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
We have now de?ned classes of k-local languages for all k ≥ 2. Together, these classes form the Strictly Local Languages in general. De?nition (Strictly Local Languages) A langu

The universe of strings is a very useful medium for the representation of information as long as there exists a function that provides the interpretation for the information carrie

Paths leading to regions B, C and E are paths which have not yet seen aa. Those leading to region B and E end in a, with those leading to E having seen ba and those leading to B no

These assumptions hold for addition, for instance. Every instance of addition has a unique solution. Each instance is a pair of numbers and the possible solutions include any third

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

The class of Strictly Local Languages (in general) is closed under • intersection but is not closed under • union • complement • concatenation • Kleene- and positive


Prove that Language is non regular TRailing count={aa ba aaaa abaa baaa bbaa aaaaaa aabaaa abaaaa..... 1) Pumping Lemma 2)Myhill nerode

Suppose A = (Q,Σ, T, q 0 , F) is a DFA and that Q = {q 0 , q 1 , . . . , q n-1 } includes n states. Thinking of the automaton in terms of its transition graph, a string x is recogn

De?nition (Instantaneous Description) (for both DFAs and NFAs) An instantaneous description of A = (Q,Σ, δ, q 0 , F) , either a DFA or an NFA, is a pair h q ,w i ∈ Q×Σ*, where