On ultrafilters and NP

The fusion method (A. Wigderson, 1993) is developed by exploring its similarities with the ultraproduct construction in model theory. We use this analogy to re-prove a result of M. Sipser (1984) regarding countable circuits, in a simpler way. In the finite case this analogy allows us to give a new characterization of co-NP in terms of the CLIQUE function. This gives a natural interpretation to the NP-completeness of the CLIQUE function.<
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