1,337 research outputs found
Fast Consensus under Eventually Stabilizing Message Adversaries
This paper is devoted to deterministic consensus in synchronous dynamic
networks with unidirectional links, which are under the control of an
omniscient message adversary. Motivated by unpredictable node/system
initialization times and long-lasting periods of massive transient faults, we
consider message adversaries that guarantee periods of less erratic message
loss only eventually: We present a tight bound of for the termination
time of consensus under a message adversary that eventually guarantees a single
vertex-stable root component with dynamic network diameter , as well as a
simple algorithm that matches this bound. It effectively halves the termination
time achieved by an existing consensus algorithm, which also works under
our message adversary. We also introduce a generalized, considerably stronger
variant of our message adversary, and show that our new algorithm, unlike the
existing one, still works correctly under it.Comment: 13 pages, 5 figures, updated reference
Towards Verifying Nonlinear Integer Arithmetic
We eliminate a key roadblock to efficient verification of nonlinear integer
arithmetic using CDCL SAT solvers, by showing how to construct short resolution
proofs for many properties of the most widely used multiplier circuits. Such
short proofs were conjectured not to exist. More precisely, we give n^{O(1)}
size regular resolution proofs for arbitrary degree 2 identities on array,
diagonal, and Booth multipliers and quasipolynomial- n^{O(\log n)} size proofs
for these identities on Wallace tree multipliers.Comment: Expanded and simplified with improved result
Collaborative Delivery with Energy-Constrained Mobile Robots
We consider the problem of collectively delivering some message from a
specified source to a designated target location in a graph, using multiple
mobile agents. Each agent has a limited energy which constrains the distance it
can move. Hence multiple agents need to collaborate to move the message, each
agent handing over the message to the next agent to carry it forward. Given the
positions of the agents in the graph and their respective budgets, the problem
of finding a feasible movement schedule for the agents can be challenging. We
consider two variants of the problem: in non-returning delivery, the agents can
stop anywhere; whereas in returning delivery, each agent needs to return to its
starting location, a variant which has not been studied before.
We first provide a polynomial-time algorithm for returning delivery on trees,
which is in contrast to the known (weak) NP-hardness of the non-returning
version. In addition, we give resource-augmented algorithms for returning
delivery in general graphs. Finally, we give tight lower bounds on the required
resource augmentation for both variants of the problem. In this sense, our
results close the gap left by previous research.Comment: 19 pages. An extended abstract of this paper was published at the
23rd International Colloquium on Structural Information and Communication
Complexity 2016, SIROCCO'1
Decision Stream: Cultivating Deep Decision Trees
Various modifications of decision trees have been extensively used during the
past years due to their high efficiency and interpretability. Tree node
splitting based on relevant feature selection is a key step of decision tree
learning, at the same time being their major shortcoming: the recursive nodes
partitioning leads to geometric reduction of data quantity in the leaf nodes,
which causes an excessive model complexity and data overfitting. In this paper,
we present a novel architecture - a Decision Stream, - aimed to overcome this
problem. Instead of building a tree structure during the learning process, we
propose merging nodes from different branches based on their similarity that is
estimated with two-sample test statistics, which leads to generation of a deep
directed acyclic graph of decision rules that can consist of hundreds of
levels. To evaluate the proposed solution, we test it on several common machine
learning problems - credit scoring, twitter sentiment analysis, aircraft flight
control, MNIST and CIFAR image classification, synthetic data classification
and regression. Our experimental results reveal that the proposed approach
significantly outperforms the standard decision tree learning methods on both
regression and classification tasks, yielding a prediction error decrease up to
35%
Classification of OBDD Size for Monotone 2-CNFs
We introduce a new graph parameter called linear upper maximum induced matching width lu-mim width, denoted for a graph G by lu(G). We prove that the smallest size of the obdd for ?, the monotone 2-cnf corresponding to G, is sandwiched between 2^{lu(G)} and n^{O(lu(G))}. The upper bound is based on a combinatorial statement that might be of an independent interest. We show that the bounds in terms of this parameter are best possible.
The new parameter is closely related to two existing parameters: linear maximum induced matching width (lmim width) and linear special induced matching width (lsim width). We prove that lu-mim width lies strictly in between these two parameters, being dominated by lsim width and dominating lmim width. We conclude that neither of the two existing parameters can be used instead of lu-mim width to characterize the size of obdds for monotone 2-cnfs and this justifies introduction of the new parameter
Analyzing Timed Systems Using Tree Automata
Timed systems, such as timed automata, are usually analyzed using their
operational semantics on timed words. The classical region abstraction for
timed automata reduces them to (untimed) finite state automata with the same
time-abstract properties, such as state reachability. We propose a new
technique to analyze such timed systems using finite tree automata instead of
finite word automata. The main idea is to consider timed behaviors as graphs
with matching edges capturing timing constraints. When a family of graphs has
bounded tree-width, they can be interpreted in trees and MSO-definable
properties of such graphs can be checked using tree automata. The technique is
quite general and applies to many timed systems. In this paper, as an example,
we develop the technique on timed pushdown systems, which have recently
received considerable attention. Further, we also demonstrate how we can use it
on timed automata and timed multi-stack pushdown systems (with boundedness
restrictions)
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