Abstract
Let 0 ≤ r < q. We will define a new kind of quantifier \(\exists^{(q,r)}\). Informally, \(\exists^{(q,r)} x\phi\) means “the number of positions x that satisfy Φ is congruent to r modulo q”. Formally, let w be a V-structure over A, and let \(x \notin \nu\). We obtain \(\left | w \right |\) different \(\left ( \nu \cup \left \{ x \right \} \right )\)-structures w’ by adjoining x to the second component of a letter of w. We define
if and only if the number of these w’ for which
is congruent to r modulo q.
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© 1994 Springer Science+Business Media New York
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Straubing, H. (1994). Modular Quantifiers. In: Finite Automata, Formal Logic, and Circuit Complexity. Progress in Theoretical Computer Science. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0289-9_7
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DOI: https://doi.org/10.1007/978-1-4612-0289-9_7
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6695-2
Online ISBN: 978-1-4612-0289-9
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