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Izv. RAN. Ser. Mat., 2011, Volume 75, Issue 5, Pages 47–64 (Mi izv4077)  

This article is cited in 4 scientific papers (total in 4 papers)

Monadic structures over an ordered universal random graph and finite automata

S. M. Dudakov

Tver State University

Abstract: We continue the investigation of the expressive power of the language of predicate logic for finite algebraic systems embedded in infinite systems. This investigation stems from papers of M. A. Taitslin, M. Benedikt and L. Libkin, among others. We study the properties of a finite monadic system which can be expressed by formulae if such a system is embedded in a random graph that is totally ordered in an arbitrary way. The Büchi representation is used to connect monadic structures and formal languages. It is shown that, if one restricts attention to formulae that are $<$-invariant in totally ordered random graphs, then these formulae correspond to finite automata. We show that $=$-invariant formulae expressing the properties of the embedded system itself can express only Boolean combinations of properties of the form ‘the cardinality of an intersection of one-place predicates belongs to one of finitely many fixed finite or infinite arithmetic progressions’.

Keywords: universal random graph, first-order logic, automaton language.

DOI: https://doi.org/10.4213/im4077

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English version:
Izvestiya: Mathematics, 2011, 75:5, 915–932

Bibliographic databases:

UDC: 510.62
MSC: Primary 05C80; Secondary 08A70, 11B85, 68P15
Received: 15.01.2009

Citation: S. M. Dudakov, “Monadic structures over an ordered universal random graph and finite automata”, Izv. RAN. Ser. Mat., 75:5 (2011), 47–64; Izv. Math., 75:5 (2011), 915–932

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Dudakov S.M., “O bezopasnosti rekursivnykh zaprosov”, Vestn. Tverskogo gos. un-ta. Ser. Prikladnaya matematika, 2012, no. 4, 71–80  mathnet  elib
    2. Dudakov S.M., “O bezopasnosti IFP-operatorov i rekursivnykh zaprosov”, Vestn. Tverskogo gos. un-ta. Ser. Prikladnaya matematika, 2013, 5–13  mathnet  elib
    3. S. M. Dudakov, “Nerazreshimost problemy opredelennosti binarnykh IFP-operatorov dlya teorii odnogo sledovaniya”, Vestnik Tverskogo gosudarstvennogo universiteta. Ser. Prikladnaya matematika, 2014, no. 4, 7–15  mathnet  elib
    4. A. S. Zolotov, “O primenenii konechnykh avtomatov k issledovaniyu razreshimosti teorii s operatorom fiksirovannoi tochki”, Vestnik TvGU. Seriya: Prikladnaya matematika, 2016, no. 1, 103–115  mathnet  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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