Proof Compression and NP Versus PSPACE II: Addendum

• Autorzy: Lew Gordeev , Edward Hermann Haeusler

Abstrakty

EN

In our previous work we proved the conjecture NP = PSPACE by advanced proof theoretic methods that combined Hudelmaier’s cut-free sequent calculus for minimal logic (HSC) with the horizontal compressing in the corresponding minimal Prawitz-style natural deduction (ND). 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 NPcomplete. Thus, loosely speaking, the proof of NP = coNP can be obtained by HSC-elimination from our proof of NP = PSPACE.

Słowa kluczowe

EN

graph theory; natural deduction; computational complexity

• Wydawca: Wydawnictwo Uniwersytetu Łódzkiego
• Czasopismo: Bulletin of the Section of Logic
• Rocznik: 2022
• Tom: 51
• Numer: 2
• Strony: 197-205

Daty

wydano

2022

Twórcy

autor

Lew Gordeev

• University of Tübingen, Department of Computer Science, Nedlitzer Str. 4a, 14612 Falkensee

autor

Edward Hermann Haeusler

• Pontificia Universidade Católica do Rio de Janeiro – RJ, Department of Informatics, Rua Marques de São Vicente, 224, Gávea, Rio de Janeiro, Brazil

• https://orcid.org/0000000249997476

Bibliografia

• S. Arora, B. Barak, Computational Complexity: A Modern Approach, Cambridge University Press (2009).
• L. Gordeev, E. H. Haeusler, Proof Compression and NP Versus PSPACE, Studia Logica, vol. 107(1) (2019), pp. 55–83, DOI: https://doi.org/10.1007/s11225-017-9773-5
• L. Gordeev, E. H. Haeusler, Proof Compression and NP Versus PSPACE II, Bulletin of the Section of Logic, vol. 49(3) (2020), pp. 213–230, DOI: https://doi.org/10.18778/0138-0680.2020.16
• E. H. Haeusler, Propositional Logics Complexity and the Sub-Formula Property, [in:] Proceedings of the Tenth International Workshop on Developments in Computational Models DCM (2014), URL: https://arxiv.org/abs/1401.8209v3
• J. Hudelmaier, An O(nlogn)-space decision procedure for intuitionistic propositional logic, Journal of Logic and Computation, vol. 3 (1993), pp. 1–13, DOI: https://doi.org/10.1093/logcom/3.1.63
• D. Prawitz, Natural deduction: A proof-theoretical study, Almqvist & Wiksell (1965).
• R. Statman, Intuitionistic propositional logic is polynomial-space complete, Theoretical Computer Science, vol. 9 (1979), pp. 67–72, DOI: https://doi.org/10.1016/0304-3975(79)90006-9

Identyfikatory

DOI

10.18778/0138-0680.2022.01

nonstd.3pn.id

2142754