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Dagstuhl Seminar 23111

Computational Complexity of Discrete Problems

( Mar 12 – Mar 17, 2023 )

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Please use the following short url to reference this page: https://www.dagstuhl.de/23111

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Motivation

Computational complexity studies the amount of resources (such as time, space, randomness, or communication) necessary to solve computational problems in various models of computation – a crucial task both in theoretical and practical applications. Despite a long line of research, for many practical problems it is not known if they can be solved efficiently. Here, “efficiently” can refer to polynomial-time algorithms, whose existence is not known for problems like Satisfiability or Factoring , but also to cubic or even quadratic time, where it would be important to establish whether these running times are best possible for basic problems, to what extent they can be improved, and whether parallel algorithms allow improvements of the runtime.

These fundamental questions motivate developments in areas from algorithm design to circuit complexity, communication complexity and proof complexity. The seminar’s topics will include new lower bounds on formula size and circuit size, complexity measures of Boolean functions, the algorithmic method for proving lower bounds, fixed-parameter tractability and hardness magnification, communication complexity and lifting techniques, as well as proof complexity. Continuing a long and successful series, this Dagstuhl Seminar will build on previous experience and retain the series’ distinctive features, while also capitalizing on new and exciting developments in the area such as the proof of the Sensitivity Conjecture, new lower bounds and results on matrix rigidity via the algorithmic method, and the remarkable success of lifting techniques in translating lower bounds from query complexity to communication complexity and from proof complexity to circuit complexity.

The bulk of the seminar will be taken up by talks and discussions. The topics will depend on and be driven by the participants, who will share their current research interests in talks, open problem sessions, and smaller group research.

Copyright Anna Gál, Meena Mahajan, Rahul Santhanam, and Till Tantau

Participants

Related Seminars
  • Dagstuhl Seminar 9235: Complexity and Realization of Boolean Functions (1992-08-24 - 1992-08-28) (Details)
  • Dagstuhl Seminar 9711: Complexity of Boolean Functions (1997-03-10 - 1997-03-14) (Details)
  • Dagstuhl Seminar 99441: Complexity of Boolean Functions (1999-10-31 - 1999-11-05) (Details)
  • Dagstuhl Seminar 02121: Complexity of Boolean Functions (2002-03-17 - 2002-03-22) (Details)
  • Dagstuhl Seminar 04141: Complexity of Boolean Functions (2004-03-28 - 2004-04-02) (Details)
  • Dagstuhl Seminar 06111: Complexity of Boolean Functions (2006-03-12 - 2006-03-17) (Details)
  • Dagstuhl Seminar 08381: Computational Complexity of Discrete Problems (2008-09-14 - 2008-09-19) (Details)
  • Dagstuhl Seminar 11121: Computational Complexity of Discrete Problems (2011-03-20 - 2011-03-25) (Details)
  • Dagstuhl Seminar 14121: Computational Complexity of Discrete Problems (2014-03-16 - 2014-03-21) (Details)
  • Dagstuhl Seminar 17121: Computational Complexity of Discrete Problems (2017-03-19 - 2017-03-24) (Details)
  • Dagstuhl Seminar 19121: Computational Complexity of Discrete Problems (2019-03-17 - 2019-03-22) (Details)
  • Dagstuhl Seminar 21121: Computational Complexity of Discrete Problems (2021-03-21 - 2021-03-26) (Details)

Classification
  • Computational Complexity
  • Data Structures and Algorithms

Keywords
  • computational complexity
  • circuit complexity
  • communication complexity
  • randomness
  • lower bounds