Related papers: A Formalization of the Turing Test
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…
The framework of generalized probabilistic theories is a powerful tool for studying the foundations of quantum physics. It provides the basis for a variety of recent findings that significantly improve our understanding of the rich physical…
The contribution of this paper is threefold: first, it defines a framework for modelling component-based systems, as well as a formalization of integration rules to combine their behavior. This is based on finite state machines (FSM).…
This paper presents the benefits of formal modelling and verification techniques for self-stabilising distributed algorithms. An algorithm is studied, that takes a set of processes connected by a tree topology and converts it to a ring…
Use case driven development methodologies put use cases at the center of the software development process. However, in order to support automated development and analysis, use cases need to be appropriately formalized. This will also help…
Consider a universal Turing machine that produces a partial or total function (or a binary stream), based on the answers to the binary queries that it makes during the computation. We study the probability that the machine will produce a…
In this paper, we define a realizability semantics for the simply typed $\lambda\mu$-calculus. We show that if a term is typable, then it inhabits the interpretation of its type. This result serves to give characterizations of the…
In this review we attempt to present an overview of some of the better known quantization techniques found in the current literature and used both by physicists and mathematicians. The treatment is more descriptive than rigorous, for we aim…
Modern vehicles become increasingly digitalized with advanced information technology-based solutions like advanced driving assistance systems and vehicle-to-x communications. These systems are complex and interconnected. Rising complexity…
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.…
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…
The paper puts into discussion the concept of universality, in particular for structures not of the power of Turing computability. The question arises if for such structures a universal structure of the same kind exists or not. For that the…
The failure of hardware or software in a critical system can lead to loss of lives. The design errors can be main source of the failures that can be introduced during system development process. Formal techniques are an alternative approach…
Infinite time Turing machines extend the operation of ordinary Turing machines into transfinite ordinal time. By doing so, they provide a natural model of infinitary computability, a theoretical setting for the analysis of the power and…
A fundamental problem in artificial intelligence is that nobody really knows what intelligence is. The problem is especially acute when we need to consider artificial systems which are significantly different to humans. In this paper we…
We present an extension to the $\mathtt{mathlib}$ library of the Lean theorem prover formalizing the foundations of computability theory. We use primitive recursive functions and partial recursive functions as the main objects of study, and…
The halting problem for Turing machines is decidable on a set of asymptotic probability one. Specifically, there is a set B of Turing machine programs such that (i) B has asymptotic probability one, so that as the number of states n…
The benchmark for computation is typically given as Turing computability; the ability for a computation to be performed by a Turing Machine. Many languages exploit (indirect) encodings of Turing Machines to demonstrate their ability to…
Building on work by Alfonseca et al. (2021), we study the conditions necessary for it to be logically possible to prove that an arbitrary artificially intelligent machine will exhibit certain behavior. To do this, we develop a formalism…
The general translator formalism and computing specific implementations are proposed. The implementation of specific elements necessary to process the source and destination information within the translators are presented. Some common…