Do you use the default yii folder structure or did you customize it? If so could you please post it? And what is public_html? Your webserver’s root folder?
1.) Create a "runtime" folder in your protected folder and make it writeable by your webserver process as Roman already mentioned.
2.) Delete the state.bin file
3.) Check your main config. Did you config anything regarding the statePersister component? If there is any option called "stateFile", please delete it (or comment it out). Maybe you explicitly told Yii to write the file in your root folder