Class of recognizable languages, Theory of Computation

Proof (sketch): Suppose L1 and L2 are recognizable. Then there are DFAs A1 = (Q,Σ, T1, q0, F1) and A2 = (P,Σ, T2, p0, F2) such that L1 = L(A1) and L2 = L(A2). We construct A′ such that L(A′ ) = L1 ∩ L2. The idea is to have A′ run A1 and A2 in parallel-keeping track of the state of both machines. It will accept a string, then, iff both machines reach an accepting state on that string.

Let A′ = (Q × P,Σ, T′ , (q0, p0), F1 × F2), where

T′ def= [{((q, pi, (q′, p′), σ) | (q, q′, σi)∈ T1 and (p, p′, σ ∈ T2}.

2294_Class of recognizable languages.png

Then

(You should prove this; it is an easy induction on the structure of w.) It follows then that

751_Class of recognizable languages1.png

Posted Date: 3/21/2013 3:13:26 AM | Location : United States







Related Discussions:- Class of recognizable languages, Assignment Help, Ask Question on Class of recognizable languages, Get Answer, Expert's Help, Class of recognizable languages Discussions

Write discussion on Class of recognizable languages
Your posts are moderated
Related Questions
All that distinguishes the de?nition of the class of Regular languages from that of the class of Star-Free languages is that the former is closed under Kleene closure while the lat

Distinguish between Mealy and Moore Machine? Construct a Mealy machine that can output EVEN or ODD According to the total no. of 1's encountered is even or odd.


Another striking aspect of LTk transition graphs is that they are generally extremely ine?cient. All we really care about is whether a path through the graph leads to an accepting


Another way of interpreting a strictly local automaton is as a generator: a mechanism for building strings which is restricted to building all and only the automaton as an inexh

build a TM that enumerate even set of even length string over a

DEGENERATE OF THE INITIAL SOLUTION

Exercise Show, using Suffix Substitution Closure, that L 3 . L 3 ∈ SL 2 . Explain how it can be the case that L 3 . L 3 ∈ SL 2 , while L 3 . L 3 ⊆ L + 3 and L + 3 ∈ SL