相关论文: Computer theorem proving in math
Computability theory is a discipline in the intersection of computer science and mathematical logic where the fundamental question is: given two mathematical objects X and Y, does X compute Y in principle? In case X and Y are real numbers,…
In the absence of any efficient classical schemes for verifying a universal quantum computer, the importance of limiting the required quantum resources for this task has been highlighted recently. Currently, most of efficient quantum…
The assumptions needed to prove Cox's Theorem are discussed and examined. Various sets of assumptions under which a Cox-style theorem can be proved are provided, although all are rather strong and, arguably, not natural.
Computer programs may go wrong due to exceptional behaviors, out-of-bound array accesses, or simply coding errors. Thus, they cannot be blindly trusted. Scientific computing programs make no exception in that respect, and even bring…
We present verification protocols to gain confidence in the correct performance of the realization of an arbitrary universal quantum computation. The derivation of the protocols is based on the fact that matchgate computations, which are…
This work discusses an approach to teach to mathematicians the importance and effectiveness of the application of Interactive Theorem Proving tools in their specific fields of interest. The approach aims to motivate the use of such tools…
This paper presents the verification of control systems implemented in Simulink. The goal is to ensure that high-level requirements on control performance, like stability, are satisfied by the Simulink diagram. A two stage process is…
In this note for the joint meeting of DMV and GDM we illustrate with examples the role of computer algebra in university mathematics education. We discuss its potential in teaching algebra, but also computer algebra as a subject in its own…
In this paper we consider Erd\"os-Mordell inequality and its extension in the plane of triangle to the Erd\"os-Mordell curve. Algebraic equation of this curve is derived, and using modern computer tools in mathematics, we verified one…
Mechanized reasoning uses computers to verify proofs and to help discover new theorems. Computer scientists have applied mechanized reasoning to economic problems but -- to date -- this work has not yet been properly presented in economics…
A recent case study from AWS by Chong et al. proposes an effective methodology for Bounded Model Checking in industry. In this paper, we report on a follow up case study that explores the methodology from the perspective of three research…
In this note, we observe that quantum logspace computations are verifiable by classical logspace algorithms, with unconditional security. More precisely, every language in BQL has an (information-theoretically secure) streaming proof with a…
In this paper we present the first-ever computer formalization of the theory of Gr\"obner bases in reduction rings, which is an important theory in computational commutative algebra, in Theorema. Not only the formalization, but also the…
A recent experiment testing the necessity of complex numbers in the standard formulation of quantum theory is recreated using IBM quantum computers. To motivate the experiment, we present a basic construction for real-valued quantum theory.…
In the words of the esteemed mathematician Paul Erd\"os, the mathematician's task is to \emph{prove and conjecture}. These two processes form the bedrock of all mathematical endeavours, and in the recent years, the mathematical community…
We prove that if our calculating capability is that of a universal Turing machine with a finite tape, then Church's thesis is true. This way we accomplish Post (1936) program.
A MATLAB toolbox is presented, with the goal of checking occurrences of design errors typically found in fixed-point digital systems, considering finite word-length effects. In particular, the present toolbox works as a front-end to a…
These lectures given to graduate students in theoretical particle physics, provide an introduction to the ``inner workings'' of computer algebra systems. Computer algebra has become an indispensable tool for precision calculations in…
The complexity of quantum computation remains poorly understood. While physicists attempt to find ways to create quantum computers, we still do not have much evidence one way or the other as to how useful these machines will be. The tools…
Recent advances in the cryptographic field of "Zero-Knowledge Proofs" have sparked a new wave of research, giving birth to many exciting theoretical approaches in the last few years. Such research has often overlapped with the need for…