In this work, we ask you to design a deterministic Finite Automaton (FA) to recognise arithmetic expressions.
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When we say arithmetic expression, we mean a kind of expression you can type in a very basic desk calculator. That is, neither variables nor brackets are allowed. It contains only numbers and four arithmetic operators, +, -, *, and /.
The following are some examples of arithmetic expression:
- Any number string with or without signs - e.g. 3, -1, +10, 3.14, -0.70 and 099.
- Number strings mixed with arithmetic operators - e.g. 3+5, -1+2*3, 7/10-0.7, and -1.4-+8.2.
An example of FA diagram for recognising a non-negative integer is given below. You may use it as a start point. You need to add a few more states and transitions to handle numbers with decimal point and signs (e.g. -5, +2, 0.21, -32.6, +99.05, but not the form 1.0E-3). Most importantly, you also need to add a few more things to deal with the arithmetic operators +, -, *, /.
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