsproblem, Proc. Lond. Math. Soc. (ser. 2) 42 (1936), 230-265; a correction 43 (1936), 544-546. O PEN P ROBLEMS Here is a compressed PostScript document containing a list of open problems in AIT. S OFTWARE FOR AIT Have a browse on Greg Chaitin's home page for some AIT-related software. Back to main page Information

46. Open Problems On Perfect Graphs In February of that year, Bruce and I prepared a list of open problems, whichwas then sent to all the invited participants. The next version of the list, http://www.cs.concordia.ca/~chvatal/perfect/problems.html

PERFECT PROBLEMS Created on 22 August, 2000 Last updated on 28 November, 2004 In May 2002, the Strong Perfect Graph Conjecture became the Strong Perfect Graph Theorem Details are here. As a part of the 1992 1993 Special Year on Combinatorial Optimization at DIMACS ftp://dimacs.rutgers.edu/pub/perfect/problems.tex If you have information on progress towards solving these problems or complaints in case I did not give credit where credit was due or suggestions for problems to add, please, send them to me Related pages: Problems from the AIM Workshop on Perfect Graphs (compiled by Maria Chudnovsky) A bibliography on perfect graphs Home pages of people interested in perfect graphs This collection is written for people with at least a basic knowledge of perfect graphs. Uninformed neophytes may look up the missing definitions on the web in Alexander Schrijver's lecture notes or in Jerry Spinrad's draft of a book on efficient graph representations etc. or in Eric Weisstein's World of Mathematics . Books on perfect graphs include M. C. Golumbic

47. The Valuation Theory Home Page A forum for all mathematicians who work in or use valuation theory. Directory of people, meetings, preprints, bibliography, open problems and news. http://math.usask.ca/fvk/Valth.html

Welcome, dear reader, to The Valuation Theory Home Page This home page is intended to be a forum for all mathematicians who work in valuation theory or apply valuation theoretical results in their own field of research. The home page offers: postscript- or dvi-files of recent papers, books and theses in valuation theory information about conferences and special events, names and email addresses of mathematicians working in or with valuation theory, and, if possible, links to their home pages a comprehensive bibliography as Bibtex-, dvi- and postscript file, which presently contains 770 entries, a page for open problems and, hopefully, their solutions, interesting NEWS in connection with valuation theory, some useful links a page for historical information and related questions, a page for errors, pitfalls and the nicest proofs in valuation theory (to come). If you have suggestions, questions, ideas, news, or if you want your name and address on the above mentioned list, or if you have a recent paper in or applying valuation theory, then write to valth [at] math.usask.ca

48. Open Problems In Graph Theory Involving Steiner Distance open problems involving Steiner distance. http://io.uwinnipeg.ca/~ooellerm/open_problems/

Some Open Problems in Graph Theory It has been shown by Chartrand, Oellermann, Tian, and Zou that, for a tree T: diam n n This inequality does not hold for graphs in general as was shown by Henning, Oellermann, and Swart . It was shown in the same paper that for a graph G and n=3 and 4: diam n n G. It was shown by Oellermann and Tian that for a tree T: C n-1 (T) is contained in C n It remains an open problem to determine whether this containment holds for general graphs. In other words, it is not known if the Steiner (n-1)-center of a graph is contained in its Steiner n-center. It was shown by Beineke, Oellermann and Pippert that if T is a tree, then M n-1 (T) is contained in M n It remains an open problem to determine whether this containment holds for general graphs. In other words, it is not known if the Steiner (n-1)-median of a graph is contained in its Steiner n-median. Oellermann and Tian ). It is known that every graph is the 2-median of some graph (see Holbert ,and Hendry ). Steiner n-medians of trees have been completely characterized by

49. Quantum Information: Problems Entangled Hbars. open problems. On this page we collect problems in QuantumInformation Theory we or our contributors find worthy of attention. http://www.imaph.tu-bs.de/qi/problems/problems.html

IMaPh Research Areas Quantum Information Introduction to QI ... Publications Problems Open Problems On this page we collect problems in Quantum Information Theory we or our contributors find worthy of attention. The list is ordered by "last submission on top". Numbering is kept stable, so you can refer to the problems by number. Click on the title to find the statement of the problem and some information on known partial results. This information will be updated whenever significant progress is brought to our attention. To make this page interesting we obviously need input from the community, so please contribute good problems . By this we mean problems in Quantum Information Theory, which are stated in a self-contained way in the current terminology of the field, are open to the best of your knowledge, and pose an interesting challenge to other researchers. We will make an effort to publish all good problems quickly, but may reject contributions we find less suitable. Send contributions by email to . The format of contributions is free. Text written in simple LaTeX, and divided into sections such as Problem/ Background/ Partial Results/ Remarks/ Literature creates the smallest workload for us.

