This is meant to be a light post, posing a perhaps naive question. One of the hallmarks of computational proof theory is the association between arithmetic theories and complexity classes, in terms of their provably recursive functions. But is there a general rule for identifying the provably recursive functions of a class of induction invariants?
Anupam Das
‘Simple’ proofs of cut-elimination II: intuitionistic logic
Cut-elimination for intuitionistic logic has particular significance to proof theorists due to the constructive nature of the logic. Cut-free proofs give rise to significant computational information, including interpolants of implications and, in the case of predicate logic, witnesses of existentials. Moreover, the process of cut-elimination can itself be viewed as a computational process thanks to…
A new linear inference of size 8
Linear inferences are propositional tautologies of the form , where and are formulas with at most one occurrence of each propositional variable. These form a -complete set, but surprisingly little is known about their structure, despite their importance in structural proof theory (and beyond). In this post I will cover some of the background on…
Checking proofs with very low complexity
The very notion of mathematical proof is founded upon the idea that a proof is ‘routine’ to check. While it may be difficult to actually prove a mathematical theorem, a proof should allow us to verify its truth . But exactly how much effort is required to check a proof, in terms of computational complexity?…
