# Download Algorithms: Their complexity and efficiency by Lydia I. Kronsjo PDF

By Lydia I. Kronsjo

ISBN-10: 0471912018

ISBN-13: 9780471912019

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Extra resources for Algorithms: Their complexity and efficiency

Example text

Are called states, and a subset of them, in this case qo and ql' are termed accepting states. The state qo is called the start state. We summarize the structure of these devices with the following definition. 2 Definition. Ajinite-state acceptor (FSA) M with input alphabet X is specified by a quadruple (Q, b, qo, F) where Q is a finite set of states (): Q x X ~ Q is the transition function qo E Q is the initial state F c Q is the set of accepting states. 3 Languages and Automata Theory: A First Look 3 Example.

The one-element subset {1Oll} of X*) is accepted by the machine The state q5 (like the state ql of the previous example) is a trap - it is a nonaccepting state wth the property that once M enters it, M never leaves it: (j(q5' x) = q5 for each x in X. We may simplify state diagrams by omitting all trap states and the edges which lead to them. Thus the above state graph can be abbreviated to it being understood that each missing transition leads to a single trap state. 2---l~Er ... ~ (Why does this diagram only show n + 1 states?

Petunias, V -. trampled tell us the parts of speech to which various words of English belong. ). Nonetheless, context1ree grammars - grammars whose grammatical rules are all of the simple replacement kind shown in Figure 10 - have played a 54 2 Induction, Strings, and Languages ~s~ ~p~ VP .............. ~ I~ Adj N I I I ~ I Det The ugly elephant ............ NP D~t~N I trampled the I petunias. Figure 10 useful role in mathematical linguistics. Grammatical systems of this kind are also extremely important in computer science.