50. RFW: Open Problems Some open problems. At conferences I like to ask people If a Fairy offers A list of open problems in Quantum Information Theory, which is planned for http://www.imaph.tu-bs.de/home/werner/problems.html

Back to Reinhard F. Werner's home page Some Open Problems At conferences I like to ask people "If a Fairy offers you the key idea for proving a Theorem of your choice, what would you pick?". It is the information you don't usually find in published papers. The following sites collect such material. A well structured list of Mathematical Physics Problems maintained by Michael Aizenman for the IAMP . Send your stuff there! A list maintained by Stephen Finch at MathSoft with many(!) links to similar pages. A list of open problems in Quantum Information Theory , which is planned for this server. We are already open for submissions. So if any of these ring a bell, or you know of partial results LET ME KNOW! . If any problem gets solved, I will also place a link to the solution. tr exp (A+itB) [Nov. 1996] A conjecture of Bessis, Moussa, and Villani ( J.Math.Phys. positive measure. This would entail a number of interesting inequalities not just for quantum partition functions, but also for their dervatives (a badly needed tool). Despite a lot of work, some by prominent mathematical physicists, only some simple cases have been decided. So far all results, including fairly extensive numerical experiments, are in agreement with the conjecture. I have been collecting material on this problem with Mark Fannes (along with our own work). Uniqueness of q-relations [Nov. 1996]

51. Daswani, Neil; Garcia-Molina, Hector; Yang, Beverly: Open Problems In Data-shari open problems in Datasharing Peer-to-peer Systems, ICDT 2003 In a 4 ConclusionMany of the open problems in P2P data sharing systems surround search http://dbpubs.stanford.edu/pub/2003-1

Pagewise preview Category Value Available via http://dbpubs.stanford.edu/pub/2003-1 Submitted on 23rd of October 2002 Author Daswani, Neil; Garcia-Molina, Hector; Yang, Beverly Title Open Problems in Data-sharing Peer-to-peer Systems Date of publication January 2003 Published in ICDT 2003 Citation Daswani, Neil; Garcia-Molina, Hector; Yang, Beverly. Open Problems in Data-sharing Peer-to-peer Systems, ICDT 2003 Number of pages Language English Project Peers Type Conference or Journal Paper Subject group Miscellaneous Abstract In a Peer-To-Peer (P2P) system, autonomous computers pool their resources (e.g., files, storage, compute cycles) in order to inexpensively handle tasks that would normally require large costly servers. The scale of these systems, their "open nature," and the lack of centralized control pose difficult performance and security challenges. Much research has recently focused on tackling some of these challenges; in this paper, we propose future directions for research in P2P systems, and highlight problems that have not yet been studied in great depth. We focus on two particular aspects of P2P systems search and security and suggest several open and important research problems for the community to address. Keywords Peer-to-peer, search, security

52. The Furstenburg Conjecture And Rigidity If two commuting endomorphisms of a torus are incommensurable (no power of one is a power of the other), then their joint action should be rigid. Some of the conjectures and open problems compiled by the AIM. http://aimath.org/WWN/furstenburg/

The Furstenburg Conjecture and Rigidity This web page highlights some of the conjectures and open problems concerning The Furstenburg Conjecture and Rigidity. Click on the subject to see a short article on that topic. If you would like to print a hard copy of the entire web page, you can download a dvi postscript or pdf version. The Furstenburg Conjecture and Rigidity Statement of the Conjecture History and past results Analogous problems ... Approaches to a counterexample

53. Logo Other Sites With This Page Open Problems In DS ET (IUPUI This collection of open problems in Dynamical Systems Ergodic Theory originatedfrom the If you would like to submit some open problems to this page, http://iml.univ-mrs.fr/~kolyada/opds/

