论文标题
关于计算机科学的证明理论
On proof theory in computer science
论文作者
论文摘要
计算机科学中的主题逻辑应需要证明理论应用。因此，出现了一个问题，是否可以通过高级证明理论技术来解决计算复杂性中的开放问题。特别是考虑复杂性类NP，Conp和Pspace。众所周知，NP和Conp包含在Pspace中，但直到最近，这些关系的精确表征仍然开放。现在[2]，[3]（另请参见[4]）提供了相应平等的证据np = conp = pspace。这些结果是通过适当的证明理论树对dag压缩技术获得的，可以在下面简要介绍。 [2] L. Gordeev，E。H。Haeusler，证明压缩和NP与PSPACE，Studia Logica（107）（1）：55 {83（2019） [3] L. Gordeev，E。H。Haeusler，证明压缩和NP与PSPACE II，逻辑部分公告（49）（3）（3）：213 {230（2020） [4] L. Gordeev，E。H。Haeusler，证明压缩和NP与PSPACE II：ADDENDUM，ARXIV：2011.09262（2020）
The subject logic in computer science should entail proof theoretic applications. So the question arises whether open problems in computational complexity can be solved by advanced proof theoretic techniques. In particular, consider the complexity classes NP, coNP and PSPACE. It is well-known that NP and coNP are contained in PSPACE, but till recently precise characterization of these relationships remained open. Now [2], [3] (see also [4]) presented proofs of corresponding equalities NP = coNP = PSPACE. These results were obtained by appropriate proof theoretic tree-to-dag compressing techniques to be briefy explained below. [2] L. Gordeev, E. H. Haeusler, Proof Compression and NP Versus PSPACE, Studia Logica (107) (1): 55{83 (2019) [3] L. Gordeev, E. H. Haeusler, Proof Compression and NP Versus PSPACE II, Bulletin of the Section of Logic (49) (3): 213{230 (2020) http://dx.doi.org/10.18788/0138-0680.2020.16 [4] L. Gordeev, E. H. Haeusler, Proof Compression and NP Versus PSPACE II: Addendum, arXiv:2011.09262 (2020)
