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cs402 midterm solved papers mega file

Method 3 (General expressions)
Consider the language L = {Λ, x, xx, xxx,…} of the strings, defined above Σ = {x}. We can write this language as Kleene star closing for words Σ or L = Σ * = {x} *. This language can also be defined in general expression x *. Similarly the language L = {x, xx, xxx,…}, defined above Σ = {x}, can be expressed in normal expression x +. Now consider another language L, which contains all possible strings, defined above Σ = {a, b}. This language is correct.

cs402 midterm solved papers mega file
Expressed in normal expression (a + b) *. Now consider another language L, of single-stranded strings, defined above Σ = {a, b}, and then the standard the expression can be b * ab *. Now consider another language L, of longer length, defined above Σ = {a, b}, then it is the most common way of expressing ((a + b) (a + b)) *. Now think of another language L, of unequal length, defined above Σ = {a, b}, where the normal expression may be (a + b) ((a + b) (a + b)) * or ((a + b) (a + b)) * (a + b). Announce It can be known that a language can be represented by more than one common expression, while it is given in normal.

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cs402 midterm solved papers mega file

For example
Consider the language, described above  Σ = {a, b} of at least one of the words a, which can be expressed in the ordinary expression (a + b) * a (a + b) *. Think of a language, defined above Σ = {a, b} of at least one and no b words, which can be expressed by common expression (a + b) * a (a + b) * b (a + b) * + (a + b) * b (a + b) * a (a + b) *. Think of a language, defined above Σ = {a, b}, of words that begin with a double and end with a double b then normal expression can be aa (a + b) * bb Think of a language, defined above Σ = {a, b} of words beginning with a and ending in b OR it starts with a b and ends with a, then its standard expression can be a (a + b) * b + b (a + b) * Common Languages.

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cs402 midterm solved papers mega file
Definition
The language produced by any common expression is called common language. It is known that if r1, r2 are common expressions, related to languages ​​L1 and L2 and languages produced with r1 + r2, r1r2 (or r2r1) and r1 * (or r2 *) are also common languages. Be careful It should be noted that if L1 and L2 are represented by r1 and r2, respectively it means that the language is indicated by r1 + r2, language L1 + L2 or L1 ∪ L2 R1r2 ,, is the L1L2 language, of the strings obtained by naming all L1 strings with all L2 strings The r1 *, the L1 * language, of the strings obtained by combining the L-strings, including the null cord.

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cs402 midterm solved papers mega file

For example
If r1 = (aa + bb) and r2 = (a + b) then the string language made by r1 + r2 , and common language, featured by (aa + bb) + (a + b) If r1 = (aa + bb) and r2 = (a + b) then the string language produced by r1r2, is also a common, expressive language ngu (aa + bb) (a + b)
If r = (aa + bb) then the language of the strings produced by r *, is also a common, expressive language (aa + bb) * There are certain pieces of paper. Some are white and some are black. Number of 64 pieces of paper or less. Arrangements in which these pieces of paper may be placed under boxes, finished. To start the game, one of the preparations should be the initial setup. There is a dice that can produce numbers 2,3,4,… 12. For each number produced, the unique order is correlation between possible arrangements. Indicates that the total number of editing modification rules is limited. One or more edits can be which should have been a win-win arrangement. It can be seen that winning a game depends on the sequence in which the numbers are made. This game structure can be considered as a limited automaton.

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