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The following operation has frequently occurred in mathematics and its applications: partition a set into several disjoint non-empty subsets, so that the elements in each partition subset are homogeneous or indistinguishable with respect to some given properties. H.-D.Ebbinghaus first (in 1991) distilled from this phenomenon, which is a monadic second order(More)
We show in this paper a special extended logic, partition logic based on so called partition quantifiers, is able to capture some important complexity classes NP, P and NL by its natural fragments. The Fagin's Theorem and Immerman-Vardi's Theorem are rephrased and strengthened into a uniform partition logic setting. Also the dual operators for the partition(More)
  • Enshao Shen
  • 1998
Introduce heuristically the newly definition (W. Thomas) for graph automata — using “tiles” to simulate the extension (over dag’s) of the classical notions of transition moves; propose a sufficient condition for when graph automata can be reduced to (simpler) tiling systems, which is a generalization of a Thomas’ result; and finally study the logic(More)
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