Let M 1 and M 2 be DFAs that have k1 and k2 states, respectively, and then let U L(M 1 ) L(M 2 ) a Show that if U , then U contains some string s, where s max(k 1 , k 2 ) b Show that if U , then U excludes some string s, where s k 1 k 2 ...

Answer A To prove the above statement first assume that the DFAs M1 and M2 which are taken abovecons ...

Let M 1 and M 2 be DFAs that have k1 and k2 states, respectively, and then

Question:

Let M₁ and M₂ be DFAs that have k1 and k2 states, respectively, and then let

U = L(M₁) ∪ L(M₂).

a. Show that if U ≠ ⌀, then U contains some string s, where |s| < max(k₁, k₂).

b. Show that if U ≠ Σ^*, then U excludes some string s, where |s| < k₁k₂.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Introduction to the theory of computation

ISBN: 978-0470530658

3rd edition

Authors: Michael Sipser

See More Books

Question Posted: Sep 02, 2020 04:15 AM

See More Questions

Let L1: U v1 and L2: U V2 be linear maps between inner product spaces, with V1, V2 not necessarily the same. Let K1 = L1* L1, K2 = L2* L2. Show that the sum K = K1 + K2 can be written as a...
Let k 1 , k 2 , . . . , k n be a random sample from the geometric probability function p X (k; p) = (1 p) k1 p, k = 1, 2, . . . Find , the generalized likelihood ratio for testing H 0 : p = p 0...
Let m1, m2, . . . , mn be pairwise relatively prime integers greater than or equal to 2. Show that if a b (mod mi) for i = 1, 2, . . . , n, then a b (mod m), where m = m1m2 mn. (This result will...
A manufacturer of cases for sound equipment requires that holes be drilled for metal screws. The drill bits wear out and must be replaced; there is expense not only in the cost of the bits but also...
The median household income divides the households into two groups: the half whose income is less than or equal to the median, and the half whose income is greater than the median. The median...
What are differences or similarities between everyday logic and mathematical logic? How can the study of mathematical logic help you in your everyday life?
Describe what acts a professional liability policy covers, as well as the risks it does not cover.
Given the schedule in Table B for a liability work package done as part of an accounting audit in a corporation, find: (a) The critical path. (b) The slack time on process confirmations. (c) The...
The following is information for Palmer Company. Year 3 Year 2 Year 1 Cost of goods sold $ 6 3 8 , 8 2 5 $ 4 2 1 , 6 5 0 $ 3 8 6 , 3 0 0 Ending inventory 9 6 , 9 0 0 8 7 , 2 5 0 9 2 , 0 0 0 Use the...
Fool Proof Software is considering a new project whose data are shown below. The equipment that would be used has a 3-year tax life, and the allowed depreciation rates for such property are 33%, 45%,...
Let = {0,1}. a. Let A = {0 k u0 k | k 1 and u * }. Show that A is regular. b. Let B = {0 k 1u0 k | k 1 and u * }. Show that B is not regular.
Let = {0,1, #}. Let C = {x#x R #x| x {0,1} * }. Show that C is a CFL.
What is the primary risk of trading in the fed funds markets? How did this risk come into play during the financial crisis of 20082009?
What accounts for gender differences in aggression? Cite relevant research findings.
Describe fully and evaluate any three of the unique defenses.
How are socialized offenders different from individual offenders?
Which of the following is included in a decedents gross estate? I. Cash values of life insurance contracts that the decedent owned on the spouses life. II. Decedents life insurance proceeds payable...
What is the difference between structured professional judgments and actuarial approaches to assessing violence risk?
The production supervisor of the Machining Department for Lei Company agreed to the following monthly static budget for the upcoming year: LEI COMPANY Machining Department Monthly Production Budget...
Find the APR in each of the following cases: NUMBER OF TIMES COMPOUNDED Semiannually Monthly Weekly Infinite EAR APR 10.4% 8.9 11.6 15.4
Assuming it is possible to sort n numbers in O(nlogn) time, show that it is possible to solve the three-way set disjointness problem in O(nlogn) time.
Describe an efficient algorithm for finding the ten largest elements in an array of size n. What is the running time of your algorithm?
Give an example of a positive function f (n) such that f (n) is neither O(n) nor (n).
1. Define latent heat and how it is different than specific heat capacity. 2. Describe how a phase diagram changes when changing from a solid to a liquid. 3. Describe how work done is related to a...
In a large vaccination clinic, patients arrive at the rate of 50 per hour. The clinic is staffed with five nurses and it takes on average 6 minutes for a nurse to vaccinate a patient. Both patient...
Calculate the missing value. Beginning cash balance add : cash receipts Collection of notes receivable Proceeds from sale of securities collection from credit sales Total receipts Total available...

Let M 1 and M 2 be DFAs that have k1 and k2 states, respectively, and then

Question:

Step by Step Answer:

Answer A To prove the above statement first assume that the DFAs M1 and M2 which are taken abovecons...View the full answer

Introduction to the theory of computation

Students also viewed these Computer science questions