Related papers: Proof of Irvine's Conjecture via Mechanized Guessi…

The paper explores known results related to the problem of identifying if a given program terminates on all inputs -- this is a simple generalization of the halting problem. We will see how this problem is related and the notion of proof…

Inductive inference is a recursion-theoretic theory of learning, first developed by E. M. Gold (1967). This paper surveys developments in probabilistic inductive inference. We mainly focus on finite inference of recursive functions, since…

Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond ${\bf NP\neq co NP}$. These conjectures formally connect computational complexity with the difficulty of…

We prove the Strengthened Hanna Neumann Conjecture, in its common graph theoretic formulation. Our original approach to this conjecture used cohomology of sheaves on graphs, although here we give a short combinatorial proof that we found in…

We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…

Watson proved Kirkman's hypothesis (partially solved by Cayley). Using Lagrange Inversion, we drastically shorten Watson's computations and generalize his results at the same time.

We prove the volume conjecture for any twist knots by using an equivalence relation, complex analysis, analytic continuation, and function of several complex variables on the basis of colored Jones polynomials.

We prove a conjecture of Durr, Kabanov and Okonek which provides an algebro-geometric theory of Seiberg-Witten invariants for all smooth projective surfaces. Our main technique is the cosection localization principle of virtual cycles.

Karush's proof of McMillan's theorem is recast as an argument involving polynomials with non-commuting indeterminates certain evaluations of which yield the Kraft sums of codes, proving a strengthened version of McMillan's theorem.

Most prime gaps results have been proven using tools from analytic or algebraic number theory in the last few centuries. In this paper, we would like to present some probabilistic way of proving many essential results. A major component of…

The notion of Craig interpolant, used as a form of explanation in automated reasoning, is adapted from logical inference to statistical inference and used to explain inferences made by neural networks. The method produces explanations that…

We give a nonstandard analytic proof of de Finetti's theorem for an exchangeable sequence of Bernoulli random variables. The theorem postulates that such a sequence is uniquely representable as a mixture of iid sequences of Bernoulli random…

The \v{C}ern\'y's conjecture states that for every synchronizing automaton with n states there exists a reset word of length not exceeding (n-11)^2. We prove this conjecture for a class of automata preserving certain properties of intervals…

In this note, we present a conjecture on intersections of set families, and a rephrasing of the conjecture in terms of principal downsets of Boolean lattices. The conjecture informally states that, whenever we can express the measure of a…

We give positive answer to two conjectures posed by M. E. H Ismail in his monograph [Classical and quantum orthogonal polynomials in one variable, Cambridge University Press, 2005].

A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.

Term rewriting has a significant presence in various areas, not least in automated theorem proving where it is used as a proof technique. Many theorem provers employ specialised proof tactics for rewriting. This results in an interleaving…

We give a generalization and a short mechanized proof of determinant conjectured by G. Kuperberg and J. Propp. Further generalizations and applications of the method to some q-analogues may be found in http://www.math.temple.edu/~tewodros

We present an elementary method for proving enumeration formulas which are polynomials in certain parameters if others are fixed and factorize into distinct linear factors over Z. Roughly speaking the idea is to prove such formulas by…

In this very short note, we give a counterexample to a recent conjecture of Gilmer which would have implied the union-closed conjecture.