
The SAT Phase Transition
Phase transition is an important feature of SAT problem. For random kSA...
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An Effective Algorithm for and Phase Transitions of the Directed Hamiltonian Cycle Problem
The Hamiltonian cycle problem (HCP) is an important combinatorial proble...
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Exact enumeration of satisfiable 2SAT formulae
We obtain exact expressions counting the satisfiable 2SAT formulae and ...
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The Potential of Restarts for ProbSAT
This work analyses the potential of restarts for probSAT, a quite succes...
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On the Average Similarity Degree between Solutions of Random kSAT and Random CSPs
To study the structure of solutions for random kSAT and random CSPs, th...
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Phase Transition and Network Structure in Realistic SAT Problems
A fundamental question in Computer Science is understanding when a speci...
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Phase Transitions for the Information Bottleneck in Representation Learning
In the Information Bottleneck (IB), when tuning the relative strength be...
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The birth of the contradictory component in random 2SAT
We prove that, with high probability, the contradictory components of a random 2SAT formula in the subcritical phase of the phase transition have only 3regular kernels. This follows from the relation between these kernels and the complex component of a random graph in the subcritical phase. This partly settles the question about the structural similarity between the phase transitions in 2SAT and random graphs. As a byproduct, we describe the technique that allows to obtain a full asymptotic expansion of the satisfiability in the subcritical phase. We also obtain the distribution of the number of contradictory variables and the structure of the spine in the subcritical phase.
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