Concatenation, Theory of Computation

Assignment Help:

We saw earlier that LT is not closed under concatenation. If we think in terms of the LT graphs, recognizing the concatenation of LT languages would seem to require knowing, while scanning a string in L1 . L2, for instance, when to switch from keeping track of factors for L1 to keeping track of factors from L2.

Assuming that the alphabets were not disjoint, there is (evidently, since LT is not closed under concatenation) no way, in general, to know that. For the recognizable languages, on the other hand, we have the convenience of being able to work with non-determinism. We don't actually have to know when to switch from one automaton to the next. Whenever we get to a point in the string that could possibly be the end of the pre?x that is in L1 we can just allow for a non-deterministic choice of whether to continue scanning for A1 (the machine recognizing L1) or to switch to scanning for A2. Since whenever the string is in L1 .  L2 there will be some correct place to switch and since acceptance by a NFA requires only that there some accepting computation, the combined automaton will accept every string in L1 . L2. Moreover, the combined automaton will accept a string iff there is some point at which it can be split into a string accepted by A1 followed by one accepted by A2: it accepts all and only the strings in L1 . L2.


Related Discussions:- Concatenation

Turing machine, Can v find the given number is palindrome or not using turi...

Can v find the given number is palindrome or not using turing machine

Myhill graph of the automaton, Exercise:  Give a construction that converts...

Exercise:  Give a construction that converts a strictly 2-local automaton for a language L into one that recognizes the language L r . Justify the correctness of your construction.

Deterministic finite state automaton, De?nition Deterministic Finite State ...

De?nition Deterministic Finite State Automaton: For any state set Q and alphabet Σ, both ?nite, a ?nite state automaton (FSA) over Q and Σ is a ?ve-tuple (Q,Σ, T, q 0 , F), w

Closure properties of recognizable languages, We got the class LT by taking...

We got the class LT by taking the class SL and closing it under Boolean operations. We have observed that LT ⊆ Recog, so certainly any Boolean combination of LT languages will also

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

Suffix substitution , Exercise Show, using Suffix Substitution Closure, tha...

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

Production, How useful is production function in production planning?

How useful is production function in production planning?

Applying the pumping lemma, Applying the pumping lemma is not fundamentally...

Applying the pumping lemma is not fundamentally di?erent than applying (general) su?x substitution closure or the non-counting property. The pumping lemma is a little more complica

Chomsky-schutzenberger, The upper string r ∈ Q+ is the sequence of states v...

The upper string r ∈ Q+ is the sequence of states visited by the automaton as it scans the lower string w ∈ Σ*. We will refer to this string over Q as the run of A on w. The automa

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