$(12$ pts$)$ JMH$-$Lisp is a simple language designed after the LISP programming language,

that can be used for evaluating arithmetic expressions. It is described by the following

components:

$($a$)$ The alphabet of JMH$-$Lisp consists of the open $\text{'}(\text{'}$ and close $\text{'})\text{'}$ parentheses,

the digits $0-9,$ the space character $\text{'},$ and the symbols $+-*\frac{*}{?}$

$($b$)$ An operator is a substring in JMH$-$Lisp containing one of the symbols $+-*\frac{*}{?}.$

$($c$)$ A number is a substring in JMH$-$Lisp containing one or more of the digits $0-9$

$($d$)$ An expression is defined as either a number or a list expression

$($e$)$ A list expression is defined by the following, in order:

i$.$ An open parenthesis: $\text{'}(\text{'}$

ii$.$ An operator

iii. A space: $\text{'}\text{'},$

iv$.$ An expression

v$.$ A space: $\text{'},$

vi$.$ An expression

vii. A close parenthesis: $\text{'})\text{'}$

$($f$)$ A string in the JMH$-$Lisp language is a single list expression.

Examples of JMH$-$Lisp strings may include:

$(*23)$

$(+(**53)(\frac{?}{84}))$

$(-25(+42))$

Is $.$JMH$-$Lisp a regular language? Why or why not? If you think it is$,$ provide a regular

expression or finite automaton which recognizes the language. If you think it is not,

provide an explanation as to why no regular expression or finite automaton should be

able to recognize it$.$