Description
How to manage this assignment
• Start work on this assignment early, and do as much as possible of it before your week 4 prac class. There will not be time during the class itself to do the assignment from scratch; there will only be time to get some help and clarification.
Instructions
Please read these instructions carefully before you attempt the assessment:
• To begin working on the assignment, download the workbench asgn1.zip from Moodle. Create a new Ed Workspace and upload this file, letting Ed automatically extract it. Edit the student-id file to contain your name and student ID. Refer to Lab 0 for a reminder on how to do these tasks.
• The workbench provides locations and names for all solution files. These will be empty, needing replacement. Do not add or remove files from the workbench.
• Solutions to written questions must be submitted as PDF documents. You can create a PDF file by scanning your legible (use a pen, write carefully, etc.) hand-written solutions, or by directly typing up your solutions on a computer. If you type your solutions, be sure to create a PDF file. There will be a penalty if you submit any other file format (such as a Word document). Refer to Lab 0 for a reminder how to upload your PDF to the Ed workspace and replace the placeholder that was supplied with the workbench.
• Before you attempt any problem—or seek help on how to do it—be sure to read and understand the question, as well as any accompanying code.
Your submission must include:
• a sed script, decomposeSyllablesIntoParts, for Problem 1(a);
• a one-line text file, Korean-NameStructure2, for Problem 1(a);
• a sed script, decomposePartsIntoLetters, for Problem 1(b);
• a one-line text file, Korean-NameStructure3, for Problem 1(b);
• an awk script, matchKorean, for Problem 1(c);
• the output file outputFile you produced by running your awk script on the provided input file, inputFileOfNames, in Problem 1(c);
• a file prob2.pdf with your solution to Problem 2.
Introduction to the Assignment
In Lab 0, you met the stream editor sed, which detects and replaces certain types of patterns in text, processing one line at a time. These patterns are actually specified by regular expressions. You will use sed again in Problem 1 of this Assignment, to help construct regular expressions.
You will also learn about awk, which is a simple programming language that is widely used in Unix/Linux systems and which also uses regular expressions. In Problem 1, you will construct an awk program to identify a class of Korean names.
Finally, Problem 2 is about applying induction to a problem of counting on graphs.
Introduction to awk
In an awk program, each line has the form
/pattern / { action }
where the pattern is a regular expression (or certain other special patterns) and the action is an instruction that specifies what to do with any line that contains a match for the pattern. The action (and the {…} around it) can be omitted, in which case any line that matches the pattern is printed.
Once you have written your program, it does not need to be compiled. It can be executed directly, by using the awk command in Linux:
$awk -f programName inputFileName
Your program is then executed on an input file in the following way.
// Initially, we’re at the start of the input file, and haven’t read any of it yet.
If the program has a line with the special pattern BEGIN, then do the action specified for this pattern.
Main loop, going through the input file:
{ inputLine := next line of input file Go to the start of the program.
Inner loop, going through the program:
{ programLine := next line of program (but ignore any BEGIN and END lines) if inputLine contains a string that matches the pattern in programLine, then if there is an action specified in the programLine, then
{ do this action
}
else
just print inputLine // it goes to standard output }
}
If the program has a line with the special pattern END, then do the action specified for this pattern.
Any output is sent to standard output.
You should read about the basics of awk, including the way it represents regular expressions and the main instruction types used in its actions. Any of the following sources should be a reasonable place to start:
• A. V. Aho, B. W. Kernighan and P. J. Weinberger, The AWK Programming Language, Addison-Wesley, New York, 1988.
(The first few sections of Chapter 1 should have most of what you need, but be aware also of the regular expression specification on p28.)
• https://www.grymoire.com/Unix/Awk.html
• the Wikipedia article looks ok
• the awk manpage
• the GNU Awk User’s Guide.
Introduction to Problem 1
The Master said, ‘What is necessary is to rectify names …. If names are not rectified, then words are not appropriate. If words are not appropriate, then deeds are not accomplished.’
Most organisations today deal with people from many different cultures and language groups, and they must often record and process people’s names in systems that work mainly with English language text. In such contexts, it is helpful to be able to recognise names from different language groups. Example applications include: determining how to pronounce students’ names when reading them out from a list at graduation ceremonies; determining how to greet a person with whom you have an appointment; determining how to enter the various parts of a person’s name into a database; determining how automatically-generated emails, sent to many different people listed in some file, should address each recipient; determining the most likely native language of a person in situations where their name is known but they cannot be spoken to directly at the time (e.g., in some emergency situations). Recognising the language group that a name belongs to is an important first step in all these situations.
