A Boolean satisfiability problem has four variables, 1, 12, 13 and 14. A literal 1 can...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
A Boolean satisfiability problem has four variables, 1₁, 12, 13 and 14. A literal 1 can be a variable or its negation, denoted 7. The formula of interest, in conjunctive normal form (CNF), is f = (12 VT3) A (T2V *3) A (1 V 1₂ V T₁). The aim is to find assignments to the variables such that f is true under the usual rules for Boolean operations. This question addresses the use of more general constraint satisfaction to solve this problem. (a) Give a general description of a constraint satisfaction problem (CSP). (b) Explain how a Boolean satisfiability problem in CNF form and with n variables can be converted to a CSP, also having n variables and having a suitable constraint for each clause. Illustrate your answer using the 4-variable formula f in (1). (c) Explain, again using a constraint corresponding to a clause from (1), how general constraints can be converted to binary constraints. Provide a graph illustrating the problem from (1) after it has been converted to a CSP with only binary constraints. (d) Explain, how forward checking works in the context of a general CSP. How does this benefit a CSP solver? (e) Using the CSP equivalent you developed for (1), with only binary constraints, demonstrate how forward checking works using the sequence of assignments 2₁ F₁ ₂ = F₁ x₁ = T. (f) How would you expect the solution obtained when applying forward checking to be affected if constraints were allowed to propagate more widely? A Boolean satisfiability problem has four variables, 1₁, 12, 13 and 14. A literal 1 can be a variable or its negation, denoted 7. The formula of interest, in conjunctive normal form (CNF), is f = (12 VT3) A (T2V *3) A (1 V 1₂ V T₁). The aim is to find assignments to the variables such that f is true under the usual rules for Boolean operations. This question addresses the use of more general constraint satisfaction to solve this problem. (a) Give a general description of a constraint satisfaction problem (CSP). (b) Explain how a Boolean satisfiability problem in CNF form and with n variables can be converted to a CSP, also having n variables and having a suitable constraint for each clause. Illustrate your answer using the 4-variable formula f in (1). (c) Explain, again using a constraint corresponding to a clause from (1), how general constraints can be converted to binary constraints. Provide a graph illustrating the problem from (1) after it has been converted to a CSP with only binary constraints. (d) Explain, how forward checking works in the context of a general CSP. How does this benefit a CSP solver? (e) Using the CSP equivalent you developed for (1), with only binary constraints, demonstrate how forward checking works using the sequence of assignments 2₁ F₁ ₂ = F₁ x₁ = T. (f) How would you expect the solution obtained when applying forward checking to be affected if constraints were allowed to propagate more widely?
Expert Answer:
Answer rating: 100% (QA)
a A constraint satisfaction problem CSP is a mathematical problem defined as a set of objects whose state must satisfy a number of constraints or limitations It consists of a set of variables each wit... View the full answer
Related Book For
Calculus Early Transcendentals
ISBN: 9781337613927
9th Edition
Authors: James Stewart, Daniel K. Clegg, Saleem Watson, Lothar Redlin
Posted Date:
Students also viewed these programming questions
-
s1 educated (SSE) student for every three public school educated (PSE) students. Reasoning that students are not very dissimilar from threads, he suggests the following entry and exit routines be...
-
Design and implement a chat server that can handle multiple clients simultaneously. Clients should be able to send messages to the server and receive updates when other clients send messages.
-
Describe, in detail, how the heapsort algorithm works. [10 marks] Show that the worst-case cost of heapsort is O(n log n). [6 marks] Would it be possible to implement a variant of heapsort based on a...
-
Date 1 July 2019 1 June 2020 30 June 2020 1 July 2020 1 July 2020 30 June 2021 1 July 2021 Particulars (???) (???) (To record acquisition of delivery truck) (???) (???) (???) (To record minor repair...
-
Refer to Exercise 16.13. Predict with 99% confidence the price of a 1999 24-ft. Sea Ray cruiser with 400 hours of engine use.
-
On its municipal website, the city of Tulsa states that the rate it charges per 5 CCF of residential water is $21.62. How do the residential water rates of other U.S. public utilities compare to...
-
8. Specify the limitations of Maximisation of Profi t as the objective of a fi rm. [C.U. B.Com. (H), 2016]
-
What would happen to the sampling distribution of the mean if we increased sample size from 5 to 25?
-
1. The following Trial Balance was extracted from books of Safa Bhd. on 31 December 2020. RM 2,300,000 Safa Bhd. Trial Balance on 31 December 2019 RM Sales Inventories at 1 Jan 2019 150,000 Purchases...
-
The yearly demand for a seasonal, profitable item follows the distribution below: A manufacturer is considering launching a project to produce this item and could produce it by one of three methods:...
-
I do not know what points questions are looking for! May it possible to help me to understand the passage? ISSN 1940-204X XYZ Company: An Integrated Capital Budgeting Instructional Case David E....
-
7. A psychiatrist is testing a new ADHD Medication, which seems to have the potentially harmful side effect of increasing the heart rate. For a sample of 50 clinical study participants whose pulse...
-
Determine the type of engagement that your colleague completed for the client. Justify the selected engagement type for the client. Assess the purpose of each financial statement for the client's...
-
Mills Corporation acquired as a long-term investment $235 million of 8% bonds, dated July 1, on July 1, 2024. Company management has classified the bonds as an available-for-sale investment. The...
-
A force of 28 pounds acts on the pipe wrench shown in the figure below. 18 in. 30 (a) Find the magnitude of the moment about O by evaluating ||OA x F||. (0 0 180) Use a graphing utility to graph the...
-
Module 1 1. There has been a rise in cases of measles in RI. The RI Health Department is wondering if the rate of MMR vaccinations has declined since the start of the COVID-19 pandemic. The...
-
( 4 . 2 . 4 ) The amortization schedule for a 1 0 0 , 5 % bond with yielding a nominal annual rate of i ( 2 ) = 6 . 6 % , gives a book value of 9 0 for the bond at the beginning of a certain 6 -...
-
The area of square PQRS is 100 ft2, and A, B, C, and D are the midpoints of the sides. Find the area of square ABCD. B A
-
The graph of a function f is shown. (The dashed lines indicate horizontal asymptotes.) Find each of the following for the given function g. (a) The domains of g and g' (b) The critical numbers of g...
-
Sketch the curve with the given polar equation by first sketching the graph of r as a function of in Cartesian coordinates. r 2 = cos 4
-
Evaluate the indefinite integral. sin x sin(cos x) dx
-
2. If you were the top manager at Hormel, name two organizational systems you would establish to encourage organization member creativity.
-
would ensure Hormels future success. Be sure to explain how each idea would contribute to that success.
-
3. List three creative ideas based on your TQM expertise that, if implemented,
![Mobile App Logo](https://dsd5zvtm8ll6.cloudfront.net/includes/images/mobile/finalLogo.png)
Study smarter with the SolutionInn App