Related papers: Turing machines deciders, part I
$\textit{Magic: The Gathering}$ is a popular and famously complicated trading card game about magical combat. In this paper we show that optimal play in real-world $\textit{Magic}$ is at least as hard as the Halting Problem, solving a…
Stuttering bisimulation is a well-known behavioral equivalence that preserves CTL-X, namely CTL without the next-time operator X. Correspondingly, the stuttering simulation preorder induces a coarser behavioral equivalence that preserves…
We implement a protocol to determine the degree of entanglement between a qubit and the rest of the system on a quantum computer. The protocol is based on results obtained in paper [Frydryszak et al. (2017)]. This protocol is tested on a…
Chain-of-thought (CoT) reasoning improves large language models (LLMs) on difficult tasks, but it also makes inference expensive because every intermediate step must be generated as a discrete token. Latent reasoning reduces visible token…
The architecture of neural Turing machines is differentiable end to end and is trainable with gradient descent methods. Due to their large unfolded depth Neural Turing Machines are hard to train and because of their linear access of…
We prove that platform-deterministic inference is necessary and sufficient for trustworthy AI. We formalize this as the Determinism Thesis and introduce trust entropy to quantify the cost of non-determinism, proving that verification…
An algebraic representation of the Turing machines is given, where the configurations of Turing machines are represented by 4 order tensors, and the transition functions by 8 order tensors. Two types of tensor product are defined, one is to…
Boson sampling, thought to be intractable classically, can be solved by a quantum machine composed of merely generation, linear evolution and detection of single photons. Such an analog quantum computer for this specific problem provides a…
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 computational advantage of noisy quantum computers has been demonstrated by sampling the bitstrings of quantum random circuits. An important issue is how the performance of quantum devices could be quantified in the so-called "supremacy…
Programs for multiprocessor machines commonly perform busy waiting for synchronization. We propose the first separation logic for modularly verifying termination of such programs under fair scheduling. Our logic requires the proof author to…
A quantum simulator is a restricted class of quantum computer that controls the interactions between quantum bits in a way that can be mapped to certain difficult quantum many-body problems. As more control is exerted over larger numbers of…
Classifying states as entangled or separable is a highly challenging task, while it is also one of the foundations of quantum information processing theory. This task is higly nontrivial even for relatively simple cases, such as two-qutrit…
In this paper, we study the quantity of computational resources (state machine states and/or probabilistic transition precision) needed to solve specific problems in a single hop network where nodes communicate using only beeps. We begin by…
Based on the propositional description of even Goldbach conjecture, in order to verify the truth of even Goldbach conjecture, we will deeply discuss this question and present a new computing model of $G{{N}_{e}}TM$ Turing Machine. This…
Checking for Non-Termination (NT) of a given program P, i.e., determining if P has at least one non-terminating run, is an undecidable problem that continues to garner significant research attention. While unintended NT is common in…
Reasoning-capable large language models solve hard problems by emitting long chains of thought, paying heavily in latency, GPU time, and energy. Casual inspection of their traces reveals extensive reformulation, verification, and circular…
This paper examines the stability of the \`a trous algorithm under arbitrary iteration in the context of a more general study of shift-invariant filter banks. The main results describe sufficient conditions on the associated filters under…
Emil Post's tag system problem posed the question of whether or not a tag system $\{N=3, P(0) = 00, P(1) = 1101\}$ has a configuration, simulation of which will never halt or end up in a loop. Over the subsequent decades, there were several…
Several studies have already shown that the transient current can be successfully used to identify electric loads. However, most of the proposed methods were validated using only a handful of loads whose electric properties often differed…