eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2015-09-07
616
630
10.4230/LIPIcs.CSL.2015.616
article
Finite-Degree Predicates and Two-Variable First-Order Logic
Paperman, Charles
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol041-csl2015/LIPIcs.CSL.2015.616/LIPIcs.CSL.2015.616.pdf
First order logic
automata theory
semigroup
modular predicates