How does the formal proof of the undecidability of the halting problem work?
Thursday, 03 August 2023
by EITCA Academy
The formal proof of the undecidability of the halting problem is a fundamental result in computational complexity theory that has significant implications for cybersecurity. This proof, first established by Alan Turing in 1936, demonstrates that there is no algorithm that can determine whether an arbitrary program will halt or run indefinitely. The proof relies on
- Published in Cybersecurity, EITC/IS/CCTF Computational Complexity Theory Fundamentals, Decidability, Undecidability of the Halting Problem, Examination review
Tagged under:
Algorithms, Computational Complexity Theory, Cybersecurity, Decidability, Diagonalization, Turing Machines
Using diagonalization, how can we prove that the set of irrational numbers is uncountable?
Thursday, 03 August 2023
by EITCA Academy
Diagonalization is a powerful technique used in mathematics to prove the uncountability of certain sets, including the set of irrational numbers. In the context of computational complexity theory, this proof has significant implications for decidability and the nature of infinity. To understand how diagonalization can be applied to demonstrate the uncountability of the set of