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

Discrete math, Find the Regular Grammar for the following Regular Expressio...

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

Grammer, write grammer to produce all mathematical expressions in c.

write grammer to produce all mathematical expressions in c.

Brain game, If the first three words are the boys down,what are the last th...

If the first three words are the boys down,what are the last three words??

Third model of computation, Computer has a single LIFO stack containing ?xe...

Computer has a single LIFO stack containing ?xed precision unsigned integers (so each integer is subject to over?ow problems) but which has unbounded depth (so the stack itself nev

Complement - operations on languages, The fact that SL 2 is closed under i...

The fact that SL 2 is closed under intersection but not under union implies that it is not closed under complement since, by DeMorgan's Theorem L 1 ∩ L 2 = We know that

Recognition problem, The Recognition Problem for a class of languages is th...

The Recognition Problem for a class of languages is the question of whether a given string is a member of a given language. An instance consists of a string and a (?nite) speci?cat

Overview of dfa, Explain Theory of Computation ,Overview of DFA,NFA, CFG, P...

Explain Theory of Computation ,Overview of DFA,NFA, CFG, PDA, Turing Machine, Regular Language, Context Free Language, Pumping Lemma, Context Sensitive Language, Chomsky Normal For

Deterministic finite automata, conversion from nfa to dfa 0 | 1 ____...

conversion from nfa to dfa 0 | 1 ___________________ p |{q,s}|{q} *q|{r} |{q,r} r |(s) |{p} *s|null |{p}

Myhill-nerode theorem, This close relationship between the SL2 languages an...

This close relationship between the SL2 languages and the recognizable languages lets us use some of what we know about SL 2 to discover properties of the recognizable languages.

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