In this problem you will write some code in sed and awk to try to recognise one type of names in a long file of Asian names. More specifically, suppose you are given an input file in which each line starts with a person’s name in some language, with each name transcribed somehow into English text. Your task is to detect which of these names come from Korean.
Further information about working with names from different cultures can be found in:
• Fiona Swee-Lin Price, Success with Asian Names, Allen & Unwin, Crows Nest, NSW, 2007.
• SBS, The Cultural Atlas, https://culturalatlas.sbs.com.au/. You can look up a country or culture (e.g., by clicking on a map) and then click on a link to “Naming” for that culture.
Names in Korean
Korean names consist of a family name followed by a given name (the reverse of the usual order in English). The family name usually consists of just a single syllable, and the given name usually consists of two syllables. We restrict ourselves to names with these numbers of syllables from now on.
Each syllable consists of an optional prefix, a compulsory middle and an optional suffix.
• The possibilities for the prefix are:
g, kk, n, d, tt, r, m, b, pp, s, ss, j, jj, ch, tch, k, t, p, h
These are also listed, one per line, in the file prefix-file.
• The possibilities for the middle are:
a, ae, ya, yae, eo, e, yeo, ye, o, wa, wae, oe, yo, u, wo, we, wi, yu, eu, ui, i, oo, ah
These are also listed, one per line, in the file middle-file.
• The possibilities for the suffix are:
k, n, t, l, m, p, ng
These are also listed, one per line, in the file suffix-file.
For example, the syllable kyung is formed from the prefix k followed by the middle yu and then the suffix ng.
Constructing a regular expression for Korean names
We will use this information, together with sed, to generate a regular expression to try to match Korean names. (The match will be quite imperfect, and later you will do some simple computations to get some idea of how well, or poorly, it does. ) Throughout, we will only do case-insensitive matching, so there is no need to capitalise initial letters of syllables in order to match names.
We describe the steps in detail now, and then list the assignment submission requirements for Problem 1.
We start with the file Korean-NameStructure0, which just contains one line consisting of the text <NAME>. Think of this as a special symbol, eventually to be transformed to a regular expression for Korean names.
We first transform <NAME> to a regular expression representing the syllable structure of Korean names. From our description of the syllable structure above, we can represent this by the regular expression <SYLLABLE> <SYLLABLE>-?<SYLLABLE> where <SYLLABLE> is a special symbol to represent any Korean syllable and putting “?” after a symbol means it can occur just once or not at all at that position. Each occurrence of <SYLLABLE> will eventually be transformed to a regular expression to represent such syllables. The first step of this transformation can be done using the following sed command:
$ sed “s/<NAME>/<SYLLABLE> <SYLLABLE>-?<SYLLABLE>/” Korean-NameStructure0 > Korean-NameStructure1
Alternatively, you can execute the sed instruction “s/<NAME>/<SYLLABLE> <SYLLABLE>-?<SYLLABLE>/” from the the file decomposeNameIntoSyllables (provided with this assignment) by doing the following:
$ sed -f decomposeNameIntoSyllables Korean-NameStructure0
> Korean-NameStructure1
Try these, using the given files, and check that you get the required result in the file Korean-NameStructure1. This use of sed is a template for what you will do next.
Now you need to replace each <SYLLABLE> by a regular expression representing possible syllable structures, using <PREFIX>, <MIDDLE> and <SUFFIX>.
Write the sed instruction to do this, in the file decomposeSyllablesIntoParts, and do the transformation from your Linux command line using
$ sed -f decomposeSyllablesIntoParts Korean-NameStructure1
> Korean-NameStructure2
Now you need to replace each occurrence of each part, <PREFIX>, <MIDDLE> and <SUFFIX>, by regular expressions representing possible letter strings, according to the sets of strings given on the previous page.
Write the sed instructions to do this, in the file decomposePartsIntoLetters. You will need three lines: one line giving the sed instruction for each part type, <PREFIX>, <MIDDLE> and <SUFFIX>. Then do the transformation from your Linux command line using
$ sed -f decomposePartsIntoLetters Korean-NameStructure2
> Korean-NameStructure3
This should put, into the file Korean-NameStructure3, a regular expression that is intended to match Korean names.
Matching names in the input file
We will now use this regular expression to construct an awk program to apply it to names in the input file, and to do some simple computations to determine how well the regular expression matches Korean names.
For each name in the input file, checking it against your regular expression gives one of four possible outcomes:
• Correct Match: a name that belongs to Korean (according to the last word on its line in inputFileOfNames) is also matched by your regular expression.
