Concept
Contracting a Boolean tensor network by summing shared wire assignments
For every assignment of bits to all M wires, evaluate each vertex tensor on its incident bits and multiply those entries. Sum these products over the 2^M assignments. This sum is the contraction Z. For two unary tensors (a0,a1) and (b0,b1) joined by one wire, Z=a0 b0+a1 b1, not (a0+a1)(b0+b1): the endpoints share the same bit. An empty network contributes one, the empty product. This definition gives a correct exhaustive algorithm but does not by itself yield a fast contraction algorithm.
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Updated 2026-11-08
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Math