Turing machines to word problems
نویسنده
چکیده
We trace the emergence of unsolvable problems in algebra and topology from the unsolvable halting problem for Turing machines. §
منابع مشابه
Some improvements in fuzzy turing machines
In this paper, we improve some previous definitions of fuzzy-type Turing machines to obtain degrees of accepting and rejecting in a computational manner. We apply a BFS-based search method and some level’s upper bounds to propose a computational process in calculating degrees of accepting and rejecting. Next, we introduce the class of Extended Fuzzy Turing Machines equipped with indeterminacy s...
متن کاملSolving the word problem in real time
The purpose of this paper is to study groups with real-time word problem, that is for which the word problem can be solved with a deterministic, multitape Turing machine which reads its input at constant speed and completes the processing of its input as it finishes reading it. We start by proving a few elementary results concerning the closure properties of this family of groups. Then we show ...
متن کاملSmall Weakly Universal Turing Machines
We give small universal Turing machines with state-symbol pairs of (6, 2), (3, 3) and (2, 4). These machines are weakly universal, which means that they have an infinitely repeated word to the left of their input and another to the right. They simulate Rule 110 and are currently the smallest known weakly universal Turing machines. Despite their small size these machines are efficient polynomial...
متن کاملAlgorithmic Problem Complexity
People solve different problems and know that some of them are simple, some are complex and some insoluble. The main goal of this work is to develop a mathematical theory of algorithmic complexity for problems. This theory is aimed at determination of computer abilities in solving different problems and estimation of resources that computers need to do this. Here we build the part of this theor...
متن کاملDecision Problems in Group Theory
At the 1976 Oxford Conference, Aanderaa introduced a new class of machines which he called F machines (later renamed as modular machines). Using these he gave two remarkably short and easy examples of finitely presented groups with unsolvable word problem. Both of these examples, together with an exposition of modular machines, will be found in a paper by Aanderaa and Cohen [2]. The aim of this...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2014