Related papers: Turing machines deciders, part I
This article describes a Turing machine which can solve for $\beta^{'}$ which is RE-complete. RE-complete problems are proven to be undecidable by Turing's accepted proof on the Entscheidungsproblem. Thus, constructing a machine which…
Violation of Mermin inequalities is tested on the 5-qubit IBM quantum computer. For 3, 4 and 5 parties, quantum states that violate the corresponding Mermin inequalities are constructed using quantum circuits on superconducting qubits.…
For any fixed $k$, a remarkably simple single-tape Turing machine can simulate $k$ independent counters in real time. Informally, a counter is a storage unit that maintains a single integer (initially 0), incrementing it, decrementing it,…
We define a class of stochastic processes based on evolutions and measurements of quantum systems, and consider the complexity of predicting their long-term behavior. It is shown that a very general class of decision problems regarding…
This work establishes a rigorous theoretical foundation for analyzing deep learning systems by leveraging Infinite Time Turing Machines (ITTMs), which extend classical computation into transfinite ordinal steps. Using ITTMs, we reinterpret…
Large Language Models often achieve strong performance by generating long intermediate chain-of-thought reasoning. However, it remains unclear when a model's final answer is actually determined during generation. If the answer is already…
The pursuit of human-like conversational agents has long been guided by the Turing test. For modern speech-to-speech (S2S) systems, a critical yet unanswered question is whether they can converse like humans. To tackle this, we conduct the…
This paper introduces a class of objects called decision rules that map infinite sequences of alternatives to a decision space. These objects can be used to model situations where a decision maker encounters alternatives in a sequence such…
Motivated by the success of bounded model checking framework for finite state machines, Ouaknine and Worrell proposed a time-bounded theory of real-time verification by claiming that restriction to bounded-time recovers decidability for…
Evaluating language models fairly is increasingly difficult as static benchmarks risk contamination by training data, obscuring whether models truly reason or recall. We introduce BeyondBench, an evaluation framework using algorithmic…
Dynamical Systems theory generally deals with fixed point iterations of continuous functions. Computation by Turing machine although is a fixed point iteration but is not continuous. This specific category of fixed point iterations can only…
The general approach taken when training deep learning classifiers is to save the parameters after every few iterations, train until either a human observer or a simple metric-based heuristic decides the network isn't learning anymore, and…
Steve Gull, in unpublished work available on his Cambridge University homepage, has outlined a proof of Bell's theorem using Fourier theory. Gull's philosophy is that Bell's theorem (or perhaps a key lemma in its proof) can be seen as a…
Scheduling with testing is a recent online problem within the framework of explorable uncertainty motivated by environments where some preliminary action can influence the duration of a task. Jobs have an unknown processing time that can be…
This paper assesses the transient stability of a synchronous machine connected to an infinite bus through the notion of invariant sets. The problem of computing a conservative approximation of the maximal positive invariant set is…
Steady states of alternating-current (AC) circuits have been studied in considerable detail. In 1982, Baillieul and Byrnes derived an upper bound on the number of steady states in a loss-less AC circuit [IEEE TCAS, 29(11): 724--737] and…
We consider an extended model of quantum computation where a scalable fault-tolerant quantum computer is coupled to one or more ancilla qubits that evolve according to a nonlinear Schr\"odinger equation. Following the approach of Abrams and…
Critical transitions, ubiquitous in nature and technology, necessitate anticipation to avert adverse outcomes. While many studies focus on bifurcation-induced tipping, where a control parameter change leads to destabilization, alternative…
We consider the task of remote state estimation and stabilization of disturbed linear plants via noisy communication channels. In 2007 Matveev and Savkin established a surprising link between this problem and Shannon's theory of zero-error…
In [ABM07], Abdulla et al. introduced the concept of decisiveness, an interesting tool for lifting good properties of finite Markov chains to denumerable ones. Later, this concept was extended to more general stochastic transition systems…