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Computation is an input-output process, where a program encoding a problem to be solved is inserted into a machine that outputs a solution. Quantum computation conventionally relies on classical, external control outside the quantum…
We report a method to convert discrete representations of molecules to and from a multidimensional continuous representation. This model allows us to generate new molecules for efficient exploration and optimization through open-ended…
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…
The rapid and successful strides in quantum chemistry in the past decades can be largely credited to a conspicuous synergy between theoretical and computational advancements. However, the architectural computer archetype that enabled such a…
Quantum computing is concerned with computer technology based on the principles of quantum mechanics, with operations performed at the quantum level. Quantum computational models make it possible to analyze the resources required for…
Turing presented a general representation scheme by which to achieve artificial intelligence - unorganised machines. Significantly, these were a form of discrete dynamical system and yet such representations remain relatively unexplored.…
The universal Turing machine is generally considered to be the simplest, most abstract model of a computer. This paper reports on the discovery of an accidental arbitrary code execution vulnerability in Marvin Minsky's 1967 implementation…
Artificial computing machinery transforms representations through an objective process, to be interpreted subjectively by humans, so the machine and the interpreter are different entities, but in the putative natural computing both…
Quantum computing exploits quantum phenomena such as superposition and entanglement to realize a form of parallelism that is not available to traditional computing. It offers the potential of significant computational speed-ups in quantum…
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,…
Large Language Models are versatile, general-purpose tools with a wide range of applications. Recently, the advent of "reasoning models" has led to substantial improvements in their abilities in advanced problem-solving domains such as…
Theory evaluation is a key problem in many areas: machine learning, scientific discovery, inverse engineering, decision making, software engineering, design, human sciences, etc. If we have a set of theories that are able to explain the…
We investigate a variant of the fuel-based approach to modeling diverging computation in type theories and use it to abstractly capture the essence of oracle Turing machines. The resulting objects we call continuous machines. We prove that…
Chemical modelling serves two purposes in dynamical models: accounting for the effect of microphysics on the dynamics and providing observable signatures. Ideally, the former must be done as part of the hydrodynamic simulation but this…
The quantum computation of electronic energies can break the curse of dimensionality that plagues many-particle quantum mechanics. It is for this reason that a universal quantum computer has the potential to fundamentally change…
Recently Quantum Computation has generated a lot of interest due to the discovery of a quantum algorithm which can factor large numbers in polynomial time. The usefulness of a quantum com puter is limited by the effect of errors. Simulation…
A fruitful way of obtaining meaningful, possibly concrete, algorithmically random numbers is to consider a potential behaviour of a Turing machine and its probability with respect to a measure (or semi-measure) on the input space of binary…
Theoretical complexity is a vital subfield of computer science that enables us to mathematically investigate computation and answer many interesting queries about the nature of computational problems. It provides theoretical tools to assess…
The notion of computability is stable (i.e. independent of the choice of an indexing) over infinite-dimensional vector spaces provided they have a finite "tensorial dimension". Such vector spaces with a finite tensorial dimension permit to…
In the first of this pair of papers, it was proven that that no physical computer can correctly carry out all computational tasks that can be posed to it. The generality of this result follows from its use of a novel definition of…