Discrete Mathematics for Computer Science

Uncomputability 317 ited time and memory resources, one can implement arithmetic procedures on arbitrarily large integers and do ...

318 CHAPTER 5 Analysis of Algorithms If A is not a legal algorithm, or if running A on input In causes a run-time error (such as ...

Uncomputability 319 If an arbitrary string d does not belong to Halt, either because d does not have the form A%%In or because ...

320 CHAPTER 5 Analysis of Algorithms Now ask: Does NegSelfRef halt on input NegSelfRef? Substituting NegSelfRef for A, we derive ...

Chapter Review 321 other than In(In). Otherwise, A does not halt; it just keeps on interpreting the computation of In(In) foreve ...

322 CHAPTER 5 Analysis of Algorithms polynomial time (7P) selection time complexity propositional satisfiability sequence verifi ...

Chapter Review 323 by means of solving Exercises 1 through 10. (Remember to show inequality.) Prove that 0(1) c 0(log(n)). Prov ...

324 CHAPTER 5 Analysis of Algorithms (b) Find the complexity of the following algorithm for computing the mean of n values: INPU ...

Chapter Review 325 Find the complexity for each of the following algorithms that evaluate a polynomial of degree n at a value x ...

326 CHAPTER^5 Analysis of Algorithms The code that follows implements Homer's algorithm for evaluating polynomials. Find its co ...

Chapter Review 327 One variant of the Merge Sort algorithm was given in Exercise 22 of Section 2.8. Analyze the complexity of M ...

328 CHAPTER 5 Analysis of Algorithms INPUT: a set C of clauses OUTPUT: "satisfiable" or "unsatisfiable" N for pal = F, T set C1 ...

Chapter Review 329 (b) Trace through the execution of the code on the set C = {Pl V P2, P1 V "-P2, -IP V P2, -P11 V -P2} (so, fo ...

330 CHAPTER 5 Analysis of Algorithms (b) Suppose that cracking a public key cryptogram depends on finding the smallest 50- digit ...

Graph Theory Computer scientists use graphs to model problems as diverse as how to detect a dead- lock condition in an operating ...

332 CHAPTER 6 Graph Theory Job Assignment Problem GIVEN: A list of jobs to be filled and a list of job applicants who may be qua ...

Introduction to Graph Theory 333 A line or edge from a person to a job represents the fact that the person is qualified for that ...

334 CHAPTER 6 Graph Theory 6.1.1 Definitions The Job Assignment Problem gives an insight regarding how graph theory can be used ...

Introduction to Graph Theory 335 regular graph is n-regular if each vertex has degree n. Graphs that are 3-regular are often cal ...

336 CHAPTER 6 Graph Theory 6.1.2 Subgraphs In the Job Assignment Problem, the graph theory answer consists in identifying a grap ...