I have a shared library written in C Language on Linux environment. How to expose those shared library API's to REST based PHP WebService?
If you don't want to do it the "exec" way, you will have to do some work before you can get it working directly from within php.
Check this http://devzone.zend.com/1435/wrapping-c-classes-in-a-php-extension/ tutorial.
You will have to write a config.m4 file and put PHP specific includes and variables in your C code.
Check this answer:
Linking a PHP Extension Written in C
It's a good example.
It's a little ugly, but you can do methods in your PHP REST Api to call the process via system, exec, passthru... parse the info returned by the library and return the result in json format by the PHP Api.