3,207 research outputs found
Reason Maintenance - State of the Art
This paper describes state of the art in reason maintenance with a focus on its future usage in the KiWi project. To give a bigger picture of the field, it also mentions closely related issues such as non-monotonic logic and paraconsistency. The paper is organized as follows: first, two motivating scenarios referring to semantic wikis are presented which are then used to introduce the different reason maintenance techniques
Solving Set Constraint Satisfaction Problems using ROBDDs
In this paper we present a new approach to modeling finite set domain
constraint problems using Reduced Ordered Binary Decision Diagrams (ROBDDs). We
show that it is possible to construct an efficient set domain propagator which
compactly represents many set domains and set constraints using ROBDDs. We
demonstrate that the ROBDD-based approach provides unprecedented flexibility in
modeling constraint satisfaction problems, leading to performance improvements.
We also show that the ROBDD-based modeling approach can be extended to the
modeling of integer and multiset constraint problems in a straightforward
manner. Since domain propagation is not always practical, we also show how to
incorporate less strict consistency notions into the ROBDD framework, such as
set bounds, cardinality bounds and lexicographic bounds consistency. Finally,
we present experimental results that demonstrate the ROBDD-based solver
performs better than various more conventional constraint solvers on several
standard set constraint problems
Enumeration of octagonal tilings
Random tilings are interesting as idealizations of atomistic models of
quasicrystals and for their connection to problems in combinatorics and
algorithms. Of particular interest is the tiling entropy density, which
measures the relation of the number of distinct tilings to the number of
constituent tiles. Tilings by squares and 45 degree rhombi receive special
attention as presumably the simplest model that has not yet been solved exactly
in the thermodynamic limit. However, an exact enumeration formula can be
evaluated for tilings in finite regions with fixed boundaries. We implement
this algorithm in an efficient manner, enabling the investigation of larger
regions of parameter space than previously were possible. Our new results
appear to yield monotone increasing and decreasing lower and upper bounds on
the fixed boundary entropy density that converge toward S = 0.36021(3)
A Forward Reachability Algorithm for Bounded Timed-Arc Petri Nets
Timed-arc Petri nets (TAPN) are a well-known time extension of the Petri net
model and several translations to networks of timed automata have been proposed
for this model. We present a direct, DBM-based algorithm for forward
reachability analysis of bounded TAPNs extended with transport arcs, inhibitor
arcs and age invariants. We also give a complete proof of its correctness,
including reduction techniques based on symmetries and extrapolation. Finally,
we augment the algorithm with a novel state-space reduction technique
introducing a monotonic ordering on markings and prove its soundness even in
the presence of monotonicity-breaking features like age invariants and
inhibitor arcs. We implement the algorithm within the model-checker TAPAAL and
the experimental results document an encouraging performance compared to
verification approaches that translate TAPN models to UPPAAL timed automata.Comment: In Proceedings SSV 2012, arXiv:1211.587
On Online Labeling with Polynomially Many Labels
In the online labeling problem with parameters n and m we are presented with
a sequence of n keys from a totally ordered universe U and must assign each
arriving key a label from the label set {1,2,...,m} so that the order of labels
(strictly) respects the ordering on U. As new keys arrive it may be necessary
to change the labels of some items; such changes may be done at any time at
unit cost for each change. The goal is to minimize the total cost. An
alternative formulation of this problem is the file maintenance problem, in
which the items, instead of being labeled, are maintained in sorted order in an
array of length m, and we pay unit cost for moving an item.
For the case m=cn for constant c>1, there are known algorithms that use at
most O(n log(n)^2) relabelings in total [Itai, Konheim, Rodeh, 1981], and it
was shown recently that this is asymptotically optimal [Bul\'anek, Kouck\'y,
Saks, 2012]. For the case of m={\Theta}(n^C) for C>1, algorithms are known that
use O(n log n) relabelings. A matching lower bound was claimed in [Dietz,
Seiferas, Zhang, 2004]. That proof involved two distinct steps: a lower bound
for a problem they call prefix bucketing and a reduction from prefix bucketing
to online labeling. The reduction seems to be incorrect, leaving a (seemingly
significant) gap in the proof. In this paper we close the gap by presenting a
correct reduction to prefix bucketing. Furthermore we give a simplified and
improved analysis of the prefix bucketing lower bound. This improvement allows
us to extend the lower bounds for online labeling to the case where the number
m of labels is superpolynomial in n. In particular, for superpolynomial m we
get an asymptotically optimal lower bound {\Omega}((n log n) / (log log m - log
log n)).Comment: 15 pages, Presented at European Symposium on Algorithms 201
Baron Munchhausen Redeems Himself: Bounds for a Coin-Weighing Puzzle
We investigate a coin-weighing puzzle that appeared in the Moscow Math
Olympiad in 1991. We generalize the puzzle by varying the number of
participating coins, and deduce an upper bound on the number of weighings
needed to solve the puzzle that is noticeably better than the trivial upper
bound. In particular, we show that logarithmically-many weighings on a balance
suffice.Comment: 19 page
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