62,186 research outputs found
Premise Selection for Mathematics by Corpus Analysis and Kernel Methods
Smart premise selection is essential when using automated reasoning as a tool
for large-theory formal proof development. A good method for premise selection
in complex mathematical libraries is the application of machine learning to
large corpora of proofs. This work develops learning-based premise selection in
two ways. First, a newly available minimal dependency analysis of existing
high-level formal mathematical proofs is used to build a large knowledge base
of proof dependencies, providing precise data for ATP-based re-verification and
for training premise selection algorithms. Second, a new machine learning
algorithm for premise selection based on kernel methods is proposed and
implemented. To evaluate the impact of both techniques, a benchmark consisting
of 2078 large-theory mathematical problems is constructed,extending the older
MPTP Challenge benchmark. The combined effect of the techniques results in a
50% improvement on the benchmark over the Vampire/SInE state-of-the-art system
for automated reasoning in large theories.Comment: 26 page
Efficient Algorithms for Distributed Detection of Holes and Boundaries in Wireless Networks
We propose two novel algorithms for distributed and location-free boundary
recognition in wireless sensor networks. Both approaches enable a node to
decide autonomously whether it is a boundary node, based solely on connectivity
information of a small neighborhood. This makes our algorithms highly
applicable for dynamic networks where nodes can move or become inoperative.
We compare our algorithms qualitatively and quantitatively with several
previous approaches. In extensive simulations, we consider various models and
scenarios. Although our algorithms use less information than most other
approaches, they produce significantly better results. They are very robust
against variations in node degree and do not rely on simplified assumptions of
the communication model. Moreover, they are much easier to implement on real
sensor nodes than most existing approaches.Comment: extended version of accepted submission to SEA 201
Simplest random K-satisfiability problem
We study a simple and exactly solvable model for the generation of random
satisfiability problems. These consist of random boolean constraints
which are to be satisfied simultaneously by logical variables. In
statistical-mechanics language, the considered model can be seen as a diluted
p-spin model at zero temperature. While such problems become extraordinarily
hard to solve by local search methods in a large region of the parameter space,
still at least one solution may be superimposed by construction. The
statistical properties of the model can be studied exactly by the replica
method and each single instance can be analyzed in polynomial time by a simple
global solution method. The geometrical/topological structures responsible for
dynamic and static phase transitions as well as for the onset of computational
complexity in local search method are thoroughly analyzed. Numerical analysis
on very large samples allows for a precise characterization of the critical
scaling behaviour.Comment: 14 pages, 5 figures, to appear in Phys. Rev. E (Feb 2001). v2: minor
errors and references correcte
Runtime Analysis of the Genetic Algorithm on Random Satisfiable 3-CNF Formulas
The genetic algorithm, first proposed at GECCO 2013,
showed a surprisingly good performance on so me optimization problems. The
theoretical analysis so far was restricted to the OneMax test function, where
this GA profited from the perfect fitness-distance correlation. In this work,
we conduct a rigorous runtime analysis of this GA on random 3-SAT instances in
the planted solution model having at least logarithmic average degree, which
are known to have a weaker fitness distance correlation.
We prove that this GA with fixed not too large population size again obtains
runtimes better than , which is a lower bound for most
evolutionary algorithms on pseudo-Boolean problems with unique optimum.
However, the self-adjusting version of the GA risks reaching population sizes
at which the intermediate selection of the GA, due to the weaker
fitness-distance correlation, is not able to distinguish a profitable offspring
from others. We show that this problem can be overcome by equipping the
self-adjusting GA with an upper limit for the population size. Apart from
sparse instances, this limit can be chosen in a way that the asymptotic
performance does not worsen compared to the idealistic OneMax case. Overall,
this work shows that the GA can provably have a good
performance on combinatorial search and optimization problems also in the
presence of a weaker fitness-distance correlation.Comment: An extended abstract of this report will appear in the proceedings of
the 2017 Genetic and Evolutionary Computation Conference (GECCO 2017
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