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Exercise Show, using Suffix Substitution Closure, that L3 . L3 ∈ SL2. Explain how it can be the case that L3 . L3 ∈ SL2, while L3 . L3 ⊆ L+3 and L+3 ∈ SL2. What happens to your counterexample to SSC?
Intuitively, closure of SL 2 under intersection is reasonably easy to see, particularly if one considers the Myhill graphs of the automata. Any path through both graphs will be a
Exercise: Give a construction that converts a strictly 2-local automaton for a language L into one that recognizes the language L r . Justify the correctness of your construction.
When we say "solved algorithmically" we are not asking about a speci?c programming language, in fact one of the theorems in computability is that essentially all reasonable program
To see this, note that if there are any cycles in the Myhill graph of A then L(A) will be infinite, since any such cycle can be repeated arbitrarily many times. Conversely, if the
Give DFA''s accepting the following languages over the alphabet {0,1}: i. The set of all strings beginning with a 1 that, when interpreted as a binary integer, is a multiple of 5.
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
In Exercise 9 you showed that the recognition problem and universal recognition problem for SL2 are decidable. We can use the structure of Myhill graphs to show that other problems
We'll close our consideration of regular languages by looking at whether (certain) problems about regular languages are algorithmically decidable.
How useful is production function in production planning?
A finite, nonempty ordered set will be called an alphabet if its elements are symbols, or characters. A finite sequence of symbols from a given alphabet will be called a string ove
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