约束多项式带拓扑

IF 0.4 4区 计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS Acta Informatica Pub Date : 2023-05-05 DOI:10.1007/s00236-023-00437-5
Niklas Kochdumper, Matthias Althoff
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引用次数: 16

摘要

我们引入了约束多项式带拓扑,这是一种新的非凸集合表示,它在线性映射、闵可夫斯基和、笛卡尔积、凸包、交、并、二次以及高阶映射下是封闭的。我们证明了上述集合运算的计算复杂度在表示大小上不超过多项式。约束多项式带共体是带共体、多边形、多项式带共体、Taylor模型和椭球体的一般化,这一事实进一步证实了这种新的集合表示的相关性。此外,从其他集合表示到约束多项式带拓扑的转换在维数上最多是多项式,我们提出了用更简单的集合表示来减小表示大小和封闭约束多项式带拓扑的有效方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

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Constrained polynomial zonotopes

We introduce constrained polynomial zonotopes, a novel non-convex set representation that is closed under linear map, Minkowski sum, Cartesian product, convex hull, intersection, union, and quadratic as well as higher-order maps. We show that the computational complexity of the above-mentioned set operations for constrained polynomial zonotopes is at most polynomial in the representation size. The fact that constrained polynomial zonotopes are generalizations of zonotopes, polytopes, polynomial zonotopes, Taylor models, and ellipsoids further substantiates the relevance of this new set representation. In addition, the conversion from other set representations to constrained polynomial zonotopes is at most polynomial with respect to the dimension, and we present efficient methods for representation size reduction and for enclosing constrained polynomial zonotopes by simpler set representations.

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来源期刊
Acta Informatica
Acta Informatica 工程技术-计算机:信息系统
CiteScore
2.40
自引率
16.70%
发文量
24
审稿时长
>12 weeks
期刊介绍: Acta Informatica provides international dissemination of articles on formal methods for the design and analysis of programs, computing systems and information structures, as well as related fields of Theoretical Computer Science such as Automata Theory, Logic in Computer Science, and Algorithmics. Topics of interest include: • semantics of programming languages • models and modeling languages for concurrent, distributed, reactive and mobile systems • models and modeling languages for timed, hybrid and probabilistic systems • specification, program analysis and verification • model checking and theorem proving • modal, temporal, first- and higher-order logics, and their variants • constraint logic, SAT/SMT-solving techniques • theoretical aspects of databases, semi-structured data and finite model theory • theoretical aspects of artificial intelligence, knowledge representation, description logic • automata theory, formal languages, term and graph rewriting • game-based models, synthesis • type theory, typed calculi • algebraic, coalgebraic and categorical methods • formal aspects of performance, dependability and reliability analysis • foundations of information and network security • parallel, distributed and randomized algorithms • design and analysis of algorithms • foundations of network and communication protocols.
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