Other sites with this page O pen P roblems in D ynamical S ystems E rgodic T heory Welcome! Katsiveli - 2000 Open Problems Session (Chairman - Benjamin Weiss ). New problems are being added to it. If you would like to submit some open problems to this page, please send them to me Anyone who has never had any (open) problem has never tried anything new. Anyone who has published a paper has solved a problem and maybe has some other open problems. Why not to present them at this www page? Sergiy Kolyada Geometric Models of Pisot Substitutions and Non-Commutative Arithmetic Submitted by Pierre Arnoux Corrections - 29.11.2001 Ergodic Ramsey Theory - an Update Submitted by Vitaly Bergelson ( See also: http://www.math.ohio-state.edu/~vitaly/ Dense Periodic Points in Cellular Automata Submitted by Francois Blanchard Non-Discrete Locally Compact Second Countable Groups Submitted by Sergey Gefter Martingale Convergence and Ergodic Theorems Submitted by Alexander Kachurovskii The problem is closed Entropy, Periodic Points and Transitivity of Maps Submitted by Sergiy Kolyada Lubomir Snoha Corrections - 26.10.2002

54. Anogia Algorithmica '05 First workshop on open problems in algorithmics. Anogia Academic Village, Crete, Greece; 30 May 3 June 2005. http://www.scs.carleton.ca/~kranakis/ANOGIA/algo05.html

ANOGIA ALGORITHMICA '05 University of Crete Deapartment of Mathematics May 30 - June 02 The 1st workshop on open problems in algorithmics will be held at the Anogia (pronounced A-no'-yia) Academic Village in the island of Crete, a conference facility located in a unique natural setting, 40 min from Heraklion and Knossos and 50 min from Rethymno. RESEARCH SUMMARY AND SCOPE Of interest are problems in Network Computing that concern the optimization of the computing capabilities and performance of classical (wireline) and modern (wireless) networks. There are no formal talks. In the first morning (plenary meeting) participants will propose open problems. Participants must be willing to discuss and work on their favorite open problem with others. Remaining time will be devoted to research in ad hoc groups (group meetings). Announcements on status of proposed problems will be made at the last plenary meeting. PROGRAM Sunday, May 29: Informal get-together (evening) Monday, May 30: 09:30-11:00 Plenary Meeting: Problem proposals 11:00-11:30 Break 11:30-13:00 Plenary Meeting: Problem proposals 13:00-16:00 Lunch 16:00-18:30 Group Meetings: Problem discussion Tuesday, May 31:

55. Mathematical Logic :: Index Problems which can be solved in a matter of weeks rather than years are especiallywelcome. Discussion of open problems in mathematical logic http://math.berkeley.edu/Logic/problems/

Mathematical Logic Discussion of open problems in mathematical logic FAQ Search Memberlist Usergroups Register Profile Log in to check your private messages Log in The time now is Fri Sep 16, 2005 4:56 pm Mathematical Logic Forum Index View unanswered posts Forum Topics Posts Last Post Community Interest Recursion Theory Set Theory Model Theory ... Mark all forums read All times are GMT - 7 Hours Who is Online Our users have posted a total of articles We have registered users The newest registered user is juhasz In total there are users online :: Registered, Hidden and Guests [ Administrator Moderator Most users ever online was on Wed Oct 20, 2004 6:29 am Registered Users: None This data is based on users active over the past five minutes Log in Username: Password: Log me on automatically each visit New posts No new posts Forum is locked Powered by phpBB

56. World Of Groups Part of the World Wide Algebra project. open problems in combinatorial group theory, a list of personal web pages, conferences and seminars, and useful links. http://www.cs.gc.cuny.edu/~cryptlab/gworld/gworld.html

Welcome to The World of Groups! This part of the World Wide Algebra project includes a list of open problems in combinatorial group theory, a list of personal web pages, a list of conferences and seminars, and a list of useful links. If you would like to see some other information posted on this site, please send us e-mail . We also invite you to visit our Algebraic Cryptography page that has a lot of information on using groups in cryptography. NEWS : One more name (Bettina Eick) has been added to our list of Personal web pages. Two more names (Ruth Corran and Yves de Cornulier) have been added to our list of Personal web pages. New problem (G9) has been added to our list of Open problems. One more name (Azer Akhmedov) has been added to our list of Personal web pages. Two more names (Martin Lustig and Rick Thomas) have been added to our list of Personal web pages. Two more conference links have been added to our list of conferences. Two more names (Thomas Delzant and Bálint Virág) have been added to our list of Personal web pages. We now have names on our list.

