论文标题
证明压缩和NP与PSPACE II：附录
Proof Compression and NP Versus PSPACE II: Addendum
论文作者
论文摘要
在[3]中，我们通过先进的证明理论方法证明了猜想的NP = PSPACE，这些方法结合了Hudelmaier的最小逻辑（HSC）[5]的无剪切顺序与相应的最小Prawitz式自然扣除量（ND）中的水平压缩[6]。在此附录中，我们展示了如何证明较弱的结果np = conp而不参考HSC。基本的想法（由于第二作者的原因）是省略完全最小的逻辑，并仅压缩“正常的树木样的nd反驳在给定的非汉米尔顿图中存在哈密顿周期的存在，因为hamiltonian grapher gragen np-complete中的汉密尔顿素描问题。 [3] L. Gordeev，E。H。Haeusler，证明压缩和NP与PSPACE II，《逻辑部分公报》（49）（3）（3）：213-230（2020）http://dx.doi.org/10.18788/0138/0138-0680.2020.16.16 [1907.038888888888888.888888888888.88888888888888888888888.88388388.8388388388.88388388388388.838838838838838288382883828838288388888888888888888888888888888888年8月份 [5] J. Hudelmaier，直觉命题逻辑的O（n log n） - 空间决策过程，J。LogicComputat。 （3）：1-13（1993） [6] D. Prawitz，《自然推论：证明理论研究》。 Almqvist＆Wiksell，1965年
In [3] we proved the conjecture NP = PSPACE by advanced proof theoretic methods that combined Hudelmaier's cut-free sequent calculus for minimal logic (HSC) [5] with the horizontal compressing in the corresponding minimal Prawitz-style natural deduction (ND) [6]. In this Addendum we show how to prove a weaker result NP = coNP without referring to HSC. The underlying idea (due to the second author) is to omit full minimal logic and compress only \naive" normal tree-like ND refutations of the existence of Hamiltonian cycles in given non-Hamiltonian graphs, since the Hamiltonian graph problem in NP-complete. Thus, loosely speaking, the proof of NP = coNP can be obtained by HSC-elimination from our proof of NP = PSPACE [3]. [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 [1907.03858] [5] J. Hudelmaier, An O (n log n)-space decision procedure for intuitionistic propositional logic, J. Logic Computat. (3): 1-13 (1993) [6] D. Prawitz, Natural deduction: a proof-theoretical study. Almqvist & Wiksell, 1965
