Workshop in computability, complexity and randomness
De Computability.
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=Upcoming talks= | =Upcoming talks= | ||
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=Recent talks= | =Recent talks= | ||
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| + | * '''24 Novembre 2010: Priority arguments in computability theory: part 1''' | ||
| + | :'''''Orateur: Laurent Bienvenu (LIAFA, Paris 7)''''' | ||
| + | :It is well-known that the halting problem for Turing machines is undecidable, but computably enumerable. In fact, the halting problem is complete among computably enumerable set: if we are given the solution of halting problem on a an infinite tape, we can use it to decide ''any'' computably enumerable set. In the 1940's, Post asked whether there exists an intermediate computably enumerable problem, i.e. one that is not decidable but cannot solve the halting problem. The answer came after more than 10 years, from the independent work of Friedberg and Muchnik, via what we now call a ''priority argument with finite injury''. We will discuss the proof of this theorem and if time permits we will see how the finite injury technique can be used to prove more advanced computability theorem. The (much) more complicated techniques involving priority with ''infinite injury'' will be presented in a later talk. | ||
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* '''17 Novembre 2010: The Moser-Tardos constructive proof of Lovasz Local Lemma''' | * '''17 Novembre 2010: The Moser-Tardos constructive proof of Lovasz Local Lemma''' | ||
Version du 26 novembre 2010 à 08:44
This informal LIAFA reading group aims at providing a forum for exchange of ideas on a certain number of topics, in particular:
- computability theory
- models of computation
- algorithmic complexity
- algorithmic randomness (Kolmogorov complexity, Martin Löf randomness, etc)
- pseudo-randomness theory (expanders, extractors, etc)
- any topic related to the one of the above
As opposed to a "standard" seminar, speakers are encouraged to present one or several theorems (with their proofs!), a classical technique, an important idea (not necessarily from their own work) rather than give an overview of their last technical paper. There is not strict time limit for talks, even though it would be preferable to not go over the hour and a half (if a talk is taking too long, it can be continued the following week). A shorter talk can also be followed by a discussion between participants, either on the topic of the talk or on any other topic.
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Time and place
The reading group takes place on Wednesdays starting from 4pm, in room 5C12 (5th floor) at 175 rue du Chevaleret, 75013 Paris (click here for directions LIAFA).
Upcoming talks
Recent talks
- 24 Novembre 2010: Priority arguments in computability theory: part 1
- Orateur: Laurent Bienvenu (LIAFA, Paris 7)
- It is well-known that the halting problem for Turing machines is undecidable, but computably enumerable. In fact, the halting problem is complete among computably enumerable set: if we are given the solution of halting problem on a an infinite tape, we can use it to decide any computably enumerable set. In the 1940's, Post asked whether there exists an intermediate computably enumerable problem, i.e. one that is not decidable but cannot solve the halting problem. The answer came after more than 10 years, from the independent work of Friedberg and Muchnik, via what we now call a priority argument with finite injury. We will discuss the proof of this theorem and if time permits we will see how the finite injury technique can be used to prove more advanced computability theorem. The (much) more complicated techniques involving priority with infinite injury will be presented in a later talk.
- 17 Novembre 2010: The Moser-Tardos constructive proof of Lovasz Local Lemma
- Orateur: Alexander Shen (LIF, Marseille)
- Last time we have shown how Kolmogorov complexity can be used to show that depth-first resampling can make a sparse CNF satisfied. However, to come close to Lovasz Local lemma and to show that the order of resampling does not matter, one needs to use more ingenious (but still simple) probabilistic argument that we plan to cover. (No previous knowledge about LLL will be really needed, so formally the talk is independent from the previous one). We also discuss some application to infinite formulas.
- November 10, 2010: The entropy compression argument, Lovasz local lemma and Kolmogorov complexity
- Speaker: Alexander Shen (LIF, Marseille)
- One of the classical applications of Kolmogorov comlexity to computational complexity and algorithms is the so called incompressibility method. This method is useful to prove lower bounds on the complexity of a problem by considering an instance of high Kolmogorov complexity and argue that for that particular instance the problem is "hard". In this talk, we present a recent new application of Kolmogorov complexity: the entropy reduction method due to Moser and Tardos. This technique is used to prove the termination of a randomized algorithm when the algorithm is "reversible" in a weak sense. This powerful technique can be applied to prove a constructive version of Lovasz local lemma (a central theorem in combinatorics), which we will discuss if time permits.
