Chapter 6

Alan Turing

British Logician, mathematician Turing Award very prestigous Homosexual

UTM

Can have input of abstract turing machine Functionally equivalent if M1 halts for some input and M2 also halts for same input

Three components of a digital computer and draw it

Control -> gates/flags ->databse -> memory bus -> memory

Digital Computers

Discrete State Machines Manipulate Letter Strings

Uncomputable Functions

Halt Check, all computable functions are turing-computable

Input of UTM two parts

Software (Description of the machine table for the TM being simulated) Data: input for the TM being simulated

Two Key Ideas of UTM

Stored programs in a formal langauge Simulation

Von Neumann Machines

TM has one register VNM has many TM has linear access memory NVM has addressable memory Modern cpu has many instruction increment, add, jump

Enigma Machine

World War 2 Third Reich Electro-mechanical rotor machine FSM

Bombe Machine

codebreaking for enigma machines