6 01 Fall Semester 2007 Assignment 3 Issued Tuesday Sept 18 1 MASSACHVSETTS INSTITVTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6 01 Introduction to EECS I Fall Semester 2007 Assignment 3 Issued Tuesday Sept 18 To do this week in Tuesday software lab 1 Start writing code and test cases for the numbered questions in the software lab Paste all your code including your test cases into the box provided in the Software Lab Part 3 1 problem on the on line Tutor This will not be graded before the start of lab on Thursday 1 Read the lecture notes 2 Do the on line Tutor problems for week 3 that are due on Thursday Part 3 2 3 Read through the entire description of Thursday s lab in Thursday robot lab 1 Answer the numbered questions in the robot lab and demonstrate them to your LA 2 Do the nanoquiz it will be based on the material in the lecture notes and the on line Tutor problems due on Thursday before the start of lecture next Tuesday 1 Do the on line Tutor problems for week 3 that are due on Tuesday Part 3 3 2 Do the lab writeup providing written answers including code and test cases for every numbered question in this handout On Athena machines make sure you do athrun 6 01 update so that you can get the Desktop 6 01 lab3 directory which has the files mentioned in this handout You need the file fsm py for the software lab You need the files sequence py and UtilityBrainTB py for the robot lab During software lab if you are using your own laptop download the files from the course Web site on the Calendar page 6 01 Fall Semester 2007 Assignment 3 Issued Tuesday Sept 18 2 Object Oriented Programming Combining Sequential Behaviors Tuesday s lecture the Tuesday software lab and the on line problems cover Python s support for object oriented programming Thursday s lab applies the tools of object oriented programming to develop a new system for defining and combining robot behaviors sequentially rather than the utility based combination we looked at last week Tuesday Software Lab Practice At the end of this lab go to the on line Tutor at http sicp csail mit edu 6 01 fall07 choose PS3 and paste all your code including your test cases into the box provided in the Software Lab problem This will not be graded it is simply a checkpoint for us to see how people are doing Complete the assignment later and hand it in as part of your lab writeup Make sure that you include the test cases and results that you used to conclude that your code was working This week we ll get practice with object oriented programming and build some tools that will be useful in future labs Polynomial Arithmetic We can represent a polynomial as a list of coefficients starting with the highest order term For example the polynomial x4 7x3 10x2 4x 6 would be represented as the list 1 7 10 4 6 Let s say that the length of a polynomial is the length of its list of coefficients Write a class called Polynomial that supports evaluation and addition on polynomials You can structure it any way you d like but it should be correct and be beautiful It should support at least an interaction like this p1 Polynomial 3 2 1 print p1 poly 3 0 2 0 1 0 This represents the polynomial 3x2 2x 1 p2 Polynomial 100 200 print p1 add p2 poly 3 0 102 0 201 0 print p1 p2 poly 3 0 102 0 201 0 p1 val 1 6 0 p1 val 10 321 0 6 01 Fall Semester 2007 Assignment 3 Issued Tuesday Sept 18 3 The constructor accepts a list of coefficients highest order first Question 1 Define the basic parts of your class with an init method and a see the lecture notes for more information about this so that if you do str method print Polynomial 3 2 1 poly 3 0 2 0 1 0 something nice and informative is printed out Question 2 Implement the add method for your class A cool thing about Python is that you can overload the arithmetic operators So for example if you add the following method to your Polynomial class def add self v return self add v or if you prefer def add self v return Polynomial add self v then you can do print Polynomial 3 2 1 Polynomial 100 200 poly 3 0 102 0 201 0 Exactly what gets printed as a result of this statement depends on how you ve defined your procedure this is just an example Question 3 Add the add str method to your class A straightforward way to evaluate polynomials is to explicitly add up the terms ai xi We can do this with list comprehension and sum Hint note that in a polynomial with k coefficients the highest power of the variable is k 1 for example our example polynomial of length 3 has the highest power of x2 Question 4 Add the val method to your class which evaluates the polynomial for the specified value Try to do things as simply as possible Don t do anything twice Finite State Machines This section builds on the FSM discussion in lecture All the code from lecture can be found in the fsm py file There is additional written material covering the lecture presentation at the end of this handout 6 01 Fall Semester 2007 Assignment 3 Issued Tuesday Sept 18 4 Figure 1 Serial parallel and feedback compositions of state machines Question 5 Assuming the elevator starts in the closed state what is the sequence of states and outputs for the following sequence of inputs commandOpen commandClose noCommand commandOpen If you have a very complicated system to model or implement writing a single monolithic state transition function would be very difficult Happily we can apply our PCA primitive combination abstraction methodology here to build more complex FSMs out of simpler ones We wil treat the PrimitiveFSM class as a primitive and consider some possible means of combination Figure 1 sketches three types of FSM composition serial parallel and feedback In this lab we ll focus on serial and feedback composition Serial composition In serial composition we take two machines and use the output of the first one as the input to the second The result is a new composite machine whose input vocabulary is the input vocabulary of the first machine and whose output vocabulary is the output vocabulary of the second machine It is of course crucial that the output vocabulary of the first machine be the same as the input vocabulary of the second machine 6 01 Fall Semester 2007 Assignment 3 Issued Tuesday Sept 18 5 Here is the skeleton of a SerialFSM class It takes two FSMs as input at initialization time and then implements the step function of the combined machine class SerialFSM def init self fsm1 fsm2 your code here def step self input your …
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