12,719 research outputs found
Pregelix: Big(ger) Graph Analytics on A Dataflow Engine
There is a growing need for distributed graph processing systems that are
capable of gracefully scaling to very large graph datasets. Unfortunately, this
challenge has not been easily met due to the intense memory pressure imposed by
process-centric, message passing designs that many graph processing systems
follow. Pregelix is a new open source distributed graph processing system that
is based on an iterative dataflow design that is better tuned to handle both
in-memory and out-of-core workloads. As such, Pregelix offers improved
performance characteristics and scaling properties over current open source
systems (e.g., we have seen up to 15x speedup compared to Apache Giraph and up
to 35x speedup compared to distributed GraphLab), and makes more effective use
of available machine resources to support Big(ger) Graph Analytics
Geometry of the faithfulness assumption in causal inference
Many algorithms for inferring causality rely heavily on the faithfulness
assumption. The main justification for imposing this assumption is that the set
of unfaithful distributions has Lebesgue measure zero, since it can be seen as
a collection of hypersurfaces in a hypercube. However, due to sampling error
the faithfulness condition alone is not sufficient for statistical estimation,
and strong-faithfulness has been proposed and assumed to achieve uniform or
high-dimensional consistency. In contrast to the plain faithfulness assumption,
the set of distributions that is not strong-faithful has nonzero Lebesgue
measure and in fact, can be surprisingly large as we show in this paper. We
study the strong-faithfulness condition from a geometric and combinatorial
point of view and give upper and lower bounds on the Lebesgue measure of
strong-faithful distributions for various classes of directed acyclic graphs.
Our results imply fundamental limitations for the PC-algorithm and potentially
also for other algorithms based on partial correlation testing in the Gaussian
case.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1080 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Distributed Graph Automata and Verification of Distributed Algorithms
Combining ideas from distributed algorithms and alternating automata, we
introduce a new class of finite graph automata that recognize precisely the
languages of finite graphs definable in monadic second-order logic. By
restricting transitions to be nondeterministic or deterministic, we also obtain
two strictly weaker variants of our automata for which the emptiness problem is
decidable. As an application, we suggest how suitable graph automata might be
useful in formal verification of distributed algorithms, using Floyd-Hoare
logic.Comment: 26 pages, 6 figures, includes a condensed version of the author's
Master's thesis arXiv:1404.6503. (This version of the article (v2) is
identical to the previous one (v1), except for minor changes in phrasing.
MSO definable string transductions and two-way finite state transducers
String transductions that are definable in monadic second-order (mso) logic
(without the use of parameters) are exactly those realized by deterministic
two-way finite state transducers. Nondeterministic mso definable string
transductions (i.e., those definable with the use of parameters) correspond to
compositions of two nondeterministic two-way finite state transducers that have
the finite visit property. Both families of mso definable string transductions
are characterized in terms of Hennie machines, i.e., two-way finite state
transducers with the finite visit property that are allowed to rewrite their
input tape.Comment: 63 pages, LaTeX2e. Extended abstract presented at 26-th ICALP, 199
Visibly Pushdown Modular Games
Games on recursive game graphs can be used to reason about the control flow
of sequential programs with recursion. In games over recursive game graphs, the
most natural notion of strategy is the modular strategy, i.e., a strategy that
is local to a module and is oblivious to previous module invocations, and thus
does not depend on the context of invocation. In this work, we study for the
first time modular strategies with respect to winning conditions that can be
expressed by a pushdown automaton.
We show that such games are undecidable in general, and become decidable for
visibly pushdown automata specifications.
Our solution relies on a reduction to modular games with finite-state
automata winning conditions, which are known in the literature.
We carefully characterize the computational complexity of the considered
decision problem. In particular, we show that modular games with a universal
Buchi or co Buchi visibly pushdown winning condition are EXPTIME-complete, and
when the winning condition is given by a CARET or NWTL temporal logic formula
the problem is 2EXPTIME-complete, and it remains 2EXPTIME-hard even for simple
fragments of these logics.
As a further contribution, we present a different solution for modular games
with finite-state automata winning condition that runs faster than known
solutions for large specifications and many exits.Comment: In Proceedings GandALF 2014, arXiv:1408.556
Automata with Nested Pebbles Capture First-Order Logic with Transitive Closure
String languages recognizable in (deterministic) log-space are characterized
either by two-way (deterministic) multi-head automata, or following Immerman,
by first-order logic with (deterministic) transitive closure. Here we elaborate
this result, and match the number of heads to the arity of the transitive
closure. More precisely, first-order logic with k-ary deterministic transitive
closure has the same power as deterministic automata walking on their input
with k heads, additionally using a finite set of nested pebbles. This result is
valid for strings, ordered trees, and in general for families of graphs having
a fixed automaton that can be used to traverse the nodes of each of the graphs
in the family. Other examples of such families are grids, toruses, and
rectangular mazes. For nondeterministic automata, the logic is restricted to
positive occurrences of transitive closure.
The special case of k=1 for trees, shows that single-head deterministic
tree-walking automata with nested pebbles are characterized by first-order
logic with unary deterministic transitive closure. This refines our earlier
result that placed these automata between first-order and monadic second-order
logic on trees.Comment: Paper for Logical Methods in Computer Science, 27 pages, 1 figur
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