• False Positive: a name that does not belong to Korean (according to the last word on its line in inputFileOfNames), but is matched by your regular expression.
• False Negative: a name that belongs to Korean (according to the last word on its line in inputFileOfNames), but is not matched by your regular expression.
• Correct Non-match: a name that does not belong to Korean (according to the last word on its line in inputFileOfNames) and is not matched by your regular expression.
Your awk program should compute the number of names, in the input file, of each of these four types, and report those numbers at the end.
You can write the awk program manually, cutting-and-pasting the regular expression as needed (and making any necessary modifications to it) from Korean-NameStructure3. The heart of your awk program will be a statement that does the following.
• The pattern matches a Korean name whenever it occurs in the specified position at the start of a line.
– Recall the general structure of an awk statement. By default, matches in awk are casesensitive. To do a case-insensitive match, you need to match the pattern against a version of the current line in which all alphabetic characters have been converted to lower case. This can be done using a statement of this form:
tolower($0) ~ /pattern / { action }
Here, $0 is a built-in awk variable that always contains the current line of the input file, and tolower() is a function that converts all alphabetic characters to lower case. You can read “ ~ ” as “matches”.
• The action increments appropriate variables in order to update the number of correct matches, false positives, false negatives, or correct non-matches, as appropriate.
The files and commands required to complete this problem are shown in Figure 1.
First, run sed, as described, using the one-line sed script decomposeNameIntoSyllables to produce Korean-NameStructure1.
(a) Write the one-line sed script, decomposeSyllablesIntoParts, and run sed, as described, to produce Korean-NameStructure2.
(b) Write the three-line sed script, decomposePartsIntoLetters, and run sed, as described, to produce Korean-NameStructure3.
(c) Write the awk script, matchKorean, and run it, as described, on input file inputFileOfNames, to produce outputFile.
Can you write a much better regular expression for Korean names? If you attempt this, then, in addition to the files required above, you should also provide:
• your new regular expression, in a one-line file called Korean-NameStructure4;
• your new awk program, in a file called matchKoreanBonus;
• the output from running your awk program on the input file, as outputFileBonus.
Korean-NameStructure0 decomposeNameIntoSyllables
sed -f decomposeNameIntoSyllables Korean-NameStructure0 > Korean-NameStructure1
Korean-NameStructure1 decomposeSyllablesIntoParts
sed -f decomposeSyllablesIntoParts Korean-NameStructure1 > Korean-NameStructure2
Korean-NameStructure2 decomposePartsIntoLetters
sed -f decomposePartsIntoLetters Korean-NameStructure2
> Korean-NameStructure3
Korean-NameStructure3
write awk code, using regular expression in Korean-NameStructure3
matchKorean inputFileOfNames
awk -f matchKorean inputFileOfNames > outputFile
outputFile
Figure 1: The plan.
As usual, be sure to cite any sources used.
An independent set in a graph is a set of mutually non-adjacent vertices in the graph. So, no edge can have both its endpoints in an independent set.
In this problem, we will count independent sets in ladder graphs. A ladder graph Ln is a graph obtained from the points and lines formed by a row of n squares. More formally:
• its vertices correspond to ordered pairs (0,0),(0,1),(1,0),(1,1),…,(n,0),(n,1);
• two vertices are adjacent if they represent points at distance exactly 1 from each other.
The number n here is called the order of the ladder. Here is L3, a ladder of order 3:
(0,1) (1,1) (2,1) (3,1)
(0,0) (1,0) (2,0) (3,0)
Examples of independent sets in L3 include: ∅, {(2,1)}, {(0,0),(2,0),(3,1)}, {(0,1),(1,0),(2,1),(3,0)}.
The simplest ladder is L0, consisting of just the vertices (0,0) and (0,1) with a single edge between them.
For all n, define
an = number of independent sets in Ln which include neither (n,0) nor (n,1);
bn = number of independent sets in Ln which include (n,0) but not (n,1);
cn = total number of independent sets in Ln.
(a) Compute a0, b0, a1, b1.
(b) Give, with justification, recurrence relations that express an+1 and bn+1 in terms of an and bn.
(Here, each of an+1 and bn+1 is expressed using both an and bn.)
(c) Prove, by induction on n, that for all n ≥ 0,
(d) Hence give a good closed-form upper bound for cn (i.e., an upper-bound expression in terms of n, not a recurrence relation). Your bound should be significantly better than 3n (which is the upper bound you get by ignoring horizontal edges and only taking vertical edges into account).
Find, and prove using similar techniques including induction, good lower bounds for an, bn and cn.
