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LTO was the closure of LT under concatenation and Boolean operations which turned out to be identical to SF, the closure of the ?nite languages under union, concatenation and complement. In moving from LT to Recog, we picked up the closure under concatenation and also added closure under Kleene closure (also known as "Kleene-∗" and "iteration closure"). Kleene closure was introduced by Stephen Kleene in his de?nition of the Regular Languages, the closure of the ?nite languages under union, concatenation and Kleene closure.
A problem is said to be unsolvable if no algorithm can solve it. The problem is said to be undecidable if it is a decision problem and no algorithm can decide it. It should be note
(c) Can you say that B is decidable? (d) If you somehow know that A is decidable, what can you say about B?
design an automata for strings having exactly four 1''s
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We'll close our consideration of regular languages by looking at whether (certain) problems about regular languages are algorithmically decidable.
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
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s-> AACD A-> aAb/e C->aC/a D-> aDa/bDb/e
One might assume that non-closure under concatenation would imply non closure under both Kleene- and positive closure, since the concatenation of a language with itself is included
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