Download e-book for iPad: Theory of Computation: An Introduction (Jones and Bartlett by James L. Hein

By James L. Hein

ISBN-10: 0867204974

ISBN-13: 9780867204971

This article deals scholars a delicately built and entire advent to the formal good judgment utilized in good judgment programming languages and computerized reasoning structures. the writer contains many illustrative examples to aid scholars clutch recommendations. broad workout units stick to each part to instantly strengthen strategies because the pupil is brought to them. Many very good tables and illustrations are integrated to extra support scholars conceptualize grammars and transitions.

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Extra info for Theory of Computation: An Introduction (Jones and Bartlett Books in Computer Science)

Example text

The statement S =>+ aab means that there exists a derivation of aab that takes one or more steps. For example, we have S => AB = aAB z: aaAB > aaB => aabB =* aab. When a grammar contains more than one nonterminal-as the preceding grammar does-it may be possible to find several different derivations of the same string. Two kinds of derivations are worthy of note. A derivation is called a leftmost derivation if at each step the leftmost nonterminal of the sentential form is reduced by some production.

Another way to combine functions is to create a tuple of functions. For example, given the pair of functions f : A -) B and g . A -- C, we can define the function (f, g) by (f , g)(x) = (f(x), g(x)). The function (f, g) has type A --ý B x C. The definition for a tuple of two functions can be extended easily to an n-tuple of functions, (f 1 , f 2, ... , fn). We can also compose tuples of functions with other functions. Suppose we are given the following three functions: 30 Elementary Notions and Notations f:A->B, g:A-4C, and h:BxC-*D.

The sequence a, b, c, a is a cycle, but the sequence a, b, a is not a cycle because the edge from a to b occurs twice. 4 The length of a walk (also trail and path) is the number of edges on it. So the length of the walk x0 , ... , xn is n. 4, the path a, b, d has length two and the cycle a, b, c, a has length three. Let's emphasize here that the definitions for walk, trail, path, and cycle apply to both graphs and directed graphs. But now we come to an idea that needs a separate definition for each type of graph.

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Theory of Computation: An Introduction (Jones and Bartlett Books in Computer Science) by James L. Hein


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