
Let C, xxis a ternary (ie., base-3) number that is a multiple of n}. Show that for eachn> 1, the language C, is regu...
Exercise 7.H.
7.Н. Show that every number in the Cantor set has a ternary (-base 3) expan- sion using only the digits 0, 2 7.I. Show that the collection of "right hand" end points in F is denumerable. Show that if all these end points are deleted from F, then what remains can be put onto one-one correspondence with all of [0, 1). Conclude that the set F is not
Let S = {a, b}. Show that the language L = {w EX : na(w)<n(w) } is not regular.
Let Σ = { a } , and consider the language L = { a n : n is a prime number } = { a 2 , a 3 , a 5 , a 7 , a 11 , . . . } . Is L a regular language? Why or why not? (Hint: L contains a 11 , a 17 , a 23 , a 29 , but not a 77 since 77 is divisible by 11. ....
Let n be an even number. How many ternary strings (i.e. strings over the alphabet 10, 1,2]) of length n are there in which the only places that zeroes can appear are in the odd-numbered positions?
DO NUMBER 3
2. Let {acgt} and let L be the language of strings consisting of repeated copies of the pairs at, ta, cg, gc. Construct both a DFSM to accept the language and a regular expression that represents the language 3. Let a,b. For a string w E X", let W denote the string w with the a's and b's flipped. For example, for w aabbab: w bbaaba wR babbaa abaabb {wwR Construct a PDA to accept the language:...
1. (5 points each) Answer the following questions a) Let 120102(3) and 10222(3) be ternary representations of two natural numbers. Use base 3 arithmetic to add them. Check the answer by converting each to base 10, adding, and converting back to base 3. b) Which integer is bigger? 333( (12) or 33336)?
) Find a recurrence relation for the number of ternary strings of length n≥1 that do not contain two or more consecutive 2s. (Hint: A ternary string consists of 0s, 1s, and 2s.)
Consider an ordered array A of size n and the following ternary search algorithm for finding the index i such that A[i] = K. Divide the array into three parts. If A[n/3] > K. the first third of the array is searched recursively, else if A[2n/3] > K then the middle part of the array is searched recursively, else the last thud of the array is searched recursively. Provisions are also made in the algorithm to return n/3 if A[n/3]...
Question 7. Let Σ = {a}, and consider the language L = {a^n : n is a prime number} = {a 2 , a3 , a5 , a7 , a11 , . . .}. Is L a regular language? Why or why not? (Hint: L contains a 11 , a 17 , a 23 , a 29, but not a 77 since 77 is divisible by 11. . . )
(d) Let L be any regular language. Use the Pumping Lemma to show that In > 1 such that for all w E L such that|> n, there is another string ve L such that lvl <n. (4 marks) (e) Let L be a regular language over {0,1}. Show how we can use the previous result to show that in order to determine whether or not L is empty, we need only test at most 2" – 1 strings. (2...