27,014 research outputs found
Game Refinement Relations and Metrics
We consider two-player games played over finite state spaces for an infinite
number of rounds. At each state, the players simultaneously choose moves; the
moves determine a successor state. It is often advantageous for players to
choose probability distributions over moves, rather than single moves. Given a
goal, for example, reach a target state, the question of winning is thus a
probabilistic one: what is the maximal probability of winning from a given
state?
On these game structures, two fundamental notions are those of equivalences
and metrics. Given a set of winning conditions, two states are equivalent if
the players can win the same games with the same probability from both states.
Metrics provide a bound on the difference in the probabilities of winning
across states, capturing a quantitative notion of state similarity.
We introduce equivalences and metrics for two-player game structures, and we
show that they characterize the difference in probability of winning games
whose goals are expressed in the quantitative mu-calculus. The quantitative
mu-calculus can express a large set of goals, including reachability, safety,
and omega-regular properties. Thus, we claim that our relations and metrics
provide the canonical extensions to games, of the classical notion of
bisimulation for transition systems. We develop our results both for
equivalences and metrics, which generalize bisimulation, and for asymmetrical
versions, which generalize simulation
Strong Equivalence Relations for Iterated Models
The Iterated Immediate Snapshot model (IIS), due to its elegant geometrical
representation, has become standard for applying topological reasoning to
distributed computing. Its modular structure makes it easier to analyze than
the more realistic (non-iterated) read-write Atomic-Snapshot memory model (AS).
It is known that AS and IIS are equivalent with respect to \emph{wait-free
task} computability: a distributed task is solvable in AS if and only if it
solvable in IIS. We observe, however, that this equivalence is not sufficient
in order to explore solvability of tasks in \emph{sub-models} of AS (i.e.
proper subsets of its runs) or computability of \emph{long-lived} objects, and
a stronger equivalence relation is needed. In this paper, we consider
\emph{adversarial} sub-models of AS and IIS specified by the sets of processes
that can be \emph{correct} in a model run. We show that AS and IIS are
equivalent in a strong way: a (possibly long-lived) object is implementable in
AS under a given adversary if and only if it is implementable in IIS under the
same adversary. %This holds whether the object is one-shot or long-lived.
Therefore, the computability of any object in shared memory under an
adversarial AS scheduler can be equivalently investigated in IIS
Distributional Equivalence and Structure Learning for Bow-free Acyclic Path Diagrams
We consider the problem of structure learning for bow-free acyclic path
diagrams (BAPs). BAPs can be viewed as a generalization of linear Gaussian DAG
models that allow for certain hidden variables. We present a first method for
this problem using a greedy score-based search algorithm. We also prove some
necessary and some sufficient conditions for distributional equivalence of BAPs
which are used in an algorithmic ap- proach to compute (nearly) equivalent
model structures. This allows us to infer lower bounds of causal effects. We
also present applications to real and simulated datasets using our publicly
available R-package
Spatial Aggregation: Theory and Applications
Visual thinking plays an important role in scientific reasoning. Based on the
research in automating diverse reasoning tasks about dynamical systems,
nonlinear controllers, kinematic mechanisms, and fluid motion, we have
identified a style of visual thinking, imagistic reasoning. Imagistic reasoning
organizes computations around image-like, analogue representations so that
perceptual and symbolic operations can be brought to bear to infer structure
and behavior. Programs incorporating imagistic reasoning have been shown to
perform at an expert level in domains that defy current analytic or numerical
methods. We have developed a computational paradigm, spatial aggregation, to
unify the description of a class of imagistic problem solvers. A program
written in this paradigm has the following properties. It takes a continuous
field and optional objective functions as input, and produces high-level
descriptions of structure, behavior, or control actions. It computes a
multi-layer of intermediate representations, called spatial aggregates, by
forming equivalence classes and adjacency relations. It employs a small set of
generic operators such as aggregation, classification, and localization to
perform bidirectional mapping between the information-rich field and
successively more abstract spatial aggregates. It uses a data structure, the
neighborhood graph, as a common interface to modularize computations. To
illustrate our theory, we describe the computational structure of three
implemented problem solvers -- KAM, MAPS, and HIPAIR --- in terms of the
spatial aggregation generic operators by mixing and matching a library of
commonly used routines.Comment: See http://www.jair.org/ for any accompanying file
- …