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

Pojects idea, i want to do projects for theory of computation subject what ...

i want to do projects for theory of computation subject what topics should be best.

Find regular grammar : a(a+b)*(ab*+ba*)b, Find the Regular Grammar for the ...

Find the Regular Grammar for the following Regular Expression:                    a(a+b)*(ab*+ba*)b.

Kleene closure, So we have that every language that can be constructed from...

So we have that every language that can be constructed from SL languages using Boolean operations and concatenation (that is, every language in LTO) is recognizable but there are r

Kleene Closure, 1. Does above all''s properties can be used to prove a lang...

1. Does above all''s properties can be used to prove a language regular? 2..which of the properties can be used to prove a language regular and which of these not? 3..Identify one

#titl, matlab v matlab

matlab v matlab

Data retriving, i have research method project and i meef to make prposal w...

i have research method project and i meef to make prposal with topic. If this service here please help me

Decision problems of regular languages, We'll close our consideration of re...

We'll close our consideration of regular languages by looking at whether (certain) problems about regular languages are algorithmically decidable.

Transition graphs, We represented SLk automata as Myhill graphs, directed g...

We represented SLk automata as Myhill graphs, directed graphs in which the nodes were labeled with (k-1)-factors of alphabet symbols (along with a node labeled ‘?' and one labeled

Boolean operations - class of recognizable languages, Theorem The class of ...

Theorem The class of recognizable languages is closed under Boolean operations. The construction of the proof of Lemma 3 gives us a DFA that keeps track of whether or not a give

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