27,986 research outputs found
Weighted Modal Transition Systems
Specification theories as a tool in model-driven development processes of
component-based software systems have recently attracted a considerable
attention. Current specification theories are however qualitative in nature,
and therefore fragile in the sense that the inevitable approximation of systems
by models, combined with the fundamental unpredictability of hardware
platforms, makes it difficult to transfer conclusions about the behavior, based
on models, to the actual system. Hence this approach is arguably unsuited for
modern software systems. We propose here the first specification theory which
allows to capture quantitative aspects during the refinement and implementation
process, thus leveraging the problems of the qualitative setting.
Our proposed quantitative specification framework uses weighted modal
transition systems as a formal model of specifications. These are labeled
transition systems with the additional feature that they can model optional
behavior which may or may not be implemented by the system. Satisfaction and
refinement is lifted from the well-known qualitative to our quantitative
setting, by introducing a notion of distances between weighted modal transition
systems. We show that quantitative versions of parallel composition as well as
quotient (the dual to parallel composition) inherit the properties from the
Boolean setting.Comment: Submitted to Formal Methods in System Desig
Imperfect-Recall Abstractions with Bounds in Games
Imperfect-recall abstraction has emerged as the leading paradigm for
practical large-scale equilibrium computation in incomplete-information games.
However, imperfect-recall abstractions are poorly understood, and only weak
algorithm-specific guarantees on solution quality are known. In this paper, we
show the first general, algorithm-agnostic, solution quality guarantees for
Nash equilibria and approximate self-trembling equilibria computed in
imperfect-recall abstractions, when implemented in the original
(perfect-recall) game. Our results are for a class of games that generalizes
the only previously known class of imperfect-recall abstractions where any
results had been obtained. Further, our analysis is tighter in two ways, each
of which can lead to an exponential reduction in the solution quality error
bound.
We then show that for extensive-form games that satisfy certain properties,
the problem of computing a bound-minimizing abstraction for a single level of
the game reduces to a clustering problem, where the increase in our bound is
the distance function. This reduction leads to the first imperfect-recall
abstraction algorithm with solution quality bounds. We proceed to show a divide
in the class of abstraction problems. If payoffs are at the same scale at all
information sets considered for abstraction, the input forms a metric space.
Conversely, if this condition is not satisfied, we show that the input does not
form a metric space. Finally, we use these results to experimentally
investigate the quality of our bound for single-level abstraction
Mixing of the symmetric exclusion processes in terms of the corresponding single-particle random walk
We prove an upper bound for the -mixing time of the symmetric
exclusion process on any graph G, with any feasible number of particles. Our
estimate is proportional to ,
where |V| is the number of vertices in G, and is
the 1/4-mixing time of the corresponding single-particle random walk. This
bound implies new results for symmetric exclusion on expanders, percolation
clusters, the giant component of the Erdos-Renyi random graph and Poisson point
processes in . Our technical tools include a variant of Morris's
chameleon process.Comment: Published in at http://dx.doi.org/10.1214/11-AOP714 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Mixing of the symmetric exclusion processes in terms of the corresponding single-particle random walk
We prove an upper bound for the -mixing time of the symmetric
exclusion process on any graph G, with any feasible number of particles. Our
estimate is proportional to ,
where |V| is the number of vertices in G, and is
the 1/4-mixing time of the corresponding single-particle random walk. This
bound implies new results for symmetric exclusion on expanders, percolation
clusters, the giant component of the Erdos-Renyi random graph and Poisson point
processes in . Our technical tools include a variant of Morris's
chameleon process.Comment: Published in at http://dx.doi.org/10.1214/11-AOP714 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Bounded Expectations: Resource Analysis for Probabilistic Programs
This paper presents a new static analysis for deriving upper bounds on the
expected resource consumption of probabilistic programs. The analysis is fully
automatic and derives symbolic bounds that are multivariate polynomials of the
inputs. The new technique combines manual state-of-the-art reasoning techniques
for probabilistic programs with an effective method for automatic
resource-bound analysis of deterministic programs. It can be seen as both, an
extension of automatic amortized resource analysis (AARA) to probabilistic
programs and an automation of manual reasoning for probabilistic programs that
is based on weakest preconditions. As a result, bound inference can be reduced
to off-the-shelf LP solving in many cases and automatically-derived bounds can
be interactively extended with standard program logics if the automation fails.
Building on existing work, the soundness of the analysis is proved with respect
to an operational semantics that is based on Markov decision processes. The
effectiveness of the technique is demonstrated with a prototype implementation
that is used to automatically analyze 39 challenging probabilistic programs and
randomized algorithms. Experimental results indicate that the derived constant
factors in the bounds are very precise and even optimal for many programs
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