did you really consider the Activiti docs/examples etc…
The Activiti is used to execute (in general long-running and most-likely async) business processes. therefore the Activiti has to store state somewhere which is done using a database. - to answer your question "no its not possible to use the activiti without a database".
however you could use an in memory database (h2 for instance) - so it is possible to use the Activiti without installing/maintaining a (real) database.
