Related papers: Coq in a Hurry
This text aims to present and explain quantum machine learning algorithms to a data scientist in an accessible and consistent way. The algorithms and equations presented are not written in rigorous mathematical fashion, instead, the…
Logical relations (LR) have been around for many years, and today they are used in many formal results. However, it can be difficult to LR beginners to find a good place to start to learn. Papers often use highly specialized LRs that use…
A key component of mathematical reasoning is the ability to formulate interesting conjectures about a problem domain at hand. In this paper, we give a brief overview of a theory exploration system called QuickSpec, which is able to…
This paper proposes a research direction to advance AI which draws inspiration from cognitive theories of human decision making. The premise is that if we gain insights about the causes of some human capabilities that are still lacking in…
Many students in introductory programming courses fare poorly in the code writing tasks of the final summative assessment. Such tasks are designed to assess whether novices have developed the analytical skills to translate from the given…
In the rapidly evolving interdisciplinary field of quantum information science and technology, a major obstacle is the need to understand advanced mathematics to solve complex problems. Current findings in educational research suggest that…
We present a comparison of several online machine learning techniques for tactical learning and proving in the Coq proof assistant. This work builds on top of Tactician, a plugin for Coq that learns from proofs written by the user to…
Quantum computing (QC) promises to be a transformative technology with impact on various application domains, such as optimization, cryptography, and material science. However, the technology has a sharp learning curve, and practical…
We present a first step towards the Coq implementation of the Theory of Tagged Objects formalism. The concept of tagged types is encoded, and the soundness proofs are discussed with some future work suggestions.
This work is a tutorial on Shor's factoring algorithm by means of a worked out example. Some basic concepts of Quantum Mechanics and quantum circuits are reviewed. It is intended for non-specialists which have basic knowledge on…
In the former article "Formal mathematical systems including a structural induction principle" we have presented a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the…
While the use of formal verification techniques is well established in the development of mission-critical software, it is still rare in the production of most other kinds of software. We share our experience that a formal verification tool…
Humans can learn individual episodes and generalizable rules and also successfully retain both kinds of acquired knowledge over time. In the cognitive science literature, (1) learning individual episodes and rules and (2) learning and…
This tutorial introduces (and provides, via the document source) the Quantikz LaTeX package for typesetting quantum circuit diagrams. This takes advantage of tikz to give greater control over the circuit options. Those familiar with the…
We propose a conjugate logic that can capture the behavior of quantum and quantum-like systems. The proposal is similar to the more generic concept of epistemic logic: it encodes knowledge or perhaps more correctly, predictions about…
This work introduces Symbolic-Aided Chain-of-Thought (CoT), an improved approach to standard CoT, for logical reasoning in large language models (LLMs). The key idea is to integrate lightweight symbolic representations into few-shot…
In the realm of formal theorem proving, the Coq proof assistant stands out for its rigorous approach to verifying mathematical assertions and software correctness. Despite the advances in artificial intelligence and machine learning, the…
The capture calculus is an extension of System F<: that tracks free variables of terms in their type, allowing one to represent capabilities while limiting their scope. While previous calculi had mechanized soundness proofs -- notably…
Chain-of-thought (CoT) prompting is a popular in-context learning (ICL) approach for large language models (LLMs), especially when tackling complex reasoning tasks. Traditional ICL approaches construct prompts using examples that contain…
We introduce a classical-quantum hybrid approach to computation, allowing for a quadratic performance improvement in the decision process of a learning agent. In particular, a quantum routine is described, which encodes on a quantum…