Boolean operations - class of recognizable languages, Theory of Computation

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 given string is in either or both of any pair of recognizable languages. We can modify the construction for other Boolean operations simply by selecting the appropriate set of accepting states:

• Union: Let F′

= {(q, p) | q ∈ F1 or p ∈ F2}. Then L(A′ ) = L1 ∪ L2.

• Relative complement: Let F′ = F1 × (Q2 - F2). Then L(A′ ) = L1 -L2.

• Complement: Let L1 = Σ* and use the construction for relative complement.

Posted Date: 3/21/2013 3:15:49 AM | Location : United States







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

Write discussion on Boolean operations - class of recognizable languages
Your posts are moderated
Related Questions
The fact that the Recognition Problem is decidable gives us another algorithm for deciding Emptiness. The pumping lemma tells us that if every string x ∈ L(A) which has length grea

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

Computer has a single FIFO queue of ?xed precision unsigned integers with the length of the queue unbounded. You can use access methods similar to those in the third model. In this

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

How useful is production function in production planning?


shell script to print table in given range

. On July 1, 2010, Harris Co. issued 6,000 bonds at $1,000 each. The bonds paid interest semiannually at 5%. The bonds had a term of 20 years. At the time of issuance, the market r

A common approach in solving problems is to transform them to different problems, solve the new ones, and derive the solutions for the original problems from those for the new ones

Strictly 2-local automata are based on lookup tables that are sets of 2-factors, the pairs of adjacent symbols which are permitted to occur in a word. To generalize, we extend the