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?
Tag: complexity
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?…
