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## Section: New Results

### Combinatorial Flows

Participant : Lutz Straßburger.

Combinatorial flows are a variation of combinatorial proofs that allow for the substitution of proofs into proofs (instead of just substituting formulas). This makes combinatorial flows p-equvalent to Frege systems with substitution, which are the strongest proof systems with respect to p-simulation, as studied in proof complexity. Since combinatorial flows have a polynomial correctness criterion, they can also be seen as an improvement to atomic flows (which do not have a correctness criterion). This work has been presented at the FCSD 2017 conference [37], [28]