Related papers: A remark on higher order RUE-resolution with EXTRU…
We show that various methods for explicitly building resolutions of unbounded complexes in fact fail when applied to a rather simple and explicit complex. We show that one way to rescue these methods is to assume Roos (Ab.4$^*$)-$k$ axiom,…
In a previous paper with the same title, we gave an upper bound for the exponent of uniform rational approximation to a quadruple of $\mathbb{Q}$-linearly independent real numbers in geometric progression. Here, we explain why this upper…
Regular resolution is a refinement of the resolution proof system requiring that no variable be resolved on more than once along any path in the proof. It is known that there exist sequences of formulas that require exponential-size proofs…
In this paper we present a constructive proof of cut elimination for a system of full second order logic with the structural rules absorbed and using sets instead of sequences. The standard problem of the cutrank growth is avoided by using…
We show that ESO universal Horn logic (existential second logic where the first order part is a universal Horn formula) is insufficient to capture P, the class of problems decidable in polynomial time. This statement is true in the presence…
We propose an algebraic geometric approach for studying rational solutions of first-order algebraic ordinary difference equations. For an autonomous first-order algebraic ordinary difference equations, we give an upper bound for the degrees…
We introduce a method to prove that a proof search method is not an instance of another. As an example of application, we show that Polarized resolution modulo, a method that mixes clause selection restrictions and literal selection…
This work is motivated by the problem of finding the limit of the applicability of the first incompleteness theorem ($\sf G1$). A natural question is: can we find a minimal theory for which $\sf G1$ holds? We examine the Turing degree…
We introduce the concept of inexact first-order oracle of degree q for a possibly nonconvex and nonsmooth function, which naturally appears in the context of approximate gradient, weak level of smoothness and other situations. Our…
The problem of super-resolution in general terms is to recuperate a finitely supported measure $\mu$ given finitely many of its coefficients $\hat{\mu}(k)$ with respect to some orthonormal system. The interesting case concerns situations,…
The paper presents a counterexample to the Hodge conjecture.
We study the MaxRes rule in the context of certifying unsatisfiability. We show that it can be exponentially more powerful than tree-like resolution, and when augmented with weakening (the system MaxResW), p-simulates tree-like resolution.…
It is consistent with constructive set theory (without Countable Choice, clearly) that the Cauchy reals (equivalence classes of Cauchy sequences of rationals) are not Cauchy complete. Related results are also shown, such as that a Cauchy…
A ``self--similar'' example is constructed that shows that a conjecture of N. U. Arakelyan on the order of decrease of deficiencies of an entire function of finite order is not true.
In this paper, we study about existence and non-existence of finite order transcendental entire solutions of the certain non-linear differential-difference equations. We also study about conjectures posed by Rong et al. and Chen et al.
The notion of computability closure has been introduced for proving the termination of the combination of higher-order rewriting and beta-reduction. It is also used for strengthening the higher-order recursive path ordering. In the present…
I apply commonly used regularization schemes to a multi-loop calculation to examine the properties of the schemes at higher orders. I find complete consistency between the conventional dimensional regularization scheme and dimensional…
In this paper we deal with verification of safety properties of term-rewriting systems. The verification problem is translated to a purely logical problem of finding a finite countermodel for a first-order formula, which further resolved by…
We study versions of the tree pigeonhole principle, $\mathsf{TT}^1$, in the context of Weihrauch-style computable analysis. The principle has previously been the subject of extensive research in reverse mathematics. Two outstanding…
Let \Omega be a set of unsatisfiable clauses, an implicit resolution refutation of \Omega is a circuit \beta with a resolution proof {\alpha} of the statement "\beta describes a correct tree-like resolution refutation of \Omega". We show…