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pro vyhledávání: '"Ken, Eitetsu"'
Autor:
Ken, Eitetsu
We give another proof of ordinal analysis of $I\Sigma_{k}$-fragments of Peano Arithmetic which is free from cut-elimination of $\omega$-logic. Our main tool is a direct witnessing argument utilizing game notion, motivated from the realm of proof comp
Externí odkaz:
http://arxiv.org/abs/2406.17315
Autor:
Ken, Eitetsu, Narusevych, Mykyta
We introduce a pebble game extended by backtracking options for one of the two players (called Prover) and reduce the provability of the pigeonhole principle for a generic predicate $R$ in the bounded arithmetic $T^2_2(R)$ to the existence of a parti
Externí odkaz:
http://arxiv.org/abs/2406.10924
In this paper, we consider interpolation by \textit{completely monotonous} polynomials (CMPs for short), that is, polynomials with non-negative real coefficients. In particular, given a finite set $S\subset \mathbb{R}_{>0} \times \mathbb{R}_{\geq 0}$
Externí odkaz:
http://arxiv.org/abs/2402.00409
Autor:
Ken, Eitetsu, Kuroda, Satoru
In arXiv:1811.04313, a definition of determinant is formalized in the bounded arithmetic $VNC^{2}$. Following the presentation of [Gathen, 1993], we can formalize a definition of matrix rank in the same bounded arithmetic. In this article, we define
Externí odkaz:
http://arxiv.org/abs/2310.05982
Autor:
Ken, Eitetsu
We formalize various counting principles and compare their strengths over $V^{0}$. In particular, we conjecture the following mutual independence between: (1) a uniform version of modular counting principles and the pigeonhole principle for injection
Externí odkaz:
http://arxiv.org/abs/2203.10237
When we investigate a type system, it is helpful if we can establish the well-foundedness of types or terms with respect to a certain hierarchy, and the Extended Calculus of Constructions (called $ECC$, defined and studied comprehensively in [Luo,199
Externí odkaz:
http://arxiv.org/abs/2009.03486
Temperature of combinatorial games have been long studied since when Conway established the modern combinatorial game theory, and there are several variations of the concepts. In this article, we focus on one of the classical versions of temperature,
Externí odkaz:
http://arxiv.org/abs/2009.02876
Akademický článek
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Autor:
Ken, Eitetsu
Publikováno v:
数理解析研究所講究録. 2228:186-205
The theorem of Ajtai ([1], improved by [11] and [12]), which shows a superpolynomial lower bound for AC⁰-Frege proofs of the pigeonhole principle, was a significant breakthrough of proof complexity and has been inspiring many other important works
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=jairo_______::47bfafb3274f8937463148bdd06cf175
http://hdl.handle.net/2433/279734
http://hdl.handle.net/2433/279734
Autor:
Ken, Eitetsu
Ajtai's discovery of $V^{0}\not \vdash ontoPHP^{n+1}_{n}$, where $ontoPHP^{n+1}_{n}$ is a $Σ^{B}_{0}$ formalization of the statement "there does not exist a bijection between $(n+1)$ pigeons and $n$ holes," was a significant breakthrough in proof co
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::fbfd7dc4653b63f70b5944ba36dda455