2} {w
13 feb. 2015 1W : every odd position in W is 1l. 0 1. 1. 0. 0
4 dec. 2015 1. DFAs: Design a DFA for each of the following languages (all over the ... (a) (5 points) {w
18 mar. 2002 {w every odd position of w is 1}. q0 q1. 1 q2. 0. 01. 0
The languages of 1.6 are on the alphabet {0 1}. 1.6 g {w
10 sept. 2019 { w
R is said to be a regular expression (or RE in short) if R has one of the following {w
1. The formal description of a DFA M is ({q1q2
{ w w has exactly one character 1 any # of 0s} 0*10* 1) 2) 3) Regular expressions: examples { w w has length ?3 and its 3rd symbol is 0 } (0 ?1)(0 ?1) 0 (0 ?1)* { w every odd position of w is a 1 } (1(0 ?1))* (??1) 9/12/2019 Sofya Raskhodnikova; based on slides by Nick Hopper L4 8
Question 1 6 Part i –{w everyoddpositionis 1} This is similar to the even/odd number of as required in question 1 4 above Here we need a gadget to keep track of whether we are looking at an odd/even numbered position which will head into an attracting failure state if the position is odd and is not 1 2
1 9a Use the construction in the proof of Theorem 1 47 to give the state diagrams of NFAs recognizing the concatenation of the languages described in Exercises 1 6g and 1 6i The languages of 1 6 are on the alphabet {0 1} 1 6 g {w the length of w is at most 5} 1 6 i {w every odd position of w is a 1} 1 6 g: 1 6 i
Let w = w 1 ?w k be in L(M { w w = ? or every odd position in w is a 1 } Assume
L = {w ? {01}* every odd position of w is a 1} w = w 1w 2 w k ? ? L See Exercise 1 6 in Sipser for more Created Date: 1/6/2022 12:28:06 AM
1 0 0 0 1 0;1 c The language fW: W contains an odd number of 1’s or exactly two 0’sg The NFA must have six states: 1 1 0 0 0 0 1 1 " " 1 6 Q: Give regular expressions describing the following languages in which the alphabet is f0;1g: A: a fW: W has length at least 3 and its second symbol is 1g: 1 b fW: Every odd position of W is a 0g