Two-tape turing machine, Theory of Computation

Assignment Help:

Let there L1 and L2 . We show that L1 ∩ L2 is CFG .

Let M1 be a decider for L1 and M2 be a decider for L2 .

Consider a 2-tape TM M:

"On input x:

1. copy x on the second tape

2. on the ?rst tape run M1 on x

M=

3. if M1 accepted then goto 4. else M rejects

4. on the second tape run M2 on x

5. if M2 accepted then M accepts else M rejects."

The machine M is a decider and it accepts a string x i? both M1 and M2 accept x.

Two-tape TM is as expressive as the single tape TM.

The process is as follows

"Given a CFG G and a string w , does G generate w ?

Language Formulation (Acceptance Problem for CFG) def

ACFG = {?G , w ? | G is a CFG, w a string and w ∈ L(G )}

The language ACFG is decidable.

 Construct a decider M for ACFG :M = " 1. On input x check if x = ?G , w ? where

G is an CFG and w is a string, if not then M rejects.

2. Convert G into Chomsky normal form.

3. List all derivations in G of length exactly 2|w | - 1,

if w = ? then check if there is the rule S → ?.

4. If w is ever generated then M accepts, else M rejects."


Related Discussions:- Two-tape turing machine

Qbasic, Ask question #Minimum 100 words accepte

Ask question #Minimum 100 words accepte

Moore machine, Construct a Moore machine to convert a binary string of radi...

Construct a Moore machine to convert a binary string of radix 4.

Turing machine, Design a turing machine to compute x + y (x,y > 0) with x a...

Design a turing machine to compute x + y (x,y > 0) with x an y in unary, seperated by a # (descrition and genereal idea is needed ... no need for all TM moves)

Toc, how to understand DFA ?

how to understand DFA ?

Finiteness of languages is decidable, To see this, note that if there are a...

To see this, note that if there are any cycles in the Myhill graph of A then L(A) will be infinite, since any such cycle can be repeated arbitrarily many times. Conversely, if the

Gdtr, What is the purpose of GDTR?

What is the purpose of GDTR?

Strictly 2 - local automata, We will assume that the string has been augmen...

We will assume that the string has been augmented by marking the beginning and the end with the symbols ‘?' and ‘?' respectively and that these symbols do not occur in the input al

First model of computation, Computer has a single unbounded precision count...

Computer has a single unbounded precision counter which you can only increment, decrement and test for zero. (You may assume that it is initially zero or you may include an explici

Example of finite state automaton, The initial ID of the automaton given in...

The initial ID of the automaton given in Figure 3, running on input ‘aabbba' is (A, aabbba) The ID after the ?rst three transitions of the computation is (F, bba) The p

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd