k-CCWL isomorphism tests are equivalent to TC_{k+2} topological counting logic and topological (k+2)-pebble games, characterizing the logical expressiveness of TNNs.
Thek-WL atomic typeatp k,Ainc(v) records: –the equality pattern among thev i’s, –which pairs(v i, vj)are adjacent inA inc, and –the initial vertex colorsc Ainc(vi)
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The Logical Expressiveness of Topological Neural Networks
k-CCWL isomorphism tests are equivalent to TC_{k+2} topological counting logic and topological (k+2)-pebble games, characterizing the logical expressiveness of TNNs.