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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 over the alphabet. A string that consists of a sequence a1, a2, . . . , an of symbols will be denoted by the juxtaposition a1a2 an. Strings that have zero symbols, called empty strings, will be denoted by .
{0, 1} is a binary alphabet, and {1} is a unary alphabet. 11 is a binary string over the alphabet {0, 1}, and a unary string over the alphabet {1}.
11 is a string of length 2, |ε| = 0, and |01| + |1| = 3.
Example-The string consisting of a sequence αβ followed by a sequence β is denoted αβ. The string αβ is called the concatenation of α and β. The notation αi is used for the string obtained by concatenating i copies of the string α.
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A common approach in solving problems is to transform them to different problems, solve the new ones, and derive the solutions for the original problems from those for the new ones
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
Can you say that B is decidable? If you somehow know that A is decidable, what can you say about B?
The fundamental idea of strictly local languages is that they are speci?ed solely in terms of the blocks of consecutive symbols that occur in a word. We'll start by considering lan
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
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