{"title":"State Complexity of Boolean Operations on Graph-Walking Automata","authors":"O. Martynova, Alexander Okhotin","doi":"10.1142/s0129054124420012","DOIUrl":null,"url":null,"abstract":"Finite automata that traverse graphs by moving along their edges are known as graph-walking automata (GWA). This paper investigates the state complexity of Boolean operations for this model. It is proved that the union of GWA with [Formula: see text] and [Formula: see text] states, with [Formula: see text], operating on graphs with [Formula: see text] labels of edge end-points, is representable by a GWA with [Formula: see text] states, and at least [Formula: see text] states are necessary in the worst case. For the intersection, the upper bound is [Formula: see text] and the lower bound is [Formula: see text]. The upper bound for the complementation is [Formula: see text], and the lower bound is [Formula: see text].","PeriodicalId":50323,"journal":{"name":"International Journal of Foundations of Computer Science","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Foundations of Computer Science","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1142/s0129054124420012","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
Finite automata that traverse graphs by moving along their edges are known as graph-walking automata (GWA). This paper investigates the state complexity of Boolean operations for this model. It is proved that the union of GWA with [Formula: see text] and [Formula: see text] states, with [Formula: see text], operating on graphs with [Formula: see text] labels of edge end-points, is representable by a GWA with [Formula: see text] states, and at least [Formula: see text] states are necessary in the worst case. For the intersection, the upper bound is [Formula: see text] and the lower bound is [Formula: see text]. The upper bound for the complementation is [Formula: see text], and the lower bound is [Formula: see text].
期刊介绍：
The International Journal of Foundations of Computer Science is a bimonthly journal that publishes articles which contribute new theoretical results in all areas of the foundations of computer science. The theoretical and mathematical aspects covered include:
- Algebraic theory of computing and formal systems
- Algorithm and system implementation issues
- Approximation, probabilistic, and randomized algorithms
- Automata and formal languages
- Automated deduction
- Combinatorics and graph theory
- Complexity theory
- Computational biology and bioinformatics
- Cryptography
- Database theory
- Data structures
- Design and analysis of algorithms
- DNA computing
- Foundations of computer security
- Foundations of high-performance computing
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