57. Groupoid Home Page Maintained by Birant Ramazan. Address book, open problems, meetings, pictures, other resources. http://unr.edu/homepage/ramazan/groupoid/

If your browser can't read tables or if you are using a text browser, try the text-based groupoid home page Groupoid Home Page Editors: Jean Renault renault@labomath.univ-orleans.fr Arlan Ramsay ramsay@euclid.colorado.edu It was created by Arlan Ramsay Rob Chiaramonte , and Loren Woo at the University of Colorado at Boulder and is maintained by Birant Ramazan at the University of Nevada Reno Address book Other sources on groupoids and links Some questions on groupoids ... Some pictures Our guestbook is now operational - please feel free to browse our guestbook This page was last updated January 31 2003. ramazan@unr.edu

58. OPEN PROBLEMS IN COMBINATORIAL OPTIMIZATION During this time I have compiled an ongoing list of open problems, which fascinateme for their apparent difficulty, their simplicity of statement and http://www.cs.clemson.edu/~hedet/preface.html

OPEN PROBLEMS IN COMBINATORIAL OPTIMIZATION compiled by Steve Hedetniemi Department of Computer Science Clemson University Clemson, SC 29634-1906 September, 1998 Preface The Friday afternoon Algorithms Seminar at Clemson has been a rich source of interesting problems over the past twelve years, as have many discrete math conferences, including our twelve Clemson mini-Conferences on Discrete Mathematics. During this time I have compiled an on-going list of open problems, which fascinate me for their apparent difficulty, their simplicity of statement and their inherent interest. Motivated by numerous requests for an updated version of this list, I am finally taking the time to update it and make it available to anyone who would like to read or copy it. For each of the following problems I will attempt to identify the originators and the approximate time of origin. If you can provide me with any historical corrections or additions to any of the problems in this list, please let me know. You will note that I have not yet provided many literature citations; it will take a LONG time to provide all of the relevant references. I hope to be able to include more and more of this information in the future. So please consider this to be a 'working' document, which will repeatedly be updated. Most of these problems are stated in the Garey and Johnson format for NP-complete problems. Unless stated otherwise, by 'Open' I mean that the complexity of the problem is not known to me (no NP-completeness proof exists), neither does any algorithm exist for solving the problem, or no solution is known to exist.

59. Education Programs At DIMACS Assistance in educating K12 and undergraduate students about discreet mathematics. Lists programs and open problems in the field. http://dimacs.rutgers.edu:80/Education/

Education Programs at DIMACS: Programs for K-12 Programs for faculty: Crash Course in Discrete Mathematics DIMACS Bio-Math Connect Institute (BMCI) DIMACS Connect Institute (DCI) DREI- DIMACS Research and Education Institute ... K-8 Teachers - Leadership Institutes: Exploring Discrete Mathematics in the Classroom Workshops In Your District: Exploring Discrete Mathematics New Jersey Mathematics Coalition - improving K-12 mathematics education. Programs for students: Young Scholars Program in Discrete Mathematics Undergraduate Education Programs for faculty: Reconnect Conference Reconnecting Teaching Faculty to the Mathematical Sciences Enterprise Series of Two Two-Day Workshops for Two-Year College Teachers Reconnecting Two Year College Faculty to the Mathematical Sciences Enterprise Programs for students: Open Problems for Undergraduates in discrete mathematics and theoretical computer sciences. The problems are contributed by DIMACS members and others. Research Experiences for Undergraduates Past Activities DIMACS Home Page Alphabetical Index of DIMACS Web Pages Contacting the Center Document last modified on August 9, 2004.

60. Interval Computations: Open Problems open problems. Grand challenge interval problems (by A. Neumaier) GuaranteeingBounds on Uncertainty in Metrology Back to the main menu of the http://www.cs.utep.edu/interval-comp/openprob.html

Open Problems "Grand challenge" interval problems (by A. Neumaier) Guaranteeing Bounds on Uncertainty in Metrology Back to the main menu of the Interval Computations website

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