Wouldn’t it be nice to be able to conveniently use ordinary real number expressions within proof assistants? In this paper we outline how this can be done within a theorem provin...
Modifying the methods of Z. Adamowicz's paper Herbrand consistency and bounded arithmetic (Fund. Math. 171 (2002)), we show that there exists a number n such that m Sm (the u...
Any valid Ramsey statement n −→ (k)2 2 can be encoded into a DNF formula RAM(n, k) of size O(nk) and with terms of size k 2 . Let rk be the minimal n for which the statement h...
A nearly logarithmic lower bound on the randomized competitive ratio for the metrical task systems problem is presented. This implies a similar lower bound for the extensively stu...
We prove that the reliable computation of any Boolean function with sensitivity s requires Ω(s log s) gates if the gates of the circuit fail independently with a fixed positive...