CS402 Final Term Short Notes

CS402 Short Notes

Q No 1 What is the difference between the strings and the words of a language?

Answer: A string is any combination of the letters of an alphabet where as the words of a language are the strings that are always made according to certain rules used to define that language. For example if we take Alphabet ぇ = { a , b } Here a , b are the letters of this alphabet. As you can see we can make a lot of strings from these letters a and b. For example a,b,aa,ab,ba,bb,aaa,aab,aba,baa,....................................................... ..... and so on. But when we define a language over this alphabet having no a's and only odd number of b's. Then the words of this language would have only those strings that have only odd number of b's and no a's.some example words of our defined language are b , bbb , bbbbb , bbbbbbb ,...................................and so on. So we can say that all the words are strings but all the strings may not be the words of a language. Hence strings are any combination of letters of an alphabet and the words of a language are strings made according to some rule. QNo.2 What is the difference between an Alphabet and an element of a set. Whether Alphabet is an element of a set or it is a set itself?

Answer: An Alphabet is a set in itself. The elements of an Alphabet are called letters .

Binary Alphabet ぇ = {0,1} Here 0,1 are the letters of binary alphabet. Binary Alphabet is very important because it the Alphabet used by the computer. Set of Natural Numbers N={1,2,3,4,5,. .................. } Here 1,2,3........................................... are the elements of set of Natural Numbers. Q No.3 What is Null String () ?

Answer: The string with zero occurrences of symbols (letters) from

It is denoted by (Small Greek letter Lambda) そ or (Capital Greek letter Lambda) , is called an empty string or null string. The capital lambda will mostly be used to denote the empty string, in further discussion. Q No.4 What is PALINDROME ?

Answer: The language consisting of (Null String) and the strings s defined over an Alphabet ぇ such that Rev(s)=s. Some example words of this language are aa As Rev(aa) = aa aba As Rev(aba) = aba bbb As Rev(bbb) = bbb aabaa As Rev(aabaa) = aabaa bbbaaabbb As Rev( bbbaaabbb ) = bbbaaabbb It is to be noted that the words of PALINDROME are called palindromes. QNo5. What is the concept of valid and invalid alphabets ? Answer:While defining an alphabet of letters consisting of more than one symbols, no letter should be started with any other the letter of the same alphabet i.e. one letter should not be the prefix of another. However, a letter may be ended in the letter of same alphabet i.e. one letter may be the suffix of another.

ぇ= { a , b } ( Valid Alphabet)

ぇ= { a , b , cd } ( Valid Alphabet)

ぇ= { a , b , ac } ( Invalid Alphabet) QNo 6. What is ALGOL ?

Answer: ALGOL (ALGOrithmic Language) is one of several high level languages designed specifically for programming scientific computations. It started out in the late 1950's, first formalized in a report titled ALGOL 58, and then progressed through reports ALGOL 60, and ALGOL 68. It was designed by an international committee to be a universal language. Their original conference, which took place in Zurich, was one of the first formal attempts to address the issue of software portability. ALGOL's machine independence permitted the designers to be more creative, but it made implementation much more difficult. Although ALGOL never reached the level of commercial popularity of FORTRAN and COBOL, it is considered the most important language of its era in terms of its influence on later language development. ALGOL’s lexical and syntactic structures became so popular that virtually all languages designed since have been referred to as "ALGOL - like"; that is they have been hierarchical in structure with nesting of both environments and control structures. QNo7. What are the Sequential Operators? Answer:Sequencing Operators: Sequencing operators a >> b Sequence Match a and b in sequence

a && b Sequentialand

Sequential-and. Same as above, match a and b in sequence a || b Sequential-or Match a or b in sequence The sequencing operator >> can alternatively be thought of as the sequential-and operator. The expression a && breads as match a and b in sequence. Continuing this logic, we can also have a sequential-or operator where the expression a || b reads as match a or b and in sequence. That is, if both a and b match, it must be in sequence; this is equivalent to a >> !b | b. QNo 8.What is Non-Determinism and Determinism and what is the difference between them ?

Answer: Determinism means that our computational model (machine) knows what to do for every possible inputs. Non determinism our machine may or may not know what it has to do on all possible inputs. As you can conclude from above definition that Non-Deterministic machine can not be implemented ( used ) on computer unless it is converted in Deterministic machine. QNo 9. What is meant by equivalent FA's ?

Answer: FA's that accept the same set of languages are called Equivalent FA's. QNo 10. What is the difference between Palindrome and Reverse function?

Answer: It is to be denoted that the words of PALINDROME are called palindromes. Reverse (w) = w Example: ぇ={a,b}, PALINDROME={ , a, b, aa, bb, aaa, aba, bab, bbb, ...} If a is a word in some language L, then reverse (a) is the same string of letters spelled backwards, called the reverse of a. e.g reverse (xxx) = xxx reverse (623) = 326 reverse (140) = 041 QNo11. Define Kleene Star?

Answer: Given ぇ, then the Kleene Star Closure of the alphabet ぇ, denoted by ぇ *, is the collection of all strings defined over ぇ , including ೦ It is to be noted that Kleene Star Closure can be defined over any set of strings. Examples If ぇ = {x}

{0,1} Then ぇ* = {೦, 0, 1, 00, 01, 10, 11, ….}

If ぇ = {aaB, c}

Then ぇ* = {೦, aaB, c, aaBaaB, aaBc, caaB, cc, ….} Note: Languages generated by Kleene Star Closure of set of strings, are infinite languages. (By infinite language, it is supposed that the language contains infinite many words, each of finite length) QNo12. Valid/In-Valid alphabets?