Semiring

• (K, ?, ?, 0, 1)

  • ? = collect paths; ? = extend path

• (K, ?, 1) is a monoid:

  • closed, associative, 1 is identity

• (K, ?, 0) is a commutative monoid:

  • closed, associative, commutative, 0 is identity

• ? distributes over ?

• 0 ? k = k ? 0 = 0

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