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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.
The generalization of the interpretation of strictly local automata as generators is similar, in some respects, to the generalization of Myhill graphs. Again, the set of possible s
A.(A+C)=A
Distinguish between Mealy and Moore Machine? Construct a Mealy machine that can output EVEN or ODD According to the total no. of 1's encountered is even or odd.
The path function δ : Q × Σ*→ P(Q) is the extension of δ to strings: Again, this just says that to ?nd the set of states reachable by a path labeled w from a state q in an
Claim Under the assumptions above, if there is an algorithm for checking a problem then there is an algorithm for solving the problem. Before going on, you should think a bit about
Another way of representing a strictly 2-local automaton is with a Myhill graph. These are directed graphs in which the vertices are labeled with symbols from the input alphabet of
how to find whether the language is cfl or not?
Find a regular expression for the regular language L={w | w is decimal notation for an integer that is a multiple of 4}
The upper string r ∈ Q+ is the sequence of states visited by the automaton as it scans the lower string w ∈ Σ*. We will refer to this string over Q as the run of A on w. The automa
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
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