Problem: Design the DFA machine for a simple calculator, where ? = {0, 1, 2, 3,
ID: 3736280 • Letter: P
Question
Problem:
Design the DFA machine for a simple calculator, where
? = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ., =, , , , , [, ] }. “[ ]” is used
for only one operation each time (e.g, [3.1 4.2] 5 [12 4.8]),
embedded [[...]] is not allowed.
Steps of the project:
(1)
Design a regular expressionrfor real number expression. A real number can be negative orpositive (e.g., – 2.5 and 0.52). A real number expression is an expression of real numbers connected by four arithmetic operations +, -, ×, , / and priority [] .
(2)Design a DFA for accepting the regular languageL(r). You can first design a NFA and then conve
do NFA form regular expression
Daing reqular ex Press ion E real lop realExplanation / Answer
(i) If ? = {a}, then ?
?
contains
?, a, aa, aaa, aaaa, . . .
(ii) If ? = {a, b}, then ?
?
contains
?, a, b, aa, ab, ba, bb, aaa, aab, aba, abb, baa, bab, bba, bbb, . . .
(iii) If ? = ? (the empty set — the unique set with no elements), then ?
? = {?}, the set just
containing the null string.
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