Phase Transition in Hard Computational Problems

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Azadkia, Mona | 2014

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 46564 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Alishahi, Kasra; HajiMirsadeghi, Mir Omid
Abstract:
In this thesis we are going to introduce the notion of k-SAT problem as one of the NP-complete problems and illustrate its importance of investigation. To study and seperate the hard and easy samples of this problem, we are going to explain the satisfiability threshold conjecture and some theorems in the infinity limit cases for the phase transition threshold. At last we are going to define the notion of sharp threshold and state a fundamental theorem which gives a necessary and sufficient condition for a threshold to be coarse
Keywords:
Fourier Transform ; NP-Hard Problems ; NP-Complete ; Phase Transition ; Moment Method ; Satisfiability Conjecture ; K-Satisfiability Problem ; Sharp Phase Transition

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