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Logical Approaches to Barriers in Complexity II

26th March 2012 to 30th March 2012

Organisers: Arnold Beckmann (Swansea), and Anuj Dawar (Cambridge)

Workshop Theme

Computational complexity theory has its origin in logic. The fundamental goal of this area is to understand the limits of efficient computation (that is understanding the class of problems which can be solved quickly and with restricted resources) and the sources of intractability (that is what takes some problems inherently beyond the reach of such efficient solutions). The most famous open problem in the area is the P = NP-problem, listed among the seven Clay Millenium Prize problems. Logic provides a multifarious toolbox of techniques to analyse questions like this, some of which promise to provide deep insights in the nature and limits of efficient computation.

In our workshop, we shall focus on logical descriptions of complexity, i.e. descriptive complexity, propositional proof complexity and bounded arithmetic. Despite considerable progress by research communities in each of these areas, the main open problems remain. In finite model theory the major open problem is whether there is a logic capturing on all structures the complexity class P of polynomial time decidable languages. In bounded arithmetic the major open problem is to prove strong independence results that would separate its levels. In propositional proof complexity the major open problem is to prove strong lower bounds for expressive propositional proof systems.

The workshop will bring together leading researchers covering all research areas within the scope of the workshop. We will especially focus on work that draws on methods from the different areas which appeal to the whole community.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute The Leverhulme Trust London Mathematical Society Microsoft Research NM Rothschild and Sons