https://scribbletogether.com/whiteboard/848EE700-2379-4423-84D2-FD1B4A2CDD0B

Overview

Last class:

• Pumping lemma
• DFAs are limited in power
• DFAs + Read/write memory tape + Head can move both ways

Today:

• Turing machines
• Definition, examples

Turing Machines

= DFAs + Read/write memory + 2-way head

Anatomy

$\Delta$: start of the tape

$\empty$: empty cell

→ $k$ states

→ $\Sigma \supseteq \{0,1,\Delta,\empty\}$ (or any finite alphabet)

Transition function → $\delta : \{0,1,…,k-1\} \times \Sigma \to \{0,1,…,k-1\} \times \Sigma \times \{L,R,S,H\}$

Steps for computation:

1. Place all input into tape
2. Start with current head at $x[0]$