Closure properties of recognizable languages, Theory of Computation

Assignment Help:

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 be recognizable. But what about the class of recognizable languages as a whole? Are Boolean combinations of recognizable (not just LT) languages also recognizable. In answering we can use the same methodology we use to show that any language is recognizable: consider what we need to keep track of in scanning a string in order to determine if it belongs to the language or not and then use that information to build our state set.

Suppose, then, that L = L1 ∩ L2, where L1 and L2 are both recognizable. A string w will be in L iff it is in both L1 and L2. Since they are recognizable there exist DFAs A1 and A2 for which L1 = L(A1) and L2 = L(A2). We can tell if the string is in L1 or L2 simply by keeping track of the state of the corresponding automaton. We can tell if it is in both by keeping track of both states simultaneously.


Related Discussions:- Closure properties of recognizable languages

Production, How useful is production function in production planning?

How useful is production function in production planning?

Decision Theroy, spam messages h= 98%, m= 90%, l= 80% non spam h=12%, m = 8...

spam messages h= 98%, m= 90%, l= 80% non spam h=12%, m = 8%, l= 5% The organization estimates that 75% of all messages it receives are spam messages. If the cost of not blocking a

Production, How useful is production function in production planning?

How useful is production function in production planning?

Flow charts, https://www.google.com/search?q=The+fomula+n%3D%28x%3D0%29%2F%...

https://www.google.com/search?q=The+fomula+n%3D%28x%3D0%29%2F%281%3D2%29.The+value+x%3D0+and+is+used+to+stop+the+algerithin.The+calculation+is+reapeated+using+values+of+x%3D0+is+in

Mealy machine, Construct a Mealy machine that can output EVEN or ODD Accord...

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

Operator p, implementation of operator precedence grammer

implementation of operator precedence grammer

Gephi, construct a social network from the real-world data, perform some si...

construct a social network from the real-world data, perform some simple network analyses using Gephi, and interpret the results.

Equivalence of nfas and dfas, In general non-determinism, by introducing a ...

In general non-determinism, by introducing a degree of parallelism, may increase the accepting power of a model of computation. But if we subject NFAs to the same sort of analysis

Pushdown automator, draw pda for l={an,bm,an/m,n>=0} n is in superscript

draw pda for l={an,bm,an/m,n>=0} n is in superscript

Gdtr, What is the purpose of GDTR?

What is the purpose of GDTR?

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