The Role of Monotonicity in Descriptive Complexity Theory

  • Iain A. Stewart
Conference paper
Part of the Collegium Logicum book series (COLLLOGICUM, volume 2)


It is well-known that monotonicity, in a variety of guises, plays an essential role in descriptive complexity theory and finite model theory. In this paper, we highlight existing well-known roles and also explain two other not so well-known roles of monotonicity. The first arises due to an anomaly in logically characterizing NP using operators corresponding to traditional NP-complete problems; and the second arises due to the consideration of the logical characterization of complexity classes defined with respect to “monotone” models of computation.


Hamiltonian Path Relation Symbol Constant Symbol Projective Formula Oracle Query 
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Copyright information

© Springer-Verlag/Wien 1996

Authors and Affiliations

  • Iain A. Stewart
    • 1
  1. 1.University of Wales SwanseaSwanseaUK

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