Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Heuristic average-case analysis of the backtrack resolution of random
  3-Satisfiability instances   An analysis of the average-case complexity of solving random 3-Satisfiability
(SAT) instances with backtrack algorithms is presented. We first interpret
previous rigorous works in a unifying framework based on the statistical
physics notions of dynamical trajectories, phase diagram and growth process. It
is argued that, under the action of the Davis--Putnam--Loveland--Logemann
(DPLL) algorithm, 3-SAT instances are turned into 2+p-SAT instances whose
characteristic parameters (ratio alpha of clauses per variable, fraction p of
3-clauses) can be followed during the operation, and define resolution
trajectories. Depending on the location of trajectories in the phase diagram of
the 2+p-SAT model, easy (polynomial) or hard (exponential) resolutions are
generated. Three regimes are identified, depending on the ratio alpha of the
3-SAT instance to be solved. Lower sat phase: for small ratios, DPLL almost
surely finds a solution in a time growing linearly with the number N of
variables. Upper sat phase: for intermediate ratios, instances are almost
surely satisfiable but finding a solution requires exponential time (2 ^ (N
omega) with omega>0) with high probability. Unsat phase: for large ratios,
there is almost always no solution and proofs of refutation are exponential. An
analysis of the growth of the search tree in both upper sat and unsat regimes
is presented, and allows us to estimate omega as a function of alpha. This
analysis is based on an exact relationship between the average size of the
search tree and the powers of the evolution operator encoding the elementary
steps of the search heuristic.

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The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph