Does anyone know how to answer this problem? SAE Grammar Let\'s create a grammar

Question

Does anyone know how to answer this problem?

SAE Grammar

Let's create a grammar for the SAE langauge. Before doing so, we'll assume the following simplifications:

“x” stands for any number or variable identifier

“p” stands for plus '+' or minus '-'

“m” stands for multiplication '*' or division '/'

@ is a terminal symbol

With these assumptions in mind, here's our SAE grammar:

Notice that this grammar is a Regular Grammar since each of the productions conforms to the constraints introduced in the beginning of this section.

S ? ( B ? x C B ? x C ? ( B C ? p D ? m D ? ) E ? @ D ? x C ? ( B E ? ) E ? p S ? m S ? @

Explanation / Answer

Definations:

Given - SAE Langauage to secify the constriants in the simplifications for lingustics.

'x' stands for any numbers

'p' stands for plus '+' or minus '-'

'm' stands for multiplications '*'.

'm' stands for divisions '/'.

@ is a terminal symbol.

SAE - Regular Language it can be expressed in regular expressions :

Definite Closure Properties of Regular Languages will be:

1. Union : If X and If Y are two regular languages, their union X ? Y will also be regular. For example: X = {an | n ? 0} and Y = {bn | n ? 0} & Z = X ? Y = {an? bn | n ? 0} is also regular.

2. Intersection : If X and If Y are two regular languages, their intersection X ? Y will also be regular. For example:  X = {am bn | n ? 0 and m ? 0} and Y = {am bn? bn am | n ? 0 and m ? 0}
Z = L1 ? L2 = {am bn | n ? 0 and m ? 0} is also regular.

3. Concatenation : If X and If Y are two regular languages, their concatenation X.Y will also be regular. For example:  X = {an | n ? 0} and L2 = {bn | n ? 0} Z = X.Y = {am . bn | m ? 0 and n ? 0} is also regular.

4. Closure : If X is a regular language, its closure Y* will also be regular. For example: X = (a ? b) Y = (a ? b)*

5. Complement : If X(G) is regular language, its complement X’(G) will also be regular. Complement of a language can be found by subtracting strings which are in L(G) from all possible strings. For example:
X(G) = {an | n > 3}
X’(G) = {an | n <= 3}

Thus, Overall expression cab be identified with Logical expression LE = { x,p,m,@} i.e., Logical operators { +,-,*,/} are considered to be SME regular expression languages.

Langauage Grammar Expressions S Union ( B Intersection xC Concatenation Closures Complement B Union xC Intersection xB Concatneation closures Complement C Union p D Intersection m D Concatnenation

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