Section: New Results

Substitution as Proof Compression

Participants : Lutz Straßburger, Novak Novakovic.

In previous work  [58] we have shown how the calculus of structures can accommodate Tseitin extension without relying on the cut (or modus ponens). Thus, cut and extension can be studied independently as proof compression mechanisms. Another such proof compression mechanism is substitution. It has been shown by Cook, Reckhow, Krajíček and Pudlák that in the presence of cut, extension and substitution are equally powerful with respect to proof complexity. This year we succeeded in showing that this is also the case in the absence of cut. I.e., we have shown that the cut-free system with extension and the cut-free system with substitution p-simulate each other. This result is presented in [34] .