相关论文: Computer validated proofs of a toolset for adaptab…

We exhibit a simple, systematic procedure for detecting and correcting errors using any of the recently reported quantum error-correcting codes. The procedure is shown explicitly for a code in which one qubit is mapped into five. The…

Mathematical reasoning is an important research direction in the field of artificial intelligence. This article proposes a novel multi tool application framework for mathematical reasoning, aiming to achieve more comprehensive and accurate…

Experimental groups are now fabricating quantum processors powerful enough to execute small instances of quantum algorithms and definitively demonstrate quantum error correction that extends the lifetime of quantum data, adding urgency to…

Quantum computers promise to efficiently solve not only problems believed to be intractable for classical computers, but also problems for which verifying the solution is also considered intractable. This raises the question of how one can…

We develop synthetic notions of oracle computability and Turing reducibility in the Calculus of Inductive Constructions (CIC), the constructive type theory underlying the Coq proof assistant. As usual in synthetic approaches, we employ a…

The design and analysis of systems that combine computational behaviour with physical processes' continuous dynamics - such as movement, velocity, and voltage - is a famous, challenging task. Several theoretical results from programming…

In this paper we consider the problem of certified static checking of module-like constructs of programming languages. We argue that there are algorithms and properties related to modules that can be defined and proven in an abstract way.…

An introductory formal languages course exposes advanced undergraduate and early graduate students to automata theory, grammars, constructive proofs, computability, and decidability. Programming students find these topics to be challenging…

Floating point arithmetic allows us to use a finite machine, the digital computer, to reach conclusions about models based on continuous mathematics. In this article we work in the other direction, that is, we present examples in which…

We present AutoformBot, a multi-agent system for building an Autoformalized Textbook Library At Scale (Atlas) in Lean 4. AutoformBot orchestrates thousands of LLM agents, equipped with formal verification tools, dependency-aware task…

Current concerns about reproducibility in many research communities can be traced back to a high value placed on empirical reproducibility of the physical details of scientific experiments and observations. For example, the detailed…

This paper formally proposes a problem about the efficient utilization of the four dimensional space-time. Given a cuboid container, a finite number of rigid cuboid items, and the time length that each item should be continuous baked in the…

Representation determines how we can reason about a specific problem. Sometimes one representation helps us find a proof more easily than others. Most current automated reasoning tools focus on reasoning within one representation. There is,…

The challenge of mastering computational tasks of enormous size tends to frequently override questioning the quality of the numerical outcome in terms of accuracy. By this we do not mean the accuracy within the discrete setting, which…

Parallel programs require software support to coordinate access to shared data. For this purpose, modern programming languages provide strongly-consistent shared objects. To account for their many usages, these objects offer a large API.…

Adaptive online testing efficiently assesses examinee proficiency by dynamically adjusting the difficulty of test items based on their performance. To achieve this, items are selected so that their difficulty closely matches the test…

Computational reproducibility of scientific results, that is, the execution of a computational experiment (e.g., a script) using its original settings (data, code, etc.), should always be possible. However, reproducibility has become a…

As modern computing moves towards smaller devices and powerful cloud platforms, more and more computation is being delegated to powerful service providers. Interactive proofs are a widely-used model to design efficient protocols for…

Network administration is an inherently complex task, in particular with regard to security. Using the Isabelle interactive proof assistant, we develop two automated, formally verified tools which help uncovering and preventing bugs in…

This paper explains a flaw in the published proof of the Scalable Commutativity Rule (SCR), presents a revised and formally verified proof of the SCR in the Coq proof assistant, and discusses the insights and open questions raised from our…