13. In the DPLL algorithm for the satisfiability problem of propositional logic clauses given in conjunctive normal form, once some clause contains only one literal that can be made true (because the choices made on that search path have already assigned every other literal in that clause to be false), that literal will be automatically chosen as the next literal to be assigned the value in backtracking without any branching on that recursion level. What is the name of this important speedup technique? (a) Unit propagation (b) Pure literal elimination (c) Index resolution (d) Refutation clause learning

13. In the DPLL algorithm for the satisfiability problem of propositional logic clauses given in conjunctive normal form, once some clause contains only one literal that can be made true (because the choices made on that search path have already assigned every other literal in that clause to be false), that literal will be automatically chosen as the next literal to be assigned the value in backtracking without any branching on that recursion level. What is the name of this important speedup technique? (a) Unit propagation (b) Pure literal elimination (c) Index resolution (d) Refutation clause learning

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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a. Correctness of dynamic programming algorithm: Usually, a dynamic programming algorithm can be seen as a recursion and proof by induction is one of the easiest way to show its correctness. The structure of a proof by strong induction for one variable, say n, contains three parts. First, we define the Proposition P(n) that we want to prove for the variable n. Next, we show that the proposition holds for Base case(s), such as n = 0, 1, . . . etc. Finally, in the Inductive step, we assume that P(n) holds for any value of n strictly smaller than n' , then we prove that P(n') also holds. Use the proof by strong induction properly to show that the algorithm of the Knapsack problem above is correct. b. Bounded Knapsack Problem: Let us consider a similar problem, in which each item i has ci > 0 copies (ci is an integer). Thus, xi is no longer a binary value, but a non-negative integer at most equal to ci , 0 ≤ xi ≤ ci . Modify the dynamic programming algorithm seen at class for this…
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A recursive algorithm must have a - This is some condition which, if satisfied, is often a simple version of the problem that can be solved directly. This stops the algorithm from for ever. A recursive algorithm must call and the values of local variables and arguments are recorded on the on each of these calls. A recursive algorithm must change its the problem in in such a way that it moves towards the base case, by some way. unwinding reducing recursing program Python increasing heap iterating base case itself algorithm call stack state transforming a friend stack case memory list
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