弱算术中替换的强度

不要抛弃婴儿：Clarithmetics作为弱算术的替代品

Do not throw out the baby: Clarithmetics as alternatives to weak arithmetics

本文提出Clarithmetics作为弱算术的替代方案，通过结合皮亚诺算术的完整算术强度和对计算资源的显式控制，避免传统复杂性导向系统丢弃有用信息的问题。

Approximate counting and NP search problems

We study a new class of NP search problems, those which can be proved total using standard combinatorial reasoning based on approximate counting. Our model for this kind of reasoning is the bounded arithmetic theory $\mathrm{APC}_2$ of [Jeřábek 2009]. In particular, the Ramsey and weak pigeonhole search problems lie in the new class. We give a purely computational characterization of this class and show that, relative to an oracle, it does not contain the problem CPLS, a strengthening of PLS. As CPLS is provably total in the theory $T^2_2$, this shows that $\mathrm{APC}_2$ does not prove every…

Polylogarithmic Cuts in Models of V^0

We study initial cuts of models of weak two-sorted Bounded Arithmetics with respect to the strength of their theories and show that these theories are stronger than the original one. More explicitly we will see that polylogarithmic cuts of models of $\mathbf{V}^0$ are models of $\mathbf{VNC}^1$ by formalizing a proof of Nepomnjascij's Theorem in such cuts. This is a strengthening of a result by Paris and Wilkie. We can then exploit our result in Proof Complexity to observe that Frege proof systems can be sub exponentially simulated by bounded depth Frege proof systems. This result has recently…