<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def _check_file(self):
 """ Checks watched file moficiation time and permission changes. """

        try:
            self.editor.toPlainText()
        except RuntimeError:
            self._timer.stop()
            return
        if self.editor and self.editor.file.path:
            if not os.path.exists(self.editor.file.path) and self._mtime:
                self._notify_deleted_file()
            else:
                mtime = os.path.getmtime(self.editor.file.path)
                if mtime > self._mtime:
                    self._mtime = mtime
                    self._notify_change()
                # check for permission change
                writeable = os.access(self.editor.file.path, os.W_OK)
                self.editor.setReadOnly(not writeable)