Given a string, the task is to check if that string contains any special character (defined special character set). If any special character found, don’t accept that string.

Here's a Python program that checks whether a given string contains any special character or not: 

import re

def contains_special_char(string):
    pattern = re.compile('[^a-zA-Z0-9]')
    if pattern.search(string):
        return True
    else:
        return False

In the above code, we first import the "re" module, which stands for regular expressions. We then define a function called "contains_special_char" that takes a string as its argument.

Inside the function, we define a regular expression pattern using the "compile" method of the "re" module. The pattern matches any character that is not a letter or a digit.

We then use the "search" method of the pattern object to search for the pattern in the input string. If the pattern is found, we return True, which indicates that the string contains a special character. Otherwise, we return False.

Here's an example usage of the function: 

>>> contains_special_char('Hello, World!')
True
>>> contains_special_char('HelloWorld')
False
>>> contains_special_char('12345')
False
>>> contains_special_char('Hello#World')
True

In the above example, the function correctly identifies strings that contain special characters and returns True for those strings.