Related papers: Observations on the Halting Problem
Recently, the presence in the literature (also recent) of voluminous discussions about the interpretation of quantum mechanics has been labelled as scandalous. We claim that a weak point of the debate which hosted such a conclusion is a…
Multi-round incomplete information tasks are crucial for evaluating the lateral thinking capabilities of large language models (LLMs). Currently, research primarily relies on multiple benchmarks and automated evaluation metrics to assess…
For optimal stopping problems with time-inconsistent preference, we measure the inherent level of time-inconsistency by taking the time needed to turn the naive strategies into the sophisticated ones. In particular, when in a repeated…
We establish H\"older stability of an inverse hyperbolic obstacle problem. Mainly, we study the problem of reconstructing an unknown function defined on the boundary of the obstacle from two measurements taken on the boundary of a domain…
We formalize hallucinations in generative models as failures to link an estimate to any plausible cause. Under this interpretation, we show that even loss-minimizing optimal estimators still hallucinate. We confirm this with a general high…
In a recent historical overview, Cristian S. Calude, Elena Calude, and Solomon Marcus identify eight stages in the development of the concept of a mathematical proof in support of an ambitious conjecture: we can express classical…
This paper has been withdrawn because of serious errors.
We consider an optimal stopping time problem related with many models found in real options problems. The main goal of this work is to bring for the field of real options, different and more realistic pay-off functions, and negative…
This comment directs attention to some fails of the Alhaidari approach to solve relativistic problems. It is shown that his gauge considerations are way off the mark and that the class of exactly solvable relativistic problems is not so…
The comment arXiv:1204.2729v1 is completely wrong. The author makes serious mistakes in calculations and judgement. The errors are made at the level of basic undergraduate statistical mechanics.
We develop a theory for solving continuous time optimal stopping problems for non-linear expectations. Our motivation is to consider problems in which the stopper uses risk measures to evaluate future rewards.
Many decision problems in economics, information technology, and industry can be transformed to an optimal stopping of adapted random vectors with some utility function over the set of Markov times with respect to filtration build by the…
Arguments are given that time must be defined in an operative manner,i.e., by constructing devices which can serve as clocks.The investigation of such devices leads to the conclusion that there is a principal uncertainity of time if one…
The purpose of this note is to give a self contained description of Walls finiteness obstruction.
In this paper, we will continue the investigation of Waring's problem, and give further improvements.
Some attack scientific rationality, others defend it, but both miss the point. What both parties take to be scientific rationality is actually a species of irrationality masquerading as scientific rationality. The current orthodox…
There have been many attempts to solve the P versus NP problem. However, with a new proof method, P not equal NP can be proved. A time limit is set for an arbitrary Turing machine and an input word is rejected on a timeout. The time limit…
Some notes and questions about the concept of time are exposed. Particular reference is given to the problem in quantum mechanics, in connection with the indeterminacy principle.
The Monty Hal problem is an attractive puzzle. It combines simple statement with answers that seem surprising to most audiences. The problem was thoroughly solved over two decades ago. Yet, more recent discussions indicate that the solution…
A set is low if A' \le_T HALT. A set is superlow if A' \le_tt HALT. A set is superduperlow if A' \le_btt HALT. While it was known that any superduperlow is decidable it does not seem to be well known. We include two unpublished proofs of…