Some results on majority quantifiers over words

The class of languages definable by majority quantifiers using the order predicate is investigated. It is shown that the additional use of first order or counting quantifiers does not increase this class. Further on, addition is in this connection a definable numerical predicate, while the converse does not hold. The emptiness problem for this class turns out to be undecidable.

[1]  Nicole Schweikardt,et al.  On the expressive power of first-order logic with built-in predicates , 2001 .

[2]  Howard Straubing.  Finite Automata, Formal Logic, and Circuit Complexity , 1994, Progress in Theoretical Computer Science.

[3]  Neil Immerman,et al.  The Crane Beach Conjecture , 2001, Proceedings 16th Annual IEEE Symposium on Logic in Computer Science.

[4]  Neil Immerman,et al.  On Uniformity within NC¹ , 1990, J. Comput. Syst. Sci..

[5]  Thomas Schwentick,et al.  The Descriptive Complexity Approach to LOGCFL , 1998, J. Comput. Syst. Sci..

[6]  Thomas Schwentick,et al.  Logics For Context-Free Languages , 1994, CSL.

[7]  Troy Lee.  Is Multiplication Harder than Addition? Arithmetical Definability over Finite Structures , 2001 .