On complexity of the tightening problem for web service discovery

A goal of the service oriented paradigm/SOA is to facilitate automated service composition. Motivated by scenarios in e-business and e-science, the automated composition problem starts with a specification of a "goal" service and a set of searchable existing services. The composition problem relies on discovering relevant services at the semantic level, mainly, through entry/exit conditions, and assembling them into a "realization" of the goal service. Based on this framework, we study in this paper a tightening problem which strengthens service discovery queries formulated from conditions in the goal service. A tighter condition can find more relevant services while a looser one may exclude the possibility of assembling a goal realization. The tightening problem is studied for conditions in different logic languages, mainly, conditions with order constraints and linear arithmetic. The complexity of the tightening problem is given for both integers and real numbers.