Further mare in pumping lemma I we have to generate all words to of a language but in Pumping Lemma II we have to generate a single word to prove a language non regular.Explanation:Some languages like PALINDROME that are proved to be regular by first versiondue to some of their symmetrical words when we pump these words they remain to bethe parts of the language likebbabbBy pumping lemma 1Let y = aNow repeating y three times results inbbaaabbThat is also a valid word of PALINDROME so by pumping lemma I PALINDROME can not be proved non regular, so there was the need of pumping lemma version version 2.Now consider for the wordbbabbif we take N=2Then by pumping y (let we take it b ) two times results inbbbbabbThat word is not in PALINDROME.But if we take N=3 and y = aThen by pumping y two times results inbbaaabbThat word is in PALINDROME. So be careful in taking total no of states of the FAand also the repeating factor (y) to prove an infinite language non regular youneed to prove only one word that is not part of the language.Q No 2. What is the significance of Pumping Lemma II ?The significance of 2nd version of ‘pumping lemma’ is that there are some infinite non regular languages like PALINDROME we can built FA that can accept there certain words but if we increase the length of their words that FA don’t accept these words so by pumping lemma version I it is very difficult to prove them non regular but with the
second version we can prove that a language is Non regular even it’s some words may be accepted by some FA’s.See page 195 of the book for further example.Q No 3.Moore and Mealy machine?1. In order to run a string on a Mealy or Moore machine, you can take directions from transition table. Running string on Mealy or Moore machine is similar to running string ona FA. For example, if want to run abba on the machine, take start from initial state. Check what is the transition for a, what state it goes. After that check what is the path ofb from that state and so on. In this way you will be able to run whole of the string. Note that there is no final state in Mealy or Moore machine. So there is no case of acceptance or rejection of string. You just have to determine what the output is. I hope that will clear your mind for further clarification please listens to your lecture carefully.2. The string is taken for the testing purposes. You can take any sort of string and determine its output using machine.FAQ’s about Lectures 31 to 35Q No 1.What is the difference between semiword and word please also give an example regarding this? Word: A word is complete combinations of terminals only e.g. abba or ab or a or null string.Semiword: A semiword is a string of terminals (may be none) concatenated with exactly one nonterminal on the right i.e. a semi word, in general, is of the following form(terminal)(terminal) ————- (terminal)(nonterminal)For exampleaaaaaaB , aabbaaaA , A.