'Induction step' presentation slideshows

Recursive Definitions: functions, structures, languages

Recursive Definitions: functions, structures, languages. Sections 5.3 & 5.4 Tuesday, June 10. 1. Recursively Defined Sets. A set S can be defined recursively as follows: Specify one or more basis elements .

804 views • 64 slides

CS4231 Parallel and Distributed Algorithms AY 2006/2007 Semester 2

539 views • 41 slides

Phylogenetic Trees (2) Lecture 12

Phylogenetic Trees (2) Lecture 12. Based on: Durbin et al Section 7.3, 7.8, Gusfield: Algorithms on Strings, Trees, and Sequences Section 17. Recall: The Four Points Condition. Theorem: A set M of L objects is additive iff any subset of four objects can be labeled i,j,k,l so that:

553 views • 34 slides

Phylogenetic Trees Lecture 11

Phylogenetic Trees Lecture 11. Sections 7.1, 7.2, in Durbin et al. Evolution. Evolution of new organisms is driven by Diversity Different individuals carry different variants of the same basic blue print Mutations

512 views • 34 slides

CS322

Week 5 - Friday. CS322. Last time. What did we talk about last time? Sequences Summation and production notation Proof by induction. Questions?. Logical warmup. Consider six straight silver chains made up of five links each What if you want to make one large circular chain?

426 views • 27 slides

Induction proofs

Induction proofs. To prove that some proposition P ( n ) is true for all n ? n 0 by induction on n ? n 0. 1. Basis : Check that P ( n 0 ) is true. 2. Inductive step . Assume that P ( n ) is true for n = k , where k is some integer, k ? n 0

373 views • 25 slides

Dynamic Programming

337 views • 25 slides

CSC212 Data Structure - Section RS

CSC212 Data Structure - Section RS. Lecture 14 Reasoning about Recursion Instructor: Zhigang Zhu Department of Computer Science City College of New York. Outline of This Lecture. Recursive Thinking: General Form recursive calls and stopping cases Infinite Recursion runs forever

293 views • 23 slides

Lecture 8: Construction Techniques (1)

ICOM 4075: Foundations of Computing. Lecture 8: Construction Techniques (1). Department of Electrical and Computer Engineering University of Puerto Rico at Mayagüez Summer 2005. Lecture Notes Originally Written By Prof. Yi Qian. Homework 7 (due Tuesday, April 6, 2010).

293 views • 22 slides

Tirgul 2

Tirgul 2. Asymptotic Analysis. Asymptotic Analysis.

412 views • 22 slides

Mathematical Induction.

448 views • 21 slides

Lecture 11 Polynomial Time Hierarchy

Lecture 11 Polynomial Time Hierarchy. Oracle TM. Query tape. yes. Query state. no. Remark:. A is polynomial-time Turing-reducible to B if there exists a polynomial-time DTM with oracle B, accepting A. Example. Example. Definition. Definition. Definition. Remark. Theorem. Proof.

288 views • 18 slides

CSCI 2670 Introduction to Theory of Computing

CSCI 2670 Introduction to Theory of Computing. September 8, 2005. Announcement. Remove problems 1.46c and 1.55(c,f,j) from your homework assignments New assignment 1.7(d,h), 1.16b, 1.21b (show the GNFA steps),1.19a Old text numbers 1.5(d,g), 1.12b, 1.16b, 1.14a. Agenda. This week

294 views • 17 slides

Recursion and Induction

Recursion and Induction. Define sets by induction zero ? N n ? N ? succ( n ) ? N Define functions on sets by recursion ? n ? N : plus(zero, n ) = n ? m, n ? N : plus(succ( m ), n ) = succ(plus( m , n ))

245 views • 17 slides

MA/CSSE 473 Day 34

MA/CSSE 473 Day 34. MST details: Kruskal's Algorithm Prim's Algorithm. MA/CSSE 473 Day 34. Topics from this week not on Friday's exam. Exam coverage: Chapters 1-8 (emphasis on 4-8) Class Days 1-32 (emphasis on 16-32) HW 1-12 (emphasis on 6-12) One more HW due date delay:

289 views • 16 slides

Lecture 3.2: Strong Induction

Lecture 3.2: Strong Induction. CS 250, Discrete Structures, Fall 2011 Nitesh Saxena. * Adopted from previous lectures by Cinda Heeren, Zeph Grunschlag. Course Admin. HW2 due tomorrow at 11am Mid-Term 1 We are grading them now, and should have the results by next weekend

401 views • 14 slides

Forward-backward algorithm

Forward-backward algorithm. CS 5368 Yin Lu 10/28/2010. Outline. HMM Definition Problem Forward probability Backward probability. HMM Definition. Set of N states: Set of M observations: State transition probabilities: Observation/emission probabilities in state j: Initial state:

284 views • 12 slides

Proofs by Counterexample & Contradiction

Proofs by Counterexample & Contradiction. There are several ways to prove a theorem: Counterexample: By providing an example of in which the theorem does not hold , you prove the theory to be false .

464 views • 12 slides

Regular expressions Regular languages

231 views • 10 slides

Review of Inductive Construction of Sets and Inductive Proof Techniques

Review of Inductive Construction of Sets and Inductive Proof Techniques. Example 1.1, page 5: Power Set Construction. Let S = {a, b, c}. Power Set The set of all the subsets of a given set S, is called power set of S. The power set of S is denoted by p (S) or 2 |S| . p (S) = { ? }.

249 views • 4 slides