We need to implement a lexical analyzer which is able to recognize octal and decimal numbers with the following requirements. An input number starts with a + or - sign. An octal number starts with a 0 and can continue with an arbitrarily number of digits. An octal number started with more than one 0 is not an acceptable number. Note: digits used in an octal number are between 0 and 7. A decimal number starts with any digit except 0 and can continue with an arbitrarily number of digits. Note: digits used in a decimal number are between 0 and 9. 0 is an acceptable number, no matter whether we accept it as a decimal or as an octal number. 1. Write a context free grammar or a regular grammar to satisfy the requirements. Note: the alphabet of this language is {+, -, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. 2. Create a finite automaton for the grammar.

Here are some examples of accepted input: {+0, +9803467, -184, -04650, ...}

Here are some examples of rejected input: {-03489, -00, +, -034-21, 146802, ...}