CSE 355: Human-aware Robo.cs Introduction to Theoretical Computer Science

Size: px

Start display at page:

Download "CSE 355: Human-aware Robo.cs Introduction to Theoretical Computer Science"

Francis Stevenson
5 years ago
Views:

1 CSE 355: Introduction to Theoretical Computer Science Instructor: Dr. Yu ( Tony ) Zhang Lecture: WGHL101, Tue/Thu, 3:00 4:15 PM Office Hours: BYENG 594, Tue/Thu, 5:00 6:00PM 1

2 Subject of interest? 2

3 Robo.cs Subject of Human-aware interest? 3

4 Robo.cs Subject of Human-aware interest? 4

5 Subject of interest? 5

6 Subject of interest? Computation 6

7 Outline for today Theory of computation Why it is important Discussion of Syllabus Questions and Answers 7

8 Theory of computation Automata Theory abstract machines Computability Theory Computation fundamental capabilities and limitations of abstract machines Complexity Theory why certain problems are harder than others 8

9 Outline for today Theory of computation Why it is important Discussion of Syllabus Automata Theory Computability Theory Complexity Theory Questions and Answers Computation 9

10 Automata Human-aware Theory Finite Robo.cs Automata An abstract machine (or mathematical model of computation) that can capture systems with a finite number of states o Automation applications where simple tasks need to be repeated o Easy to implement with limited resources (HW/SW) o Easy to design and visualize o Easy to verify correctness 10

11 Robo.cs Automata Human-aware Theory Finite Automata Exampe 11

12 Automata Human-aware Theory Finite Robo.cs Automata Exampe 12

13 Robo.cs Automata Human-aware Theory Finite Automata Exampe 13

14 Automata Human-aware Theory Pushdown Robo.cs Automata An abstract machine (or mathematical model of computation) that can capture systems with a finite number of states and a stack o A PDA can write to a stack o At each step, the read write head can only access the top symbol in the stack, which can be poped or kept; a new symbol may be pushed onto the stack 14

15 Robo.cs Automata Automata Human-aware Theory Pushdown Exampe 15

16 Automata Human-aware Theory Turing Robo.cs Machines An abstract machine (or mathematical model of computation) that can capture systems that can manipulate symbols on a strip of tape Ø Despite the model's simplicity, given any computer algorithm, a Turing machine can be constructed that is capable of simulating that algorithm's logic. o A Turing machine can both write on the tape and read from it. o The read write head can move both to the left and to the right. o The tape is infinite. o The special states for rejecting and accepting take effect immediately. 16

17 Robo.cs Automata Human-aware Theory Turing Machine Exampe Ø Turing completeness is the ability for a system of instructions to simulate a Turing Machine. A programming language that is Turing complete is theoretically capable of expressing all tasks accomplishable by computers; nearly all programming languages are Turing complete if the limitations of finite memory are ignored. 17

18 Automata Theory 18

19 Outline for today Theory of computation Why it is important Discussion of Syllabus Automata Theory Computability Theory Complexity Theory Questions and Answers 19

20 Computability Theory What are the fundamental capabilities and limitations of computers? o Can we design a turing machine (or program) that could examine another turing machine (or program) M with input I, and decide whether M on input I will terminate? o Can we design a turing machine (or program) that could determine whether a mathematical statement is true of false? Ø Can be used to identify other unsolvable problems via reducibility Q: If classical computers cannot solve a problem, can quantum computers solve it? o Can quantum computing solve classically unsolvable problems, A. Hodges, arxiv preprint quant-ph/ ,

21 Outline for today Theory of computation Why it is important Discussion of Syllabus Automata Theory Computability Theory Complexity Theory Questions and Answers 21

22 Complexity Theory What makes some problems computationally hard and others easy? o Can we predict how fast a program will run? Sorting problem Scheduling problem TSP Ø In this course, we will learn how to distinguish between problems that can be solve efficiently (computationally easy problems) and problems that can take long time to be solved (computationally hard problems). 22

23 Learning goals We will learn how to abstract (i.e., abstract machines)! Familiarize ourselves with the mathematical formalisms and build strong foundations o You will understand the hardness results of various problems and rationals behind their solutions o You will be able to access the related literature o You will be able to analyze a new problem and design solutions for it o 23

24 Outline for today Theory of computation Why it is important Discussion of Syllabus Automata Theory Computability Theory Complexity Theory Questions and Answers 24

25 Syllabus 25

26 Outline for today Theory of computation Why it is important Discussion of Syllabus Automata Theory Computability Theory Complexity Theory Questions and Answers Reading assignment for the next class: o Sipser Sec. 0.1, 0.2 and 1.1 Quiz link will be sent out; due date is before the beginning of the next class 26

CITS2211 Discrete Structures Turing Machines

CITS2211 Discrete Structures Turing Machines October 23, 2017 Highlights We have seen that FSMs and PDAs are surprisingly powerful But there are some languages they can not recognise We will study a new