A Boolean satisfiability problem has four variables, 1, 12, 13 and 14. A literal 1 can...
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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 4variable 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 4variable 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?
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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
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