16,712 research outputs found
Optimal Testing for Planted Satisfiability Problems
We study the problem of detecting planted solutions in a random
satisfiability formula. Adopting the formalism of hypothesis testing in
statistical analysis, we describe the minimax optimal rates of detection. Our
analysis relies on the study of the number of satisfying assignments, for which
we prove new results. We also address algorithmic issues, and give a
computationally efficient test with optimal statistical performance. This
result is compared to an average-case hypothesis on the hardness of refuting
satisfiability of random formulas
Reweighted belief propagation and quiet planting for random K-SAT
We study the random K-satisfiability problem using a partition function where
each solution is reweighted according to the number of variables that satisfy
every clause. We apply belief propagation and the related cavity method to the
reweighted partition function. This allows us to obtain several new results on
the properties of random K-satisfiability problem. In particular the
reweighting allows to introduce a planted ensemble that generates instances
that are, in some region of parameters, equivalent to random instances. We are
hence able to generate at the same time a typical random SAT instance and one
of its solutions. We study the relation between clustering and belief
propagation fixed points and we give a direct evidence for the existence of
purely entropic (rather than energetic) barriers between clusters in some
region of parameters in the random K-satisfiability problem. We exhibit, in
some large planted instances, solutions with a non-trivial whitening core; such
solutions were known to exist but were so far never found on very large
instances. Finally, we discuss algorithmic hardness of such planted instances
and we determine a region of parameters in which planting leads to satisfiable
benchmarks that, up to our knowledge, are the hardest known.Comment: 23 pages, 4 figures, revised for readability, stability expression
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Advantages of Unfair Quantum Ground-State Sampling
The debate around the potential superiority of quantum annealers over their
classical counterparts has been ongoing since the inception of the field by
Kadowaki and Nishimori close to two decades ago. Recent technological
breakthroughs in the field, which have led to the manufacture of experimental
prototypes of quantum annealing optimizers with sizes approaching the practical
regime, have reignited this discussion. However, the demonstration of quantum
annealing speedups remains to this day an elusive albeit coveted goal. Here, we
examine the power of quantum annealers to provide a different type of quantum
enhancement of practical relevance, namely, their ability to serve as useful
samplers from the ground-state manifolds of combinatorial optimization
problems. We study, both numerically by simulating ideal stoquastic and
non-stoquastic quantum annealing processes, and experimentally, using a
commercially available quantum annealing processor, the ability of quantum
annealers to sample the ground-states of spin glasses differently than
classical thermal samplers. We demonstrate that i) quantum annealers in general
sample the ground-state manifolds of spin glasses very differently than thermal
optimizers, ii) the nature of the quantum fluctuations driving the annealing
process has a decisive effect on the final distribution over ground-states, and
iii) the experimental quantum annealer samples ground-state manifolds
significantly differently than thermal and ideal quantum annealers. We
illustrate how quantum annealers may serve as powerful tools when complementing
standard sampling algorithms.Comment: 13 pages, 11 figure
Timed Soft Concurrent Constraint Programs: An Interleaved and a Parallel Approach
We propose a timed and soft extension of Concurrent Constraint Programming.
The time extension is based on the hypothesis of bounded asynchrony: the
computation takes a bounded period of time and is measured by a discrete global
clock. Action prefixing is then considered as the syntactic marker which
distinguishes a time instant from the next one. Supported by soft constraints
instead of crisp ones, tell and ask agents are now equipped with a preference
(or consistency) threshold which is used to determine their success or
suspension. In the paper we provide a language to describe the agents behavior,
together with its operational and denotational semantics, for which we also
prove the compositionality and correctness properties. After presenting a
semantics using maximal parallelism of actions, we also describe a version for
their interleaving on a single processor (with maximal parallelism for time
elapsing). Coordinating agents that need to take decisions both on preference
values and time events may benefit from this language. To appear in Theory and
Practice of Logic Programming (TPLP)
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