2,000 research outputs found
Polynomial-time Solvable #CSP Problems via Algebraic Models and Pfaffian Circuits
A Pfaffian circuit is a tensor contraction network where the edges are
labeled with changes of bases in such a way that a very specific set of
combinatorial properties are satisfied. By modeling the permissible changes of
bases as systems of polynomial equations, and then solving via computation, we
are able to identify classes of 0/1 planar #CSP problems solvable in
polynomial-time via the Pfaffian circuit evaluation theorem (a variant of L.
Valiant's Holant Theorem). We present two different models of 0/1 variables,
one that is possible under a homogeneous change of basis, and one that is
possible under a heterogeneous change of basis only. We enumerate a series of
1,2,3, and 4-arity gates/cogates that represent constraints, and define a class
of constraints that is possible under the assumption of a ``bridge" between two
particular changes of bases. We discuss the issue of planarity of Pfaffian
circuits, and demonstrate possible directions in algebraic computation for
designing a Pfaffian tensor contraction network fragment that can simulate a
swap gate/cogate. We conclude by developing the notion of a decomposable
gate/cogate, and discuss the computational benefits of this definition
Automatic frequency assignment for cellular telephones using constraint satisfaction techniques
We study the problem of automatic frequency assignment for cellular telephone
systems. The frequency assignment problem is viewed as the problem
to minimize the unsatisfied soft constraints in a constraint satisfaction problem
(CSP) over a finite domain of frequencies involving co-channel, adjacent
channel, and co-site constraints. The soft constraints are automatically derived
from signal strength prediction data. The CSP is solved using a generalized
graph coloring algorithm. Graph-theoretical results play a crucial
role in making the problem tractable. Performance results from a real-world
frequency assignment problem are presented.
We develop the generalized graph coloring algorithm by stepwise refinement,
starting from DSATUR and augmenting it with local propagation,
constraint lifting, intelligent backtracking, redundancy avoidance, and iterative
deepening
Even Delta-Matroids and the Complexity of Planar Boolean CSPs
The main result of this paper is a generalization of the classical blossom
algorithm for finding perfect matchings. Our algorithm can efficiently solve
Boolean CSPs where each variable appears in exactly two constraints (we call it
edge CSP) and all constraints are even -matroid relations (represented
by lists of tuples). As a consequence of this, we settle the complexity
classification of planar Boolean CSPs started by Dvorak and Kupec.
Using a reduction to even -matroids, we then extend the tractability
result to larger classes of -matroids that we call efficiently
coverable. It properly includes classes that were known to be tractable before,
namely co-independent, compact, local, linear and binary, with the following
caveat: we represent -matroids by lists of tuples, while the last two
use a representation by matrices. Since an matrix can represent
exponentially many tuples, our tractability result is not strictly stronger
than the known algorithm for linear and binary -matroids.Comment: 33 pages, 9 figure
Pseudo-Boolean Constraint Encodings for Conjunctive Normal Form and their Applications
In contrast to a single clause a pseudo-Boolean (PB) constraint is much more expressive and hence it is easier to define problems with the help of PB constraints. But while PB constraints provide us with a high-level problem description, it has been shown that solving PB constraints can be done faster with the help of a SAT solver. To apply such a solver to a PB constraint we have to encode it with clauses into conjunctive normal form (CNF). While we can find a basic encoding into CNF which is equivalent to a given PB constraint, the solving time of a SAT solver significantly depends on different properties of an encoding, e.g. the number of clauses or if generalized arc consistency (GAC) is maintained during the search for a solution.
There are various PB encodings that try to optimize or balance these properties. This thesis is about such encodings. For a better understanding of the research field an overview about the state-of-the art encodings is given. The focus of the overview is a simple but complete description of each encoding, such that any reader could use, implement and extent them in his own work. In addition two novel encodings are presented: The Sequential Weight Counter (SWC) encoding and the Binary Merger Encoding. While the SWC encoding provides a very simple structure – it is listed in four lines – empirical evaluation showed its practical usefulness in various applications. The Binary Merger encoding reduces the number of clauses a PB encoding needs while having the important GAC property. To the best of our knowledge currently no other encoding has a lower upper bound for the number of clauses produced by a PB encoding with this property. This is an important improvement of the state-of-the art, since both GAC and a low number of clauses are vital for an improved solving time of the SAT solver. The thesis also contributes to the development of new applications for PB constraint encodings. The programming library PBLib provides researchers with an open source implementation of almost all PB encodings – including the encodings for the special cases at-most-one and cardinality constraints. The PBLib is also the foundation of the presented weighted MaxSAT solver optimax, the PBO solver pbsolver and the WBO, PBO and weighted MaxSAT solver npSolver
Towards Symbolic Model-Based Mutation Testing: Combining Reachability and Refinement Checking
Model-based mutation testing uses altered test models to derive test cases
that are able to reveal whether a modelled fault has been implemented. This
requires conformance checking between the original and the mutated model. This
paper presents an approach for symbolic conformance checking of action systems,
which are well-suited to specify reactive systems. We also consider
nondeterminism in our models. Hence, we do not check for equivalence, but for
refinement. We encode the transition relation as well as the conformance
relation as a constraint satisfaction problem and use a constraint solver in
our reachability and refinement checking algorithms. Explicit conformance
checking techniques often face state space explosion. First experimental
evaluations show that our approach has potential to outperform explicit
conformance checkers.Comment: In Proceedings MBT 2012, arXiv:1202.582
Fifty years of Hoare's Logic
We present a history of Hoare's logic.Comment: 79 pages. To appear in Formal Aspects of Computin
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