关于在正则ILP实例集中找到正ILP实例的判定性

IF 0.4 4区 计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS Acta Informatica Pub Date : 2022-08-04 DOI:10.1007/s00236-022-00429-x
Petra Wolf
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引用次数: 0

摘要

决策问题P (\({{\textit{int}}_{{\mathrm {Reg}}}}\) (P))的正则相交空性问题是决定编码P-实例的潜在无限正则集是否包含一个正的P-实例。由于\({{\textit{int}}_{{\mathrm {Reg}}}}\) (P)对于某些np完全问题是可决定的,而对于其他np完全问题是不可决定的,因此对它的研究提供了对np完全问题本质的见解。此外,\({{\textit{int}}_{{\mathrm {Reg}}}}\) -问题的可判定性通常是通过利用实例集的规律性来实现的;因此,它也与形式语言和自动机理论建立了联系。我们考虑了众所周知的np完全问题整数线性规划(ILP)的\({{\textit{int}}_{{\mathrm {Reg}}}}\) -问题。证明了描述一组ilp实例(以自然编码)的任何DFA都可以简化为包含正的实例的有限核,当且仅当原始实例集包含正的实例。该结果得到\({{\textit{int}}_{{\mathrm {Reg}}}}\) (ILP)的可判定性。
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On the decidability of finding a positive ILP-instance in a regular set of ILP-instances

The regular intersection emptiness problem for a decision problem P (\({{\textit{int}}_{{\mathrm {Reg}}}}\)(P)) is to decide whether a potentially infinite regular set of encoded P-instances contains a positive one. Since \({{\textit{int}}_{{\mathrm {Reg}}}}\)(P) is decidable for some NP-complete problems and undecidable for others, its investigation provides insights in the nature of NP-complete problems. Moreover, the decidability of the \({{\textit{int}}_{{\mathrm {Reg}}}}\)-problem is usually achieved by exploiting the regularity of the set of instances; thus, it also establishes a connection to formal language and automata theory. We consider the \({{\textit{int}}_{{\mathrm {Reg}}}}\)-problem for the well-known NP-complete problem Integer Linear Programming (ILP). It is shown that any DFA that describes a set of ILP-instances (in a natural encoding) can be reduced to a finite core of instances that contains a positive one if and only if the original set of instances did. This result yields the decidability of \({{\textit{int}}_{{\mathrm {Reg}}}}\)(ILP).

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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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