Peter J. L. Wallis's Ada Software Tools Interfaces: Workshop, Bath, July 13–15, PDF

By Peter J. L. Wallis

ISBN-10: 3540138781

ISBN-13: 9783540138785

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Extra resources for Ada Software Tools Interfaces: Workshop, Bath, July 13–15, 1983 Proceedings

Example text

An example of this is the language {an bn | n ≥ 0}, that is, any sequence of as followed by a sequence of the same number of bs. If we must decide membership in this language by a DFA that reads the input from left to right, we must, at the time we have read all the as, know how many there were, so we can compare this to the number of bs. But since a finite automaton cannot count arbitrarily high, the language is not regular. A similar non-regular language is the language of matching parentheses.

We can use this method for calculating the epsilon-closure of the set {1} with respect to the NFA shown in Fig. 5. Since we want to find ε-closure({1}), M = {1}, so FM = F{1} . 5 Converting an NFA to a DFA 15 As ∅ ̸= {1}, we continue. F{1} ({1}) = {1} ∪ {t | s ∈ {1} and s ε t ∈ T } = {1} ∪ {2, 5} = {1, 2, 5} F{1} ({1, 2, 5}) = {1} ∪ {t | s ∈ {1, 2, 5} and s ε t ∈ T } = {1} ∪ {2, 5, 6, 7} = {1, 2, 5, 6, 7} F{1} ({1, 2, 5, 6, 7}) = {1} ∪ {t | s ∈ {1, 2, 5, 6, 7} and s ε t ∈ T } = {1} ∪ {2, 5, 6, 7} = {1, 2, 5, 6, 7} We have now reached a fixed-point and found our solution.

4 will treat these differently and may hence decree a group to be inconsistent even though it is not. This will make the algorithm split a group that does not need to be split, hence producing a non-minimal DFA. Consider, for example, the following DFA: a start b 3 2 1 a States 1 and 2 are, in fact, equivalent, as starting from either one, any sequence of a’s (and no other sequences) will lead to an accepting state. A minimal equivalent DFA has only one accepting state with a transition to itself on a.

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Ada Software Tools Interfaces: Workshop, Bath, July 13–15, 1983 Proceedings by Peter J. L. Wallis

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