Related papers: What is Cook's theorem?
A resource-bounded version of the statement "no algorithm recognizes all non-halting Turing machines" is equivalent to an infinitely often (i.o.) superpolynomial speedup for the time required to accept any coNP-complete language and also…
Neuron identification is a popular tool in mechanistic interpretability, aiming to uncover the human-interpretable concepts represented by individual neurons in deep networks. While algorithms such as Network Dissection and CLIP-Dissect…
We live in a world brimming with uncertainty, where we constantly have to make a lot of decisions under incomplete information. We are firm believers that our subjective belief cannot be computed by rigorous mathematical formula; instead…
Nonmonotonic reasoning is a pattern of reasoning that allows an agent to make and retract (tentative) conclusions from inconclusive evidence. This paper gives a possible-worlds interpretation of the nonmonotonic reasoning problem based on…
Two theorems about the P versus NP problem be proved in this article (1) There exists a language $L$, that the statement $L \in \textbf{P}$ is independent of ZFC. (2) There exists a language $L \in \textbf{NP}$, for any polynomial time…
Predicting the future is an important component of decision making. In most situations, however, there is not enough information to make accurate predictions. In this paper, we develop a theory of causal reasoning for predictive inference…
The concept of decomposition in computer science and engineering is considered a fundamental component of computational thinking and is prevalent in design of algorithms, software construction, hardware design, and more. We propose a simple…
The Kochen-Specker theorem is one of the fundamental no-go theorems in quantum theory. It has far-reaching consequences for all attempts trying to give an interpretation of the quantum formalism. In this work, we examine the hypotheses…
Knockoffs are a popular statistical framework that addresses the challenging problem of conditional variable selection in high-dimensional settings with statistical control. Such statistical control is essential for the reliability of…
It is a widespread belief that results like G\"odel's incompleteness theorems or the intrinsic randomness of quantum mechanics represent fundamental limitations to humanity's strive for scientific knowledge. As the argument goes, there are…
Hidden-variable models aim to reproduce the results of quantum theory and to satisfy our classical intuition. Their refutation is usually based on deriving predictions that are different from those of quantum mechanics. Here instead we…
Theory of mind (ToM) refers to humans' ability to understand and infer the desires, beliefs, and intentions of others. The acquisition of ToM plays a key role in humans' social cognition and interpersonal relations. Though indispensable for…
I discuss some of the main interpretations given to explain the indeterministic nature of quantum measurements and show that all has some loopholes in one corner or another. I propose an alternative interpretation based on the notion of…
General relativity treats spacetime as dynamical and exhibits its breakdown at singularities. This failure is interpreted as evidence that quantum gravity is not a theory formulated within spacetime; instead, it must explain the very…
In this paper, we take a closer look at Czerwinski's "${\rm P}\neq{\rm NP}$ relative to a ${\rm P}$-complete oracle" [Cze23]. There are (uncountably) infinitely-many relativized worlds where ${\rm P}$ and ${\rm NP}$ differ, and it is…
The CMI Millennium "P vs NP Problem" can be resolved e.g. if one shows at least one counterexample to the conjecture "P is equal to NP". A certain class of problems being such counterexamples is formulated. This implies the rejection of the…
We identify a fundamental incompatibility between the goals of accuracy, trust, and human-level reasoning in artificial intelligence (AI) systems, for strict mathematical definitions of these notions. We define accuracy of a system as the…
Among perhaps many things common to Kuratowski's Theorem in graph theory, Reidemeister's Theorem in topology, and Cook's Theorem in theoretical computer science is this: all belong to the phenomenon of simultaneous discovery in mathematics.…
It is well-known (cf. K.-Pudl\'ak 1989) that a polynomial time algorithm finding tautologies hard for a propositional proof system $P$ exists iff $P$ is not optimal. Such an algorithm takes $1^{(k)}$ and outputs a tautology $\tau_k$ of size…
Non-locality, or quantum-non-locality, are buzzwords in the community of quantum foundation and information scientists, which purportedly describe the implications of Bell's theorem. When such phrases are treated seriously, that is it is…