COS 126

Theory of Computation Exercises 		Assignment

  1. Huntington's disease diagnostic. Huntington's disease (HD) is an inherited and fatal neurological disorder. Although there is currently no cure, in 1993 scientists discovered a very accurate genetic test. The gene that causes Huntington's disease is located on the short arm of chromosome 4, and it has a variable number of (consecutive) repeats of the CAG trinucleotide. These "stuttering" repeats lead to an excess in the amount of the amino acid glutamine in the protein huntington. The normal range of CAG repeats is between 10 and 35. Individuals with HD may have between 36 and 180 repeats. Doctors can use a simple PCR-based DNA test, count the number of repeats, and inform patients whether they are at risk.

     Repeats   Diagnosis 
     0 - 9  not human
     10 - 35  normal
     36 - 39  high risk
     40 - 180  Huntington's disease
     181 - ∞  not human

    Write a program Huntingtons.java to read in a human DNA sequence from a file and identify whether the patient is at risk for HD by determining the maximum number of CAG repeats. Output the maximum number of repeats, and an appropriate medical diagnosis based on the table above. The data file format will consist of a sequence of the letters A, C, G, and T, along with arbitrary amounts of whitespace separating the letters. For full credit, your program should use regular expressions and should identify CAG repeats, even if there is intervening whitespace.

    For example, the following sequence has a CAG repeat of size 4. 

    TTTTTTTTTT TTTTTTTTTT TTTTTTTTCA
GCAGCAGCAG TTTCAGCAGT TTTTTTTTTT 
TTTTTTTTTT TTTTTTTTTT TTTTTTTTTT
TTTCAGTTTT TTTTTTTTTT T
    Here is a sample run of your program: 
    % java Huntingtons test1.txt
max number of CAG repeats = 4
not human

  2. Turing machine. Design a Turing machine that takes as input a series of parentheses and angle brackets and terminates in a yes state if it is a well-balanced sequence of parentheses and angle brackets and a no state otherwise. Well-balanced means that for every opening parenthesis or angle bracket there should be a matching closing parenthesis or angle bracket, nested appropriately. Use only the following six symbols: ( ) < > X #.

    Download turing.jar and launch it by typing java -jar turing.jar from the command line in the command prompt window (windows) or terminal window (mac). Your job is to create and submit a text file parenbrack.tur containing the description of your Turing machine like paren.tur below, but instead of matching just parentheses, you are to match both parentheses and angle brackets. 

    % more paren.tur
title
Parenthesis Matcher

description
Accepts the input if it is a 
well-balanced sequence of parentheses.

vertices
0 R 0.2 0.5 
1 L 0.5 0.5
2 L 0.5 0.9
3 Y 0.8 0.9
4 N 0.8 0.5

edges
0 1 ) X 0.2
1 0 ( X 0.2
0 2 # #
2 3 # #
2 4 ( (
1 4 # #

tapes
[(] )
[(]
[)] (
[(] ( ) ) ( ( ( ) ) ) ( ) 
[(] ( ( ( ) ) 
[(] ( ( ) ) ) 
[(] ) ) ( ( ) ( )
[(] ( ) ) ) ( ) )

    The data file is divided into 5 sections (title, description, vertices, edges, tapes), and each section begins with the corresponding name. Each vertex (state) is specified with 4 required values: its name (a string), its type (L, R, Y, N, H), and its x- and y-coordinates (between 0 and 1, where (0, 0) is the upper left corner). The first state listed is the start state. Each edge (transition) is specified with 4 required values: the starting state, the ending state, the symbol to read, and the symbol to write. An optional 5th parameter specifies the curvature with which to draw the edge (straight line by default). Each sample input tape is specified by listing its symbols, separated by spaces. The tape head starts at the symbol delimited by square braces - for this assignment, it should always be the leftmost non-blank character.

    Deliverables. Submit Huntingtons.java, parenbrack.tur, and readme.txt.

    This assignment was created by Kevin Wayne and Maia Ginsburg.
    Copyright © 2004.