Can you help me code problem $1$ and $2.$

To compile your code and run the testbench press F$9$ in an Emacs buffer in a properly set up

account. The testbench will apply inputs to several instantiations of modules pmatch$\_$base and

pmatch$\_$mark. The instantiations differ in the length of the string. At the end of execution the

number of errors for each module at each size are shown. The output below is from a correctly

solved assignment:

Total pmatch$\_$base n$=4$: Errors: $0$cl$,0$op$,0$mk$.$

Total pmatch$\_$base n$=5$: Errors: $0$cl$,0$op$,0$mk$.$

Total pmatch$\_$base n$=7$: Errors: $0$cl$,0$op$,0$mk$.$

Total pmatch$\_$base n$=8$: Errors: $0$cl$,0$op$,0$mk$.$

Total pmatch$\_$base n$=9$: Errors: $0$cl$,0$op$,0$mk$.$

Total pmatch$\_$base n$=17$: Errors: $0$cl$,0$op$,0$mk$.$

Total pmatch$\_$mark n$=4$: Errors: $0$cl$,0$op$,0$mk$.$

Total pmatch$\_$mark n$=5$: Errors: $0$cl$,0$op$,0$mk$.$

Total pmatch$\_$mark n$=7$: Errors: $0$cl$,0$op$,0$mk$.$

Total pmatch$\_$mark n$=8$: Errors: $0$cl$,0$op$,0$mk$.$

Total pmatch$\_$mark n$=9$: Errors: $0$cl$,0$op$,0$mk$.$

Total pmatch$\_$mark n$=17$: Errors: $0$cl$,0$op$,0$mk$.$

Each line starting with Total shows a tally of results. After Total the line shows the module name,

either pmatch$\_$base or pmatch$\_$mark, and n$,$ the length of the string. A tally of each output's error

is shown after Errors:, cl is the number of incorrect closing$-$parentheses values, op is the number

of opening$-$parenthesis values, and mk is the number of incorrectly marked strings.

Further up$,$ the testbench shows sample output and error details. For each instantiation the

first n$\_$errors$\_$show $=5$ incorrect outputs are shown on lines starting with Error. If it would

help to see more then feel free to search for n$\_$errors$\_$show and increase the value. In addition the

details of the first n$\_$samples$\_$show $=6$ correct outputs are shown on lines starting with Sample.

The output below shows correct outputs:

Starting pmatch$\_$base tests for n$=5.$

Sample pmatch$\_$base n$=5\text{'}()\text{'}$: close $=0,$ open $=0($both correct$)$

Sample pmatch$\_$base n$=5\text{'}.()\text{'}$: close $=0,$ open $=0($both correct$)$

Sample pmatch$\_$base n$=5\text{'})(\text{'}$: close $=1,$ open $=1($both correct$)$

Sample pmatch$\_$base n$=5\text{'})\text{'}$: close $=1,$ open $=0($both correct$)$

Sample pmatch$\_$base n$=5\text{'}))\text{'}$: close $=2,$ open $=0($both correct$)$

Sample pmatch$\_$base n$=5\text{'}()))\text{'}$: close $=2,$ open $=0($both correct$)$

Sample pmatch$\_$base n$=5\text{'}())(\text{'}$: close $=1,$ open $=1($both correct$)$

Sample pmatch$\_$base n$=5\text{'}())((\text{'}$: close $=1,$ open $=2($both correct$)$

Sample pmatch$\_$base n$=5\text{'}))((\text{'}$: close $=2,$ open $=2($both correct$)$

In the sample above the first Error line indicates that for input $()$ both the left$\_$out$\_$n$\_$unmat$\_$close

and right$\_$out$\_$n$\_$unmat$\_$open outputs were $0,$ which is correct because there were no unmatched

parentheses. The second sample is also properly matched. It consists of parentheses, a dot $($which

is just an ordinary character$),$ and spaces. The third sample has both one unmatched opening

parenthesis and an unmatched closing parenthesis.

The testbench starts applying patterns found in str$\_$special. Feel free to add your own to

help with debugging. After the patterns in str$\_$special are used the testbench will make up

random patterns.

The output below is of a run using a partially correct pmatch$\_$base:

The testbench starts applying patterns found in str$\_$special. Feel free to add your own to

help with debugging. After the patterns in str$\_$special are used the testbench will make up

random patterns.

The output below is of a run using a partially correct pmatch$\_$base:

Sample pmatch$\_$base n$=5\text{'}()\text{'}$: close $=0,$ open $=0($both correct$)$

Sample pmatch$\_$base n$=5\text{'}.()\text{'}$: close $=0,$ open $=0($both correct$)$

Sample pmatch$\_$base n$=5\text{'})(\text{'}$: close $=1,$ open $=1($both correct$)$

Sample pmatch$\_$base n$=5\text{'})\text{'}$: close $=1,$ open $=0($both correct$)$

Error pmatch$\_$base n$=5\text{'}))\text{'}$: close $0!=2($correct$)$

Sample pmatch$\_$base n$=5\text{'}()))\text{'}$: close $=2,$ open $=0($both correct$)$

Error pmatch$\_$base n$=5\text{'}))((\text{'}$: close $0!=2($correct$)$

Error pmatch$\_$base n$=5\text{'}))\text{'}$: close $0!=2($correct$)$

The errors reported above seem to show that the left$\_$out$\_$n$\_$unmat$\_$close is wrong when the

string starts with two consecutive opening parentheses.

The str$\_$marked output of module pmatch$\_$mark is supposed to show the string with the cor$-$

rectly matched parentheses replaced by angle brackets $($actually less$-$than and greater$-$than sym$-$

bols$).$ Appearing below is sample output of the module in a correctly solved assignment. Two lines

are used to show the result of each input. The first shows the input string, such as $()$ in the first

sample, the second line shows the marked string, such as

Sample pmatch$\_$mark n$=5\text{'}()\text{'}$: close $=0,$ open $=0($both correct$)$

Sample pmatch$\_$mark nmarked$\_$outpuut$)$

Sample pmatch$\_$mark n$=5\text{'}.()\text{'}$: close $=0,$ open $=0($both correct$)$

Sample pmatch$\_$mark nmarked$\_$outpuut$)$

Sample pmatch$\_$mark n$=5\text{'})(\text{'}$: close $=1,$ open $=1($both correct$)$

Sample pmatch$\_$mark n$=5\text{'})(\text{'}($marked$\_$outpuut$)$

Sample pmatch$\_$mark n$=5\text{'})\text{'}$: close $=1,$ open $=0($both correct$)$

Sample pmatch$\_$mark n$=5\text{'}),($marked$\_$outpuut$)$

Sample pmatch$\_$mark n$=5\text{'}))\text{'}$: close $=2,$ open $=0($both correct$)$

Sample pmatch$\_$mark n$=5\text{'})),($marked$\_$outpuut$)$

Sample pmatch$\_$mark n$=5\text{'}()))\text{'}$:

$5$ of $6$

Problem $1$: Module pmatc

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