Module09 - Module 9 Closure Properties Definition Language...

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1 Module 9 Closure Properties Definition Language class definition set of languages Closure properties and first-order logic statements For all, there exists
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2 Closure Properties A set is closed under an operation if applying the operation to elements of the set produces another element of the set Example/Counterexample set of integers and addition set of integers and division
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3 Integers and Addition Integers 2 5 7
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4 Integers and Division Integers 2 5 .4
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5 Language Classes We will be interested in closure properties of language classes A language class is a set of languages Thus, the elements of a language class (set of languages) are languages which are sets themselves Crucial Observation When we say that a language class is closed under some set operation, we apply the set operation to the languages (elements of the language classes) rather than the language classes themselves
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6 Example Language Classes *
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Module09 - Module 9 Closure Properties Definition Language...

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