A non-expert view on Turing machines, Proof Verifiers, and Mental reasoning
Computational Complexity
2012-03-02 v6 Formal Languages and Automata Theory
Logic in Computer Science
Abstract
The paper explores known results related to the problem of identifying if a given program terminates on all inputs -- this is a simple generalization of the halting problem. We will see how this problem is related and the notion of proof verifiers. We also see how verifying if a program is terminating involves reasoning through a tower of axiomatic theories -- such a tower of theories is known as Turing progressions and was first studied by Alan Turing in the 1930's. We will see that this process has a natural connection to ordinal numbers. The paper is presented from the perspective of a non-expert in the field of logic and proof theory.
Cite
@article{arxiv.1011.0046,
title = {A non-expert view on Turing machines, Proof Verifiers, and Mental reasoning},
author = {Rina Panigrahy},
journal= {arXiv preprint arXiv:1011.0046},
year = {2012}
}