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Finite-Degree Predicates and Two-Variable First-Order Logic

Author Charles Paperman

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  • First order logic
  • automata theory
  • semigroup
  • modular predicates

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Abstract

We consider two-variable first-order logic on finite words with a fixed number of quantifier alternations. We show that all languages with a neutral letter definable using the order and finite-degree predicates are also definable with the order predicate only. From this result we derive the separation of the alternation hierarchy of two-variable logic on this signature. Replacing finite-degree by arbitrary numerical predicates in the statement would entail a long standing conjecture on the circuit complexity of the addition function. Thus, this result can be viewed as a uniform version of this circuit lower bound.

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Charles Paperman. Finite-Degree Predicates and Two-Variable First-Order Logic. In 24th EACSL Annual Conference on Computer Science Logic (CSL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 41, pp. 616-630, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015) https://doi.org/10.4230/LIPIcs.CSL.2015.616

Author Details

Charles Paperman

References

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