1. Markov-Chain Algorithm In Perl
Robert Brown – 10/21/09

2. Markov-Chain Algorithm
Sting-rewriting system:
Uses input to write “random” output
Grammar rules from input helps write output
An example in Pseudo-Code:
Set w1 and w2 to the first two strings in the text
loop:
w3 is the result of markov(w1, w2);
w1 = w2; w2 = w3;
Repeat loop

3. Algorithm in Perl, pt.1:
#markov.pl: markov chain algorithm for 2-word prefixes #part 1: take input and create data-relationship table $MAXGEN = 10000; $NONWORD = “\n”; $w1 = $w2 = $NONWORD; # initial state while (<>) { # read each line of input foreach (split) { $_); ($w1, $w2) = ($w2, $_); # multiple assignment } $NONWORD); #add tail

4. Explanation of code, pt. 1:
# constants and variables $MAXGEN = 10000; $NONWORD = “\n”; $w1 = $w2 = $NONWORD;
$MAXGEN – Maximum number of times function is called (constant)
$NONWORD – Used at the beginning of loops and acts as terminating condition (constant)
$w1, $w2 are static variables used through loops. Initially defined as $NONWORD

5. Explanation of code, pt. 2:
# read in data while (<>) { foreach (split) { ... } }, $NONWORD);
while (<>) reads in the current line of input
foreach (split) splits the input line into each individual word
foreach() then runs internal code on each word of input
while (<>) runs foreach() for every line of input
push() explained in next slide

6. Explanation of code, pt. 3:
# internal code of foreach(split)
$_);
($w1, $w2) = ($w2, $_);
*In previous slide, $NONWORD); inserts $NONWORD as the last item in the $statetab. This is used as a terminating condition in part 2.
push() inserts word ($_) from foreach() into $statetab*
$w1 and $w2 are used as index for stored value
$statetab{$w1}{$w2} is equal an array-- can contain multiple entries
During first execution, $statetab is created
Reassign $w1 and $w2
$w1 = $w2
$w2 = word

7. Example of $statetab:
Text used: “Show your flowcharts and conceal your tables and I will be mystified. Show your tables and your flowcharts will be obvious.”
$statetab{\n}{\n} = Show
$statetab{\n}{Show} = your
$statetab{Show}{your} = [flowcharts, tables]
$statetab{your}{flowcharts} = [and, will]
$statetab{flowcharts}{and} = conceal
$statetab{flowcharts}{will} = be
… etc …
$statetab{be}{obvious.} = ‘\n’ #Terminating condition

8. Algorithm in Perl , pt.2:
#part 2: create output from data table created in part 1 $w1 = $w2 = $NONWORD; for ($i = 0; $i < $MAXGEN; $i++) { $suf = $statetable{$w1}{$w2}; # array reference $r = is number of elems exit if (($t = $suf->[$r]) eq $NONWORD); print “$t\n”; ($w1, $w2) = ($w2, $t); # advance chain }

9. Explanation of code, pt. 4:
# output data $w1 = $w2 = $NONWORD; for ($i = 0; $i < $MAXGEN; $i++){ … }
Start at beginning of table
$w1 and $w2 becomes ‘\n’
$statetab{\n}{\n} is first item in input
$statetab{\n}{first item} is second item in input
Loop the output at most $MAXGEN times
Loop may exit early if terminating condition is met-- see next slide

10. Explanation of code, pt. 5:
# internal data of for(), pt. 1 $suf = $statetable{$w1}{$w2}; $r = exit if (($t = $suf->[$r]) eq $NONWORD);
$suf – reference to $statetable{$w1}{$w2}
If only one word, $suf is the word
If an array, $suf is the entire array
$r - random index of $suf
1 word – always 1
Array – between 1 and size of $suf
exit() – Terminate loop
$suf->[$r] is the ith item in array $suf
Only terminates if $suf->[$r] = ‘\n’

11. Explanation of code, pt. 6:
# internal data of for(), pt. 2 print “$t\n”; ($w1, $w2) = ($w2, $t);
Print the value contained in $t
$t defined in previous expression
Only occurs if loop was not terminated
Reassign $w1 and $w2
$w1 = $w2
$w2 = $suf->[$r]
Update allows the function to assess new values

12. Example of output, pt. 1: Input: “Now is the time for all good people”
Output: Now NOTE: When there are no is arrays in $statetab, the then the output mimics time the input word for for word all good people

13. Example of output, pt. 1: Input: “Now is the time for all good people”
Output: Now NOTE: When there are no is arrays in $statetab, the then the output mimics time the input word for for word all good people

14. Example of output, pt. 2
Input: “Show your flowcharts and conceal your tables and I will be mystified. Show your tables and your flowcharts will be obvious.”
Output: Show NOTE: With a large enough input, your text may not end with last [flowcharts, tables] three words [and, will] … etc … will be obvious

15. Now is the time for all good questions…