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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.
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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Suppose G = (N, Σ, P, S) is a reduced grammar (we can certainly reduce G if we haven't already). Our algorithm is as follows: 1. Define maxrhs(G) to be the maximum length of the
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
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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DEGENERATE OF THE INITIAL SOLUTION
The Equivalence Problem is the question of whether two languages are equal (in the sense of being the same set of strings). An instance is a pair of ?nite speci?cations of regular
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