1 / 6

Multitape Turing Machines

Multitape Turing Machines. TM - Tape Head can Stay (TMS). Modify definition of transition function:  : Q x   Q x  x {L, R, S } Claim 1: If L is the language of some TM M then  TMS M S such that L = L( M S ) If M decides L then  TMS M S that decides L

magda
Télécharger la présentation

Multitape Turing Machines

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Multitape Turing Machines

  2. TM - Tape Head can Stay (TMS) • Modify definition of transition function: •  : Q x   Q x  x {L, R, S} • Claim 1: If L is the language of some TM M then •  TMS MS such that L = L(MS) • If M decides L then  TMS MS that decides L • Claim 2: If L is the language of some TMS MS then •  TM M such that L = L(M) • If MS decides L then  TM M that decides L

  3. Formal Defn of a k-tape TM A 7-Tuple (Q, , , , q0, B, F) where • Q – Set of states •  – Input alphabet (B  ) •  – Tape alphabet (  and B  ) •  – Transition Function •  : Q x k  Q x k x {L,R,S}k • q0 – Start state (q0  Q ) • B - Blank symbol • F  Q – accepting states

  4. Equivalence of MTMs and TMs • Claim 1: For all languages L, L = L(M) for some TM M if and only if L = L(M‘) for some MTM M‘ • Claim 2: For all languages L, L is decided by some TM M if and only if L is decided by some MTM M‘

  5. Construct TMS from MTM • Input: MTM M = (Q, , , , q0,B, F) • Output TMS M’ = (Q’, , ’, ’, q’0,B, F’)where ’ =   {  |    }  {#} and remainder is built using following steps • Format tape • Scan and remember • Update tape and tape head • Change to appropriate state

  6. Correctness of Constructions • Claim 1: L(M) = L(M‘) • Claim 2: For all w  * M halts on w if and only if M‘ halts on w.

More Related