Relational Complexity and Higher Order Logics

  • José Maria Turull-TorresEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9616)


Relational machines (RM) were introduced as abstract machines that compute queries to relational database instances (dbi’s), that are generic (i.e., that preserve isomorphisms). As RM’s cannot discern between tuples that are equivalent in first order logic with k variables, Relational Complexity was introduced as a complexity theory where the input dbi to a query is measured as its \(\textit{size}_k\), i.e., as the number of classes in the equivalence relation of equality of \(\mathrm {FO}^k\) types of k-tuples in the dbi. We describe the basic notions of Relational Complexity, and survey known characterizations of some of its main classes through different fixed point logics and through fragments of second and third order logics.


Turing Machine Order Logic Relation Symbol Input Structure Relational Language 
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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Depto. de Ingeniería e Investigaciones TecnológicasUniversidad Nacional de La MatanzaBuenos AiresArgentina
  2. 2.Massey UniversityPalmerston NorthNew Zealand

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