Related papers: A Relatively Small Turing Machine Whose Behavior I…
In this paper, we extend the techniques used in our previous work to show that there exists a probabilistic Turing machine running within time $O(n^k)$ for all $k\in\mathbb{N}_1$ accepting a language $L_d$ that is different from any…
The notion of Reactive Turing machine (RTM) was proposed as an orthogonal extension of Turing machines with interaction. RTMs are used to define the notion of executable transition system in the same way as Turing machines are used to…
We consider the following problem for various infinite time machines. If a real is computable relative to large set of oracles such as a set of full measure or just of positive measure, a comeager set, or a nonmeager Borel set, is it…
We study a variant of the parallel Moser-Tardos Algorithm. We prove that if we restrict attention to a class of problems whose dependency graphs have subexponential growth, then the expected total number of random bits used by the algorithm…
As an example of the concept of rulial space, we explore the case of simple Turing machines. We construct the rulial multiway graph which represents the behavior of all possible Turing machines with a certain class of rules. This graph…
Large pre-trained multilingual models like mBERT, XLM-R achieve state of the art results on language understanding tasks. However, they are not well suited for latency critical applications on both servers and edge devices. It's important…
This paper is an experimental exploration of the relationship between the runtimes of Turing machines and the length of proofs in formal axiomatic systems. We compare the number of halting Turing machines of a given size to the number of…
We start a systematic investigation concerning bipartite Tur\'an number for trees. For a graph $F$ and integers $1 \leq a \leq b$ we define: $(i)$\quad $ex_b(a, b, F)$ is the largest number of edges that an $F$-free bipartite graph can have…
The binary perceptron is the simplest artificial neural network formed by $N$ input units and one output unit, with the neural states and the synaptic weights all restricted to $\pm 1$ values. The task in the teacher--student scenario is to…
Estimating the uncertainty of responses from Large Language Models (LLMs) remains a critical challenge. While recent Bayesian methods have demonstrated effectiveness in quantifying uncertainty through low-rank weight updates, they typically…
We study the structure of the non-perturbative free energy of a one-parameter class of little string theories (LSTs) of A-type in the so-called unrefined limit. These theories are engineered by $N$ M5-branes probing a transverse flat space.…
Slot and van Emde Boas' weak invariance thesis states that reasonable machines can simulate each other within a polynomially overhead in time. Is $\lambda$-calculus a reasonable machine? Is there a way to measure the computational…
The article introduces some ideas for solving special cases of the following problem, proposed in a somewhat generalized form by Marcus Hutter in 2000. Given two Turing machines $A$ and $C$, it is required to build a Turing machine $B$,…
Addressing questions raised in recent papers, we study the $r$-distance graph $H_r(n)$ on the Boolean cube $\{0,1\}^n$, where two vertices are adjacent if their Hamming distance is exactly $r$. For fixed integers $s \ge 2$ and even $r \ge…
We construct an explicit Hamiltonian cycle in the state graph of the 5-puzzle on a toroidal 2x 3 grid, a graph with 720 vertices. The cycle is described by a short symbolic sequence of 48 moves over the alphabet {L,R,V}, repeated $15$…
Chandrasekaran, Chertkov, Gamarnik, Shah, and Shin recently proved that the average number of independent sets of random regular graphs of size n and degree 3 approaches w^n for large n, where w is approximately 1.54563, consistent with the…
Despite rapid progress in the recent past, current speech recognition systems still require labeled training data which limits this technology to a small fraction of the languages spoken around the globe. This paper describes wav2vec-U,…
Word discovery is the task of extracting words from unsegmented text. In this paper we examine to what extent neural networks can be applied to this task in a realistic unwritten language scenario, where only small corpora and limited…
Numerous Bayesian Network (BN) structure learning algorithms have been proposed in the literature over the past few decades. Each publication makes an empirical or theoretical case for the algorithm proposed in that publication and results…
A fundamental question of longstanding theoretical interest is to prove the lowest exact count of real additions and multiplications required to compute a power-of-two discrete Fourier transform (DFT). For 35 years the split-radix algorithm…