I have downloaded JBPM starters kit. In the documentation it is written that there is a directory called $jbpm_home/core and under it there is a file schema.generation.properties. In addition it is written to run "ant generate.ddl ".
In my downloaded package I can't find core directory and no build.xml contains generate.ddl ant task.
Is there any other scripts I can run in order to generate database schema?
Look in the jbpm.db subproject in order to generate database schema's for plenty of supported databases.