55 research outputs found
Robust Exponential Worst Cases for Divide-et-Impera Algorithms for Parity Games
The McNaughton-Zielonka divide et impera algorithm is the simplest and most
flexible approach available in the literature for determining the winner in a
parity game. Despite its theoretical worst-case complexity and the negative
reputation as a poorly effective algorithm in practice, it has been shown to
rank among the best techniques for the solution of such games. Also, it proved
to be resistant to a lower bound attack, even more than the strategy
improvements approaches, and only recently a family of games on which the
algorithm requires exponential time has been provided by Friedmann. An easy
analysis of this family shows that a simple memoization technique can help the
algorithm solve the family in polynomial time. The same result can also be
achieved by exploiting an approach based on the dominion-decomposition
techniques proposed in the literature. These observations raise the question
whether a suitable combination of dynamic programming and game-decomposition
techniques can improve on the exponential worst case of the original algorithm.
In this paper we answer this question negatively, by providing a robustly
exponential worst case, showing that no intertwining of the above mentioned
techniques can help mitigating the exponential nature of the divide et impera
approaches.Comment: In Proceedings GandALF 2017, arXiv:1709.0176
A Delayed Promotion Policy for Parity Games
Parity games are two-player infinite-duration games on graphs that play a
crucial role in various fields of theoretical computer science. Finding
efficient algorithms to solve these games in practice is widely acknowledged as
a core problem in formal verification, as it leads to efficient solutions of
the model-checking and satisfiability problems of expressive temporal logics,
e.g., the modal muCalculus. Their solution can be reduced to the problem of
identifying sets of positions of the game, called dominions, in each of which a
player can force a win by remaining in the set forever. Recently, a novel
technique to compute dominions, called priority promotion, has been proposed,
which is based on the notions of quasi dominion, a relaxed form of dominion,
and dominion space. The underlying framework is general enough to accommodate
different instantiations of the solution procedure, whose correctness is
ensured by the nature of the space itself. In this paper we propose a new such
instantiation, called delayed promotion, that tries to reduce the possible
exponential behaviours exhibited by the original method in the worst case. The
resulting procedure not only often outperforms the original priority promotion
approach, but so far no exponential worst case is known.Comment: In Proceedings GandALF 2016, arXiv:1609.0364
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
Priority Promotion with Parysian Flair
We develop an algorithm that combines the advantages of priority promotion - one of the leading approaches to solving large parity games in practice - with the quasi-polynomial time guarantees offered by Parys' algorithm. Hybridising these algorithms sounds both natural and difficult, as they both generalise the classic recursive algorithm in different ways that appear to be irreconcilable: while the promotion transcends the call structure, the guarantees change on each level. We show that an interface that respects both is not only effective, but also efficient
REGISTER GAMES
The complexity of parity games is a long standing open problem that saw a
major breakthrough in 2017 when two quasi-polynomial algorithms were published.
This article presents a third, independent approach to solving parity games in
quasi-polynomial time, based on the notion of register game, a parameterised
variant of a parity game. The analysis of register games leads to a
quasi-polynomial algorithm for parity games, a polynomial algorithm for
restricted classes of parity games and a novel measure of complexity, the
register index, which aims to capture the combined complexity of the priority
assignement and the underlying game graph.
We further present a translation of alternating parity word automata into
alternating weak automata with only a quasi-polynomial increase in size, based
on register games; this improves on the previous exponential translation.
We also use register games to investigate the parity index hierarchy: while
for words the index hierarchy of alternating parity automata collapses to the
weak level, and for trees it is strict, for structures between trees and words,
it collapses logarithmically, in the sense that any parity tree automaton of
size n is equivalent, on these particular classes of structures, to an
automaton with a number of priorities logarithmic in n
Data Collection and Quality Challenges in Deep Learning: A Data-Centric AI Perspective
Data-centric AI is at the center of a fundamental shift in software
engineering where machine learning becomes the new software, powered by big
data and computing infrastructure. Here software engineering needs to be
re-thought where data becomes a first-class citizen on par with code. One
striking observation is that a significant portion of the machine learning
process is spent on data preparation. Without good data, even the best machine
learning algorithms cannot perform well. As a result, data-centric AI practices
are now becoming mainstream. Unfortunately, many datasets in the real world are
small, dirty, biased, and even poisoned. In this survey, we study the research
landscape for data collection and data quality primarily for deep learning
applications. Data collection is important because there is lesser need for
feature engineering for recent deep learning approaches, but instead more need
for large amounts of data. For data quality, we study data validation,
cleaning, and integration techniques. Even if the data cannot be fully cleaned,
we can still cope with imperfect data during model training using robust model
training techniques. In addition, while bias and fairness have been less
studied in traditional data management research, these issues become essential
topics in modern machine learning applications. We thus study fairness measures
and unfairness mitigation techniques that can be applied before, during, or
after model training. We believe that the data management community is well
poised to solve these problems
Computer Aided Verification
This open access two-volume set LNCS 10980 and 10981 constitutes the refereed proceedings of the 30th International Conference on Computer Aided Verification, CAV 2018, held in Oxford, UK, in July 2018. The 52 full and 13 tool papers presented together with 3 invited papers and 2 tutorials were carefully reviewed and selected from 215 submissions. The papers cover a wide range of topics and techniques, from algorithmic and logical foundations of verification to practical applications in distributed, networked, cyber-physical, and autonomous systems. They are organized in topical sections on model checking, program analysis using polyhedra, synthesis, learning, runtime verification, hybrid and timed systems, tools, probabilistic systems, static analysis, theory and security, SAT, SMT and decisions procedures, concurrency, and CPS, hardware, industrial applications
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