Cse 105 Homework Solutions

Pre-class reading and post-class practice questions

Week 1

Pre-requisites
Reading Sec 0.2, 0.3, 0.4: In particular, review the definitions of set, element, subset, infinite set, proper subset, natural numbers, integers, empty set, union, intersection, complement, sequence, Cartesian product, function, domain, range, graph, self-loop, alphabet, symbol, string over an alphabet, length, empty string, substring, concatenation, lexicographic order, shortlex/string order, prefix, proof by contradiction.
Optional extra practice: Chapter 0 Exercise # 1, 2, 3, 4, 5, 6.

Regular expressions
Reading Sec 1.3: Def 1.52 of regular expressions (p. 64), example 1.53 (p. 65)
Optional extra practice: Chapter 1 Exercise # 20

DFAReading Sec 1.1: Figure 1.4 (p. 34), Definition 1.5 (p. 35)
Optional extra practice: Chapter 1 Exercise # 1, 2, 3

Week 2

Closure operations (Wednesday)
Reading Pages 45-47 (paragraph before Theorem 1.25 and Theorem 1.25 and its proof).
Optional extra practice Chapter 1 Exercise # 4, 5

Nondeterminism (Friday)
Reading Page 48 (Figure 1.27 and description below it), Example 1.35 on page 52.
Optional extra practice Chapter 1 Exercise # 7, 9

Week 3

NFA to DFA (Monday)
Reading Pages 55 paragraph that starts "Recall the "reader as automaton"..." and Example 1.41 on pages 56-58..
Optional extra practice Chapter 1 Exercise # 13, 14, 16

NFA to RegExp (Wednesday)
Reading Example 1.56 on page 68.
Optional extra practice Chapter 1 Exercise # 7, 17

Nonregular sets (Friday)
Reading Page 77.
Optional extra practice Chapter 1 Exercise # 30

Week 4

Pumping Lemma (Monday)
Reading Example 1.75 (page 81) and Example 1.77 (page 82)
Optional extra practice Chapter 1 Exercise # 29, 30

PDA (Wednesday)
Reading Informal description of PDA on pages 111-112.

PDA Design (Friday)
Reading Example 2.16 (page 115) and Example 2.18 (page 116)
Optional extra practice Chapter 2 Exercise # 5

Week 5

Context-free grammars> (Monday)
Reading Intro to section 2.1 (pp. 102-103)
Optional extra practice Chapter 2 Exercise # 2,4

Context-free languages (Friday)
Reading Designing CFGs (pp. 106-107), Ambiguity Definition 2.7 (p. 108)
Optional extra practice Chapter 2 Exercise # 15

Week 6

Turing Machines (Monday)
Reading Pages 166-167 on differences between finite automata and Turing machines.

Turing machines (Wednesday)
Reading Example 3.7 on page 171, Example 3.9 page 173.<
Optional extra practice Chapter 3 Exercise # 2

Turing machines (Friday)
Reading Bottom of page 166 and top of page 167 (high-level and implementation level definitions of M1), then terminology for describing Turing machines pages 184-185
Optional extra practice Chapter 3 Exercise # 7,8

Week 7

Variants of Turing machines (Wednesday)
Reading Section 3.2, especially "Equivalence with other models" on page 181.
Optional extra practice Chapter 3 Exercise # 18

Computational problems (Friday)
Reading Format and notation for describing Turing machines, middle of page 185
Optional extra practice Chapter 3 Exercise # 15, 16; Chapter 4 Exercise # 1

Week 8

Decidable problems (Monday)
Reading Section 4.1, Theorem 4.5 (page 197) and Theorem 4.8 (page 199)
Optional extra practice Chapter 4 Exercise # 3,5

Undecidability (Wednesday)
Reading Section 4.2 page 207-209
Optional extra practice Chapter 4 Exercise # 7,8

Week 9

Reductions (Monday)
Reading Section 4.2 Theorem 4.22, Section 5.1 Theorem 5.1

Reductions (Wednesday)
Reading Section 5.1 Theorem 5.2

Reductions (Friday)
Reading Section 5.1 Theorem 5.3, 5.4
Optional extra practice Chapter 5 Exercise # 18 (without Rice's theorem)

Week 10

Complexity: P and NP (Monday)
Reading Section 7.1 example at the top of page 279, Theorem 7.8, Theorem 7.11; Section 7.2 Definition 7.12, Theorem 7.14; Section 7.3 Theorem 7.24
Optional extra practice Chapter 7 Exercise # 6, 7, 8, 10

NP-completeness (Wednesday)
Reading Section 7.1 example at the top of page 279, Theorem 7.8, Theorem 7.11; Section 7.2 Definition 7.12, Theorem 7.14; Section 7.3 Theorem 7.24
Optional extra practice Chapter 7 Exercise # 5, read through sample solution of 28

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