268 research outputs found
Equivalence Classes and Conditional Hardness in Massively Parallel Computations
The Massively Parallel Computation (MPC) model serves as a common abstraction of many modern large-scale data processing frameworks, and has been receiving increasingly more attention over the past few years, especially in the context of classical graph problems. So far, the only way to argue lower bounds for this model is to condition on conjectures about the hardness of some specific problems, such as graph connectivity on promise graphs that are either one cycle or two cycles, usually called the one cycle vs. two cycles problem. This is unlike the traditional arguments based on conjectures about complexity classes (e.g., P ? NP), which are often more robust in the sense that refuting them would lead to groundbreaking algorithms for a whole bunch of problems.
In this paper we present connections between problems and classes of problems that allow the latter type of arguments. These connections concern the class of problems solvable in a sublogarithmic amount of rounds in the MPC model, denoted by MPC(o(log N)), and some standard classes concerning space complexity, namely L and NL, and suggest conjectures that are robust in the sense that refuting them would lead to many surprisingly fast new algorithms in the MPC model. We also obtain new conditional lower bounds, and prove new reductions and equivalences between problems in the MPC model
Verification of Information Flow Properties under Rational Observation
Information flow properties express the capability for an agent to infer
information about secret behaviours of a partially observable system. In a
language-theoretic setting, where the system behaviour is described by a
language, we define the class of rational information flow properties (RIFP),
where observers are modeled by finite transducers, acting on languages in a
given family . This leads to a general decidability criterion for
the verification problem of RIFPs on , implying
PSPACE-completeness for this problem on regular languages. We show that most
trace-based information flow properties studied up to now are RIFPs, including
those related to selective declassification and conditional anonymity. As a
consequence, we retrieve several existing decidability results that were
obtained by ad-hoc proofs.Comment: 19 pages, 7 figures, version extended from AVOCS'201
The Gremlin Graph Traversal Machine and Language
Gremlin is a graph traversal machine and language designed, developed, and
distributed by the Apache TinkerPop project. Gremlin, as a graph traversal
machine, is composed of three interacting components: a graph , a traversal
, and a set of traversers . The traversers move about the graph
according to the instructions specified in the traversal, where the result of
the computation is the ultimate locations of all halted traversers. A Gremlin
machine can be executed over any supporting graph computing system such as an
OLTP graph database and/or an OLAP graph processor. Gremlin, as a graph
traversal language, is a functional language implemented in the user's native
programming language and is used to define the of a Gremlin machine.
This article provides a mathematical description of Gremlin and details its
automaton and functional properties. These properties enable Gremlin to
naturally support imperative and declarative querying, host language
agnosticism, user-defined domain specific languages, an extensible
compiler/optimizer, single- and multi-machine execution models, hybrid depth-
and breadth-first evaluation, as well as the existence of a Universal Gremlin
Machine and its respective entailments.Comment: To appear in the Proceedings of the 2015 ACM Database Programming
Languages Conferenc
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