1. A recognizer for binary strings containing the sequence 0111.

2. A recognizer for binary strings containing the sequence 0101.

3. A recognizer for binary strings containing the sequence 01.

4. recognizer for binary strings containing at most 4 consecutive 1's.

5. A recognizer for strings of characters (alphabet is uppercase letters) that include at least one vowel (A,E,I,O,U).

6. A recognizer for strings of characters (alphabet is the ASCII character set) that are valid variable names.  Assume that a variable name must start with an alphabetic character and can contain only letters, digits or underscores.

7. Include the restriction that variable names cannot exceed 20 characters. (consider building a separate FSA for counting string length)

8. A recognizer for strings of characters that can be interpreted as octal numbers (only digits 0 through 7 allowed).

9. A recognizer for binary encoded values that are divisible by 2.

10. A recognizer for binary encoded values that are divisible by 4.

11.A recognizer for binary encoded values that are divisible by 3. (tough, maybe impossible???)

12. A recognizer that accepts binary strings with an even number of 1's.

13. A crecognizer that accepts binary strings with an even number of 1's and an even number of 0's.

14. A recognizer that accepts binary strings with an even number of 1's or an even number of 0's.

15. A recognizer that accepts binary strings with an even number of 1's and an odd number of 0's.

16. A recognizer that accepts binary strings that have at least three 1's in a row.

17. A recognizer that accepts binary strings that have no more than three 1's in a row.

18. A recognizer that accepts binary strings with the same number of 1's as 0's. (impossible)

19. A recognizer that accepts binary strings in which the number of 0's never exeeds the number of 1's in a left-to-right scan. (still impossible???)

20. A serial 2-bit comparator that reads two, 2-bit binary encoded values and outputs true if the second 2-bit number is greater than the first.

21. A Finite State Machine that outputs a random sequence of 1's and 0's.

22. A Finite State Machine that outputs the sequence 01001000100001...

23. A recognizer for binary strings with a repeated (non-overlapping) 4-bit sequence.

24. A recognizer for binary strings that have no repeated 4-bit sequences.

25. A recognizer for binary strings that are palindromes.