Lecture 7 (Abraham) - Turing machine

Date Pre-lecture slides Post-lecture scribbles Async video Lecture recording
September 19 2024 Lecture 7 (Abraham) - Turing machine Lecture 7 (Abraham) - Turing machine Lecture 7 (Abraham) - Turing machine Lecture 7 (Abraham) - Turing machine
 

Notes

Context-Sensitive Language

Definition

Context-Sensitive Grammar

Definition

A CSG is a quadruple G = (V, T, P, S)

Example

The language L = { $a^{n} b^{n} c^{n}$ | $n \ge 1$} is a context-sensitive language.

Turing Machines

Definition

A Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model’s simplicity, it is capable of implementing any computer algorithm

Concatenation

Formal definition

A Turing machine is a 7-tuple(Q, $\Sigma ,\Gamma ,\delta , q_{0}, q_{acc}, q_{rej}$)

Transition Function

$\delta$ : Q x $\Gamma → Q$ x $\Gamma$ x {L, R, S}

Concatenation

Can also be written as c → d, L

$\delta$ : (q, c) = (p, d, L)

Languages defined by a Turing Machine

Linear Bounded Automata

Concatenation

Additional Resources

Contributors

Sindhu Vydana