相关论文: Gems of Corrado B\"ohm
This paper introduces CodeGemma, a collection of specialized open code models built on top of Gemma, capable of a variety of code and natural language generation tasks. We release three model variants. CodeGemma 7B pretrained (PT) and…
Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same…
From the philosopher's perspective, the interest in quantum computation stems primarily from the way that it combines fundamental concepts from two distinct sciences: physics (especially quantum mechanics) and computer science, each long a…
Qubits are a great way to build a quantum computer, but a limited way to program one. We replace the usual "states and gates" formalism with a "props and ops" (propositions and operators) model in which (a) the C*-algebra of observables…
In certain scientific domains, there is a need for tensor operations. To facilitate tensor computations,computer algebra systems are employed. In our research, we have been using Cadabra as the main computer algebra system for several…
The authors have been using a largely algebraic form of ``computational discovery'' in various undergraduate classes at their respective institutions for some decades now to teach pure mathematics, applied mathematics, and computational…
Choreographic programming is an emerging programming paradigm for concurrent and distributed systems, whereby developers write the communications that should be enacted and then a distributed implementation is automatically obtained by…
It is becoming increasingly clear that, if a useful device for quantum computation will ever be built, it will be embodied by a classical computing machine with control over a truly quantum subsystem, this apparatus performing a mixture of…
Computability logic (CoL) is a formal theory of interactive computation. It understands computational problems as games played by two players: a machine and its environment, uses logical formalism to describe valid principles of…
In machine learning, fewer features reduce model complexity. Carefully assessing the influence of each input feature on the model quality is therefore a crucial preprocessing step. We propose a novel feature selection algorithm based on a…
What can humans compute in their heads? We are thinking of a variety of Crypto Protocols, games like Sudoku, Crossword Puzzles, Speed Chess, and so on. The intent of this paper is to apply the ideas and methods of theoretical computer…
Concordant computation is a circuit-based model of quantum computation for mixed states, that assumes that all correlations within the register are discord-free (i.e. the correlations are essentially classical) at every step of the…
A computational abstract machine based on two operations: referencing and bit copying is presented. These operations are sufficient for carrying out any computation. They can be used as the primitives for a Turing-complete programming…
Algorithms are the engine for reproducible problem-solving. We present a framework automating algorithm discovery by conceptualizing them as sequences of operations, represented as tokens. These computational tokens are chained using a…
Our aim here is to illustrate how the benefits of structural corecursion can be found in a broader swath of the programming landscape than previously thought. Beginning from a tutorial on structural corecursion in the total, pure functional…
Framed combinatorial topology is a novel theory describing combinatorial phenomena arising at the intersection of stratified topology, singularity theory, and higher algebra. The theory synthesizes elements of classical combinatorial…
Quantum models of computation are widely believed to be more powerful than classical ones. Efforts center on proving that, for a given problem, quantum algorithms are more resource efficient than any classical one. All this, however,…
Quantum computers are designed to outperform standard computers by running quantum algorithms. Areas in which quantum algorithms can be applied include cryptography, search and optimisation, simulation of quantum systems, and solving large…
Discrete mathematics is the foundation of computer science. It focuses on concepts and reasoning methods that are studied using math notations. It has long been argued that discrete math is better taught with programming, which takes…
Quantum computer is the key to controlling complex processes. If its hardware, in general is successfully created on the basis of the physical baggage of the 20th century, the mathematical software is fundamentally lagging behind. Feynman's…