4,338 research outputs found
On Characterizing the Data Access Complexity of Programs
Technology trends will cause data movement to account for the majority of
energy expenditure and execution time on emerging computers. Therefore,
computational complexity will no longer be a sufficient metric for comparing
algorithms, and a fundamental characterization of data access complexity will
be increasingly important. The problem of developing lower bounds for data
access complexity has been modeled using the formalism of Hong & Kung's
red/blue pebble game for computational directed acyclic graphs (CDAGs).
However, previously developed approaches to lower bounds analysis for the
red/blue pebble game are very limited in effectiveness when applied to CDAGs of
real programs, with computations comprised of multiple sub-computations with
differing DAG structure. We address this problem by developing an approach for
effectively composing lower bounds based on graph decomposition. We also
develop a static analysis algorithm to derive the asymptotic data-access lower
bounds of programs, as a function of the problem size and cache size
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Robocrystallographer: Automated crystal structure text descriptions and analysis
Our ability to describe crystal structure features is of crucial importance when attempting to understand structure-property relationships in the solid state. In this paper, the authors introduce robocrystallographer, an open-source toolkit for analyzing crystal structures. This package combines new and existing open-source analysis tools to provide structural information, including the local coordination and polyhedral type, polyhedral connectivity, octahedral tilt angles, component-dimensionality, and molecule-within-crystal and fuzzy prototype identification. Using this information, robocrystallographer can generate text-based descriptions of crystal structures that resemble descriptions written by human crystallographers. The authors use robocrystallographer to investigate the dimensionalities of all compounds in the Materials Project database and highlight its potential in machine learning studies
On the Monadic Second-Order Transduction Hierarchy
We compare classes of finite relational structures via monadic second-order
transductions. More precisely, we study the preorder where we set C \subseteq K
if, and only if, there exists a transduction {\tau} such that
C\subseteq{\tau}(K). If we only consider classes of incidence structures we can
completely describe the resulting hierarchy. It is linear of order type
{\omega}+3. Each level can be characterised in terms of a suitable variant of
tree-width. Canonical representatives of the various levels are: the class of
all trees of height n, for each n \in N, of all paths, of all trees, and of all
grids
Tree-width for first order formulae
We introduce tree-width for first order formulae \phi, fotw(\phi). We show
that computing fotw is fixed-parameter tractable with parameter fotw. Moreover,
we show that on classes of formulae of bounded fotw, model checking is fixed
parameter tractable, with parameter the length of the formula. This is done by
translating a formula \phi\ with fotw(\phi)<k into a formula of the k-variable
fragment L^k of first order logic. For fixed k, the question whether a given
first order formula is equivalent to an L^k formula is undecidable. In
contrast, the classes of first order formulae with bounded fotw are fragments
of first order logic for which the equivalence is decidable.
Our notion of tree-width generalises tree-width of conjunctive queries to
arbitrary formulae of first order logic by taking into account the quantifier
interaction in a formula. Moreover, it is more powerful than the notion of
elimination-width of quantified constraint formulae, defined by Chen and Dalmau
(CSL 2005): for quantified constraint formulae, both bounded elimination-width
and bounded fotw allow for model checking in polynomial time. We prove that
fotw of a quantified constraint formula \phi\ is bounded by the
elimination-width of \phi, and we exhibit a class of quantified constraint
formulae with bounded fotw, that has unbounded elimination-width. A similar
comparison holds for strict tree-width of non-recursive stratified datalog as
defined by Flum, Frick, and Grohe (JACM 49, 2002).
Finally, we show that fotw has a characterization in terms of a cops and
robbers game without monotonicity cost
Symbolic Algorithms for Graphs and Markov Decision Processes with Fairness Objectives
Given a model and a specification, the fundamental model-checking problem
asks for algorithmic verification of whether the model satisfies the
specification. We consider graphs and Markov decision processes (MDPs), which
are fundamental models for reactive systems. One of the very basic
specifications that arise in verification of reactive systems is the strong
fairness (aka Streett) objective. Given different types of requests and
corresponding grants, the objective requires that for each type, if the request
event happens infinitely often, then the corresponding grant event must also
happen infinitely often. All -regular objectives can be expressed as
Streett objectives and hence they are canonical in verification. To handle the
state-space explosion, symbolic algorithms are required that operate on a
succinct implicit representation of the system rather than explicitly accessing
the system. While explicit algorithms for graphs and MDPs with Streett
objectives have been widely studied, there has been no improvement of the basic
symbolic algorithms. The worst-case numbers of symbolic steps required for the
basic symbolic algorithms are as follows: quadratic for graphs and cubic for
MDPs. In this work we present the first sub-quadratic symbolic algorithm for
graphs with Streett objectives, and our algorithm is sub-quadratic even for
MDPs. Based on our algorithmic insights we present an implementation of the new
symbolic approach and show that it improves the existing approach on several
academic benchmark examples.Comment: Full version of the paper. To appear in CAV 201
Monadic second-order definable graph orderings
We study the question of whether, for a given class of finite graphs, one can
define, for each graph of the class, a linear ordering in monadic second-order
logic, possibly with the help of monadic parameters. We consider two variants
of monadic second-order logic: one where we can only quantify over sets of
vertices and one where we can also quantify over sets of edges. For several
special cases, we present combinatorial characterisations of when such a linear
ordering is definable. In some cases, for instance for graph classes that omit
a fixed graph as a minor, the presented conditions are necessary and
sufficient; in other cases, they are only necessary. Other graph classes we
consider include complete bipartite graphs, split graphs, chordal graphs, and
cographs. We prove that orderability is decidable for the so called
HR-equational classes of graphs, which are described by equation systems and
generalize the context-free languages
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