Related papers: Passages of Proof
Writing and argumentation are critical to both professional physics and physics education. However, the skill of making an extended argument in writing is often overlooked in physics classrooms, apart from certain practices like lab…
This paper explores the relationship of artificial intelligence to the task of resolving open questions in mathematics. We first present an updated version of a traditional argument that limitative results from computability and complexity…
Mathematical understanding is built in many ways. Among these, illustration has been a companion and tool for research for as long as research has taken place. We use the term illustration to encompass any way one might bring a mathematical…
The discovery of an algorithm for factoring which runs in polynomial time on a quantum computer has given rise to a concerted effort to understand the principles, advantages, and limitations of quantum computing. At the same time, many…
This is a short paper about the relationship between logic and computation. More specifically, it is about a relationship between the completeness proof for intuitionistic propositional logic within the form of proof-theoretic semantics…
Quantum advantage is notoriously hard to find and even harder to prove. For example the class of functions computable with classical physics actually exactly coincides with the class computable quantum-mechanically. It is strongly believed,…
In this note we demonstrate that a number of case-heavy combinatorial proofs in the mathematical phylogenetics literature can be proven more compactly using computational support. We use these techniques to also prove several new…
Future-Proof Yourself is a practical guide that helps readers navigate the fast-changing world of artificial intelligence in everyday life. The book begins by explaining how computers learn from data in simple, relatable terms, and…
Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning. In…
This report describes three particular technological advances in formal proofs. The HOL Light proof assistant will be used to illustrate the design of a highly reliable system. Today, proof assistants can verify large bodies of advanced…
Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this paper, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using…
Quantum computation is an emerging technology that promises to be a powerful tool in many areas. Though some years likely still remain until significant quantum advantage is demonstrated, the development of the technology has led to a range…
In this paper, we develop a novel verification technique to reason about programs featuring concurrency, pointers and randomization. While the integration of concurrency and pointers is well studied, little is known about the combination of…
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…
Deeper insight leads to better practice. We show how the study of the foundations of quantum mechanics has led to new pictures of open systems and to a method of computation which is practical and can be used where others cannot. We…
Quantum computation teaches us that quantum mechanics exhibits exponential complexity. We argue that the standard scientific paradigm of "predict and verify" cannot be applied to testing quantum mechanics in this limit of high complexity.…
Encryption study basically deals with three levels of algorithms. The first algorithm deals with encryption mechanism, second deals with decryption Mechanism and the third discusses about the generation of keys and sub keys used in the…
This article surveys quantum computational complexity, with a focus on three fundamental notions: polynomial-time quantum computations, the efficient verification of quantum proofs, and quantum interactive proof systems. Properties of…
Proof theory began in the 1920's as a part of Hilbert's program, which aimed to secure the foundations of mathematics by modeling infinitary mathematics with formal axiomatic systems and proving those systems consistent using restricted,…
Traditional human-computer interaction takes place through formally-specified systems like structured UIs and programming languages. Recent AI systems promise a new set of informal interactions with computers through natural language and…