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We study the satisfiability of randomly generated formulas formed by M clauses of exactly K literals over N Boolean variables. For a given value of N the problem is known to be most difficult when α = M/N is close to the experimental threshold α c separating the region where almost all formulas are SAT from the region where all formulas are UNSAT. Recent… (More)

- Re Â Mi Monasson, Riccardo Zecchina, Scott Kirkpatrick, Bart Selman, Lidror Troyanskyk
- 1999

Non-deterministic polynomial time (commonly termed`NP-complete') problems are relevant to many computational tasks of practical interestÐsuch as thètravelling salesman problem'Ðbut are dif®cult to solve: the computing time grows exponentially with problem size in the worst case. It has recently been shown that these problems exhibit`phase boundaries',… (More)

Using the cavity we derive the various threshold values for the number of clauses per variable of the random K-satisfiability problem, generalizing the previous results to K ≥ 4. We also give an analytic solution of the equations, and some closed expressions for these thresholds, in an expansion around large K. The stability of the solution is also… (More)

The evolutionary trajectory of a protein through sequence space is constrained by its function. Collections of sequence homologs record the outcomes of millions of evolutionary experiments in which the protein evolves according to these constraints. Deciphering the evolutionary record held in these sequences and exploiting it for predictive and engineering… (More)

- Faruck Morcos, Andrea Pagnani, Bryan Lunt, Arianna Bertolino, Debora S Marks, Chris Sander +4 others
- Proceedings of the National Academy of Sciences…
- 2011

The similarity in the three-dimensional structures of homologous proteins imposes strong constraints on their sequence variability. It has long been suggested that the resulting correlations among amino acid compositions at different sequence positions can be exploited to infer spatial contacts within the tertiary protein structure. Crucial to this… (More)

- Ré Mi Monasson, Riccardo Zecchina
- 1997

The random K-satisfiability problem, consisting in verifying the existence of an assignment of N Boolean variables that satisfy a set of M ϭ␣N random logical clauses containing K variables each, is studied using the replica symmetric framework of diluted disordered systems. We present an exact iterative scheme for the replica symmetric functional order… (More)

Survey Propagation (SP) is an algorithm designed for solving typical instances of random constraint satisfiability problems. It has been successfully tested on random 3-satisfiability (3-sat) and random G(n, c n) graph 3-coloring (3-col), in the hard region of the parameter space, relatively close the the SAT/UNSAT phase transition. Here we provide a… (More)

We derive analytical solutions for p-spin models with finite connectivity at zero temperature. These models are the statistical mechanics equivalent of p-XORSAT problems in theoretical computer science. We give a full characterization of the phase diagram: location of the phase transitions (static and dynamic), together with a description of the clustering… (More)

It has been shown experimentally that a decimation algorithm based on Survey Propagation (SP) equations allows to solve efficiently some combinatorial problems over random graphs. We show that these equations can be derived as sum-product equations for the computation of marginals in an extended space where the variables are allowed to take an additional… (More)

We consider the general problem of finding the minimum weight b-matching on arbitrary graphs. We prove that, whenever the linear programming (LP) relaxation of the problem has no fractional solutions, then the belief propagation (BP) algorithm converges to the correct solution. We also show that when the LP relaxation has fractional solution then BP… (More)