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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.
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Another way of interpreting a strictly local automaton is as a generator: a mechanism for building strings which is restricted to building all and only the automaton as an inexh
For example, the question of whether a given regular language is positive (does not include the empty string) is algorithmically decidable. "Positiveness Problem". Note that
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Computer has a single unbounded precision counter which you can only increment, decrement and test for zero. (You may assume that it is initially zero or you may include an explici
Both L 1 and L 2 are SL 2 . (You should verify this by thinking about what the automata look like.) We claim that L 1 ∪ L 2 ∈ SL 2 . To see this, suppose, by way of con
. 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
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Proof (sketch): Suppose L 1 and L 2 are recognizable. Then there are DFAs A 1 = (Q,Σ, T 1 , q 0 , F 1 ) and A 2 = (P,Σ, T 2 , p 0 , F 2 ) such that L 1 = L(A 1 ) and L 2 = L(
We will specify a computation of one of these automata by specifying the pair of the symbols that are in the window and the remainder of the string to the right of the window at ea
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