The Polylog-Time Hierarchy Captured by Restricted Second-Order Logic

@article{Ferrarotti2018ThePH,
  title={The Polylog-Time Hierarchy Captured by Restricted Second-Order Logic},
  author={Flavio Ferrarotti and Sen{\'e}n Gonz{\'a}lez and Klaus-Dieter Schewe and Jos{\'e} Maria Turull Torres},
  journal={2018 20th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)},
  year={2018},
  pages={133-140}
}
Let SO^plog denote the restriction of second-order logic, where second-order quantification ranges over relations of size at most poly-logarithmic in the size of the structure. In this article we investigate the problem, which Turing machine complexity class is captured by Boolean queries over ordered relational structures that can be expressed in this logic. For this we define a hierarchy of fragments Σ^plog_m (and Σ^plog_m) defined by formulae with alternating blocks of existential and… Expand
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