Before closure : vernacular conclusion is that the original prefix string comprises all the language L All The prefixes of strings in L The All .
If the same language L and its previous closures, it can be said that the language L is closed before ( prefix-Closed )
Star Closure : operation of the E mentioned earlier is the same, in addition there is a word personally think is worth learning about - Note that at The IS * Operation idempotent: (L *) * = L *.
In its explanation of the theory of programming as " any of its impact on the resources themselves repeatedly produced all the effects of the first execution of the same ."
Post-language
The operator did not see the later case, for the time being labeled as ※, there is a need to add the latter.
Observe that in expressions invovling several operations on languages, prefix-closure and Kleene-closerure should be applied first, and concatenation always precedes operations such as union, intersection, and set difference.(This was implicitly assumed in the above definition of L*)
The calculation means is higher than the priority and complement difference.
Example 2.1
I said earlier so-called empty set, this translation may cause some deviation, here given precise explanations of the "empty set" non-empty language which contains only an empty string .
Remaining a look at a few well-understood to understand, difficult to understand to back down,
Projections of Strings and Languages
Natural and simple projection projection (natural projection and simple projection)
l to s (large to small) containing small to large
Definition of the abstract book quite simple explanation is given for the El and Es, l to s call this mapping operation, the calculation method is the eliminating of a small set of elements from the remaining elements in the large collection, then the element is made from the operation of the P, so called natural mapping.
The inverse mapping
Inverse mapping
First, the concept of power set: SET A 2 and A means A. The Power of SET is the set of all subsets of A.
Then say what concrete operational mapping and inverse mapping, understanding this part of me is consuming effort, mostly because of their own stupid, right ???? I'm going to explain in simple words and then go take a closer look to understand this formula more thorough.
In the extended to the language L mapping calculation, L is contained in the satellite bag large collection, a calculation result in the elements belonging to a small set of satellite bags, concrete operational principle L of elements is s, each s are mapping operation is made large to a small set from the set, first removed from the large collection is not small set of elements, and then compared with the L s s left like elements in such a composition is set mappings P L (L). This explanation is more straightforward but can help us better understand.
Inverse mapping, the same we can get from custom formula, language Ls is included Star package for small collections, the inverse mapping result elements are s, s is an element belonging to a small star package, its operation principle is the target language Ls, the elements of a large bag of star mapping operations to meet its operational result to find an element t, s set of such composition is the result of the inverse mapping.
Natural projection plays an important role in the DES, the following are some of the nature of the book, I proved to be very interested in these properties, to be later learning knowledge will make a proof.
Representation of Languages
A simple word to pave the way for the next section