{"title":"Embedding Arbitrary Boolean Circuits into Fungal Automata","authors":"Augusto Modanese, Thomas Worsch","doi":"10.1007/s00453-024-01222-7","DOIUrl":null,"url":null,"abstract":"<div><p>Fungal automata are a variation of the two-dimensional sandpile automaton of Bak et al. (Phys Rev Lett 59(4):381–384, 1987. https://doi.org/10.1103/PhysRevLett.59.381). In each step toppling cells emit grains only to <i>some</i> of their neighbors chosen according to a specific update sequence. We show how to embed any Boolean circuit into the initial configuration of a fungal automaton with update sequence <i>HV</i>. In particular we give a constructor that, given the description <i>B</i> of a circuit, computes the states of all cells in the finite support of the embedding configuration in <span>\\(O(\\log \\left| {B}\\right| )\\)</span> space. As a consequence the prediction problem for fungal automata with update sequence <i>HV</i> is <span>\\(\\textsf {P}\\)</span>-complete. This solves an open problem of Goles et al. (Phys Lett A 384(22):126541, 2020. https://doi.org/10.1016/j.physleta.2020.126541).</p></div>","PeriodicalId":50824,"journal":{"name":"Algorithmica","volume":"86 7","pages":"2069 - 2091"},"PeriodicalIF":0.9000,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00453-024-01222-7.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algorithmica","FirstCategoryId":"94","ListUrlMain":"https://link.springer.com/article/10.1007/s00453-024-01222-7","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, SOFTWARE ENGINEERING","Score":null,"Total":0}
引用次数: 0
Abstract
Fungal automata are a variation of the two-dimensional sandpile automaton of Bak et al. (Phys Rev Lett 59(4):381–384, 1987. https://doi.org/10.1103/PhysRevLett.59.381). In each step toppling cells emit grains only to some of their neighbors chosen according to a specific update sequence. We show how to embed any Boolean circuit into the initial configuration of a fungal automaton with update sequence HV. In particular we give a constructor that, given the description B of a circuit, computes the states of all cells in the finite support of the embedding configuration in \(O(\log \left| {B}\right| )\) space. As a consequence the prediction problem for fungal automata with update sequence HV is \(\textsf {P}\)-complete. This solves an open problem of Goles et al. (Phys Lett A 384(22):126541, 2020. https://doi.org/10.1016/j.physleta.2020.126541).
期刊介绍：
Algorithmica is an international journal which publishes theoretical papers on algorithms that address problems arising in practical areas, and experimental papers of general appeal for practical importance or techniques. The development of algorithms is an integral part of computer science. The increasing complexity and scope of computer applications makes the design of efficient algorithms essential.
Algorithmica covers algorithms in applied areas such as: VLSI, distributed computing, parallel processing, automated design, robotics, graphics, data base design, software tools, as well as algorithms in fundamental areas such as sorting, searching, data structures, computational geometry, and linear programming.
In addition, the journal features two special sections: Application Experience, presenting findings obtained from applications of theoretical results to practical situations, and Problems, offering short papers presenting problems on selected topics of computer science.
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