Question

6. [4 marks] Write a regular expression over the alphabet of numeric digits that matches strings formatted as integers between 33 and 526 (inclusive). For example, the following strings should be accepted: • 33 • 51 • 290 • 526 But the following strings should not be accepted: • 9 • 31 • 607 • 1000

Answer 1

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regular expression from 33 to 99 is

(3+4+5+6+7+8+9)(0+1+2+3+4+5+6+7+8+9)

regular expression from 100 to 499 is

(1+2+3+4)(0+1+2+3+4+5+6+7+8+9)(0+1+2+3+4+5+6+7+8+9)

regular expression from 500 to 526 is

5(0+1)(0+1+2+3+4+5+6+7+8+9) + 52(0+1+2+3+4+5+6)

so the final answer is

(3+4+5+6+7+8+9)(0+1+2+3+4+5+6+7+8+9) + (1+2+3+4)(0+1+2+3+4+5+6+7+8+9)(0+1+2+3+4+5+6+7+8+9) + 5(0+1)(0+1+2+3+4+5+6+7+8+9) + 52(0+1+2+3+4+5+6)