374 research outputs found
A Parity Game Tale of Two Counters
Parity games are simple infinite games played on finite graphs with a winning
condition that is expressive enough to capture nested least and greatest
fixpoints. Through their tight relationship to the modal mu-calculus, they are
used in practice for the model-checking and synthesis problems of the
mu-calculus and related temporal logics like LTL and CTL. Solving parity games
is a compelling complexity theoretic problem, as the problem lies in the
intersection of UP and co-UP and is believed to admit a polynomial-time
solution, motivating researchers to either find such a solution or to find
superpolynomial lower bounds for existing algorithms to improve the
understanding of parity games. We present a parameterized parity game called
the Two Counters game, which provides an exponential lower bound for a wide
range of attractor-based parity game solving algorithms. We are the first to
provide an exponential lower bound to priority promotion with the delayed
promotion policy, and the first to provide such a lower bound to tangle
learning.Comment: In Proceedings GandALF 2019, arXiv:1909.0597
How do neural networks see depth in single images?
Deep neural networks have lead to a breakthrough in depth estimation from
single images. Recent work often focuses on the accuracy of the depth map,
where an evaluation on a publicly available test set such as the KITTI vision
benchmark is often the main result of the article. While such an evaluation
shows how well neural networks can estimate depth, it does not show how they do
this. To the best of our knowledge, no work currently exists that analyzes what
these networks have learned.
In this work we take the MonoDepth network by Godard et al. and investigate
what visual cues it exploits for depth estimation. We find that the network
ignores the apparent size of known obstacles in favor of their vertical
position in the image. Using the vertical position requires the camera pose to
be known; however we find that MonoDepth only partially corrects for changes in
camera pitch and roll and that these influence the estimated depth towards
obstacles. We further show that MonoDepth's use of the vertical image position
allows it to estimate the distance towards arbitrary obstacles, even those not
appearing in the training set, but that it requires a strong edge at the ground
contact point of the object to do so. In future work we will investigate
whether these observations also apply to other neural networks for monocular
depth estimation.Comment: Submitte
Symbolic Parity Game Solvers that Yield Winning Strategies
Parity games play an important role for LTL synthesis as evidenced by recent
breakthroughs on LTL synthesis, which rely in part on parity game solving. Yet
state space explosion remains a major issue if we want to scale to larger
systems or specifications. In order to combat this problem, we need to
investigate symbolic methods such as BDDs, which have been successful in the
past to tackle exponentially large systems. It is therefore essential to have
symbolic parity game solving algorithms, operating using BDDs, that are fast
and that can produce the winning strategies used to synthesize the controller
in LTL synthesis.
Current symbolic parity game solving algorithms do not yield winning
strategies. We now propose two symbolic algorithms that yield winning
strategies, based on two recently proposed fixpoint algorithms. We implement
the algorithms and empirically evaluate them using benchmarks obtained from
SYNTCOMP 2020. Our conclusion is that the algorithms are competitive with or
faster than an earlier symbolic implementation of Zielonka's recursive
algorithm, while also providing the winning strategies.Comment: In Proceedings GandALF 2020, arXiv:2009.0936
Simple Fixpoint Iteration To Solve Parity Games
A naive way to solve the model-checking problem of the mu-calculus uses
fixpoint iteration. Traditionally however mu-calculus model-checking is solved
by a reduction in linear time to a parity game, which is then solved using one
of the many algorithms for parity games. We now consider a method of solving
parity games by means of a naive fixpoint iteration. Several fixpoint
algorithms for parity games have been proposed in the literature. In this work,
we introduce an algorithm that relies on the notion of a distraction. The idea
is that this offers a novel perspective for understanding parity games. We then
show that this algorithm is in fact identical to two earlier published fixpoint
algorithms for parity games and thus that these earlier algorithms are the
same. Furthermore, we modify our algorithm to only partially recompute deeper
fixpoints after updating a higher set and show that this modification enables a
simple method to obtain winning strategies. We show that the resulting
algorithm is simple to implement and offers good performance on practical
parity games. We empirically demonstrate this using games derived from
model-checking, equivalence checking and reactive synthesis and show that our
fixpoint algorithm is the fastest solution for model-checking games.Comment: In Proceedings GandALF 2019, arXiv:1909.0597
Multi-core Decision Diagrams
Decision diagrams are fundamental data structures that revolutionized fields such as model checking, automated reasoning and decision processes. As performance gains in the current era mostly come from parallel processing, an ongoing challenge is to develop data structures and algorithms for modern multicore architectures. This chapter describes the parallelization of decision diagram operations as implemented in the parallel decision diagram package Sylvan, which allows sequential algorithms that use decision diagrams to exploit the power of multi-core machines
A Distributed Hash Table for Shared Memory
Distributed algorithms for graph searching require a high-performance CPU-efficient hash table that supports find-or-put. This operation either inserts data or indicates that it has already been added before. This paper focuses on the design and evaluation of such a hash table, targeting supercomputers. The latency of find-or-put is minimized by using one-sided RDMA operations. These operations are overlapped as much as possible to reduce waiting times for roundtrips. In contrast to existing work, we use linear probing and argue that this requires less roundtrips. The hash table is implemented in UPC. A peak-throughput of 114.9 million op/s is reached on an Infiniband cluster. With a load-factor of 0.9, find-or-put can be performed in 4.5μs on average. The hash table performance remains very high, even under high loads
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