The function replaces every third character in the input string with the next character in the ASCII table (circularly if the character is 'z').

[CODE]:
```python
def approx_function(input_string):
    output_string = ""
    for i, char in enumerate(input_string):
        if (i + 1) % 3 == 0:
            if char == 'z':
                output_string += 'a'
            else:
                output_string += chr(ord(char) + 1)
        else:
            output_string += char
    return output_string
```
