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We prove the Extended Church-Turing Thesis: Every effective algorithm can be efficiently simulated by a Turing machine. This is accomplished by emulating an effective algorithm via an abstract state machine, and simulating such an abstract…
Universality of neural networks describes the ability to approximate arbitrary function, and is a key ingredient to keep the method effective. The established models for universal quantum neural networks(QNN), however, require the…
Artificial organisms are computer programs that self-replicate, mutate, compete and evolve. How do these lifelike information-processing behaviours could arise in diverse far-from-equilibrium physical systems remains an open question. Here,…
Tsetlin Machines (TsMs) are a promising and interpretable machine learning method which can be applied for various classification tasks. We present an exact encoding of TsMs into propositional logic and formally verify properties of TsMs…
Recent advancements in cognitive science and multi-round reasoning techniques for Large Language Models (LLMs) suggest that iterative thinking processes improve problem-solving performance in complex tasks. Inspired by this, approaches like…
Universality in cellular automata theory is a central problem studied and developed from their origins by John von Neumann. In this paper, we present an algorithm where any Turing machine can be converted to one-dimensional cellular…
We have defined the Conscious Turing Machine (CTM) for the purpose of investigating a Theoretical Computer Science (TCS) approach to consciousness. For this, we have hewn to the TCS demand for simplicity and understandability. The CTM is…
Linear Finite State Machines (LFSMs) are particular primitives widely used in information theory, coding theory and cryptography. Among those linear automata, a particular case of study is Linear Feedback Shift Registers (LFSRs) used in…
Among the fundamental questions in computer science, at least two have a deep impact on mathematics. What can computation compute? How many steps does a computation require to solve an instance of the 3-SAT problem? Our work addresses the…
We discuss quantum information processing machines. We start with single purpose machines that either redistribute quantum information or identify quantum states. We then move on to machines that can perform a number of functions, with the…
This paper extends work done to date on quantum computation by associating potentials with different types of computation steps. Quantum Turing machine Hamiltonians, generalized to include potentials, correspond to sums over tight binding…
In this paper, we propose a real-world benchmark for studying robotic learning in the context of functional manipulation: a robot needs to accomplish complex long-horizon behaviors by composing individual manipulation skills in functionally…
Molecular robotics is challenging, so it seems best to keep it simple. We consider an abstract molecular robotics model based on simple folding instructions that execute asynchronously. Turning Machines are a simple 1D to 2D folding model,…
Geometrical Computation as a new model of computation is the counterpart of Cellular Automata that has Turing computing ability. In this paper we provide an algorithm to simulate Alternating Turing Machine in the context of Signal Machine…
In recent years, general matrix-matrix multiplication with non-regular-shaped input matrices has been widely used in many applications like deep learning and has drawn more and more attention. However, conventional implementations are not…
In industrial applications Finite State Machines (FSMs) are often used to implement decision making policies for autonomous systems. In recent years, the use of Behavior Trees (BT) as an alternative policy representation has gained…
Neural reasoners such as Tiny Recursive Models (TRMs) solve complex problems by combining neural backbones with specialized inference schemes. Such inference schemes have been a central component of stochastic reasoning systems, where…
We report the first end-to-end hardware-validated demonstration of a reversible Quantum Memory Matrix QMM imprint retrieval cycle. Using IBM Quantum back ends, we realize five imprint retrieval experiments that scale from a minimal…
Simulated Tempering (ST) is an MCMC algorithm for complex target distributions that operates on a path between the target and a more amenable reference distribution. Crucially, if the reference enables i.i.d. sampling, ST is regenerative…
Length generalization refers to the ability to extrapolate from short training sequences to long test sequences and is a challenge for current large language models. While prior work has proposed some architecture or data format changes to…