How could a BPM convert to a computer system ? Is there any program or programming language to do this convertion?
Though I could not make much from your question, some of the tags that you have added to this question itself are the answers. BPM formally represented in a notation and that is the BPMN standard.
To achieve the BPM requirements there are a couple of technical approaches.
Implement the BPM requirements as a system of webservices call... that would be BPEL (Business process expression language)
implement the BPM engine as a application (like JBPM, Activiti, Bonitasoft stc.) These adhere to BPMN standards.
It's a matter of choice based on application requirements/design which way fits your needs.
To answer your question on how BPM can convert to a computer system, you have to be very clear about the business rules (requirements) first. Second you draw these business rules (decision sequences like automated rules or human decisions like approval rejection etc.) as per the BPMN notations. Once you have drawn the BPMN flow, most free and commercial BPM engines comply to BPMN standards (BPMN 1.1 or BPMN 2.0 standards).
These BPM applications provide tools (either IDE or web based designer tools) to convert the above mentioned BPMN diagram to a BPM implementation in that BPM engine.
Please keep in mind: 1. If you have an existing (would be) application that needs integration with BPM; will require very careful thinking and planning. 2. sometimes; just using a custom written workflow solution (assuming the need of BPM is very very minimal) is way better than involving a heavy resource hungry BPM application that causes more problems than it can solve.
If you want to get a hang of what BPM can do; jbpm and Activiti BPM are free and open source alternatives worth looking at.
HTH ~Ayusman