18 - 18 Universal Turing Machines So far each Turing...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
18. Universal Turing Machines So far, each Turing machine appears to be specialized at solving one particular problem. Can we ‘program’ a Turing machine to obtain a general- purpose programmable Turing machine? Yes, such a machine is called a Universal Turing machine; they can be programmed to solve any problem that can be solved by specialized Turing machines. In fact, the universal Turing machine played an important early role in stimulating the development of stored-program computers. Universal Turing Machine, U Input to U : The encoding of a TM M , denoted as “ M ”, and the encoding of a string w Σ , denoted as “ w ”. Behavior: U halts on input “ M ”“ w ”iF M halts on w . ( U emulates the running of M on w ). 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Encoding Turing machines and their input strings HowdoweencodeaTur ingmach ineasastr ing? Example: M =( K, Σ ,δ,s,H )where K = { s, q, h } Σ= , ± ,a } H = { h } δ : State Symbol δ s a ( q, ± ) s ± ( h, ± ) s ± ( s, ) q a ( s, a ) q ± ( s, ) q ± ( ) Encode the states: s q 00 q q 01 h
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 09/22/2011 for the course COMP 272 taught by Professor Prof.tai during the Spring '10 term at HKUST.

Page1 / 7

18 - 18 Universal Turing Machines So far each Turing...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online