Abstract
AbstractIt is proved that if definability of regular languages in the \(\Sigma _n\) fragment of the first-order logic on finite words is decidable, then it is decidable also for the \(\Delta _{n+1}\) fragment. In particular, the decidability for \(\Delta _5\) is obtained. More generally, for every concatenation hierarchy of regular languages, it is proved that decidability of one of its half levels implies decidability of the intersection of the following half level with its complement.KeywordsBinary RelationTransitive ClosureRegular LanguagePositive VarietyContinuous HomomorphismThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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