Proof of `Computing chains of small width`

groundedproofs/Lax185574Proofs/ComputingChains.lean · lax-185574

What this proof establishes

Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.

Read the Lean proof on GitHub

In the paper

  • page 30 of this submission's paper

Description

The statement for graphs, graph classes and Algorithm.ComputesAlgorithm.Computes, from the version for simple graphs applied to the class of the simple graphs of the members. The algorithm is the program with its exponent, the chain of a graph is that of its simple graph, and the constant cc becomes ⌈c⋅2(3+δ)⌉⌈c · 2^(3+δ)⌉, so that c′⋅n(3+δ)+c′c' · n^(3+δ) + c' bounds the time ⌊c⋅(n+1)(3+δ)⌋⌊c · (n+1)^(3+δ)⌋.