34,525 research outputs found
Hidden Structure in Unsatisfiable Random 3-SAT: an Empirical Study
Recent advances in propositional satisfiability (SAT) include studying the hidden structure of unsatisfiable formulas, i.e. explaining why a given formula is unsatisfiable. Although theoretical work on the topic has been developed in the past, only recently two empirical successful approaches have been proposed: extracting unsatisfiable cores and identifying strong backdoors. An unsatisfiable core is a subset of clauses that defines a sub-formula that is also unsatisfiable, whereas a strong backdoor defines a subset of variables which assigned with all values allow concluding that the formula is unsatisfiable. The contribution of this paper is two-fold. First, we study the relation between the search complexity of unsatisfiable random 3-SAT formulas and the sizes of unsatisfiable cores and strong backdoors. For this purpose, we use an existing algorithm which uses an approximated approach for calculating these values. Second, we introduce a new algorithm that optimally reduces the size of unsatisfiable cores and strong backdoors, thus giving more accurate results. Experimental results indicate that the search complexity of unsatisfiable random 3-SAT formulas is related with the size of unsatisfiable cores and strong backdoors. 1
On Computing Minimum Unsatisfiable Cores
Certifying the correctness of a SAT solver is straightforward for satisfiable instances of SAT. Given
On Tackling the Limits of Resolution in SAT Solving
The practical success of Boolean Satisfiability (SAT) solvers stems from the
CDCL (Conflict-Driven Clause Learning) approach to SAT solving. However, from a
propositional proof complexity perspective, CDCL is no more powerful than the
resolution proof system, for which many hard examples exist. This paper
proposes a new problem transformation, which enables reducing the decision
problem for formulas in conjunctive normal form (CNF) to the problem of solving
maximum satisfiability over Horn formulas. Given the new transformation, the
paper proves a polynomial bound on the number of MaxSAT resolution steps for
pigeonhole formulas. This result is in clear contrast with earlier results on
the length of proofs of MaxSAT resolution for pigeonhole formulas. The paper
also establishes the same polynomial bound in the case of modern core-guided
MaxSAT solvers. Experimental results, obtained on CNF formulas known to be hard
for CDCL SAT solvers, show that these can be efficiently solved with modern
MaxSAT solvers
Migration energy aware reconfigurations of virtual network function instances in NFV architectures
Network function virtualization (NFV) is a new network architecture framework that implements network functions in software running on a pool of shared commodity servers. NFV can provide the infrastructure flexibility and agility needed to successfully compete in today's evolving communications landscape. Any service is represented by a service function chain (SFC) that is a set of VNFs to be executed according to a given order. The running of VNFs needs the instantiation of VNF instances (VNFIs) that are software modules executed on virtual machines. This paper deals with the migration problem of the VNFIs needed in the low traffic periods to turn OFF servers and consequently to save energy consumption. Though the consolidation allows for energy saving, it has also negative effects as the quality of service degradation or the energy consumption needed for moving the memories associated to the VNFI to be migrated. We focus on cold migration in which virtual machines are redundant and suspended before performing migration. We propose a migration policy that determines when and where to migrate VNFI in response to changes to SFC request intensity. The objective is to minimize the total energy consumption given by the sum of the consolidation and migration energies. We formulate the energy aware VNFI migration problem and after proving that it is NP-hard, we propose a heuristic based on the Viterbi algorithm able to determine the migration policy with low computational complexity. The results obtained by the proposed heuristic show how the introduced policy allows for a reduction of the migration energy and consequently lower total energy consumption with respect to the traditional policies. The energy saving can be on the order of 40% with respect to a policy in which migration is not performed
An adaptive prefix-assignment technique for symmetry reduction
This paper presents a technique for symmetry reduction that adaptively
assigns a prefix of variables in a system of constraints so that the generated
prefix-assignments are pairwise nonisomorphic under the action of the symmetry
group of the system. The technique is based on McKay's canonical extension
framework [J.~Algorithms 26 (1998), no.~2, 306--324]. Among key features of the
technique are (i) adaptability---the prefix sequence can be user-prescribed and
truncated for compatibility with the group of symmetries; (ii)
parallelizability---prefix-assignments can be processed in parallel
independently of each other; (iii) versatility---the method is applicable
whenever the group of symmetries can be concisely represented as the
automorphism group of a vertex-colored graph; and (iv) implementability---the
method can be implemented relying on a canonical labeling map for
vertex-colored graphs as the only nontrivial subroutine. To demonstrate the
practical applicability of our technique, we have prepared an experimental
open-source implementation of the technique and carry out a set of experiments
that demonstrate ability to reduce symmetry on hard instances. Furthermore, we
demonstrate that the implementation effectively parallelizes to compute
clusters with multiple nodes via a message-passing interface.Comment: Updated manuscript submitted for revie
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