The Subgraph Bisimulation Problem and its Complexity

In this paper we study the complexity of the Subgraph Bisimulation Problem, which stands to graph bisimulation as subgraph isomorphism stands to graph isomorphism, and we prove its NP-completeness. Our analysis is motivated by recent requirements coming from semistructured databases, where Subgraph Bisimulation can be used for retrieving semistructured data, even in presence of ‘cyclic’ queries and instances. The problem could be interesting also for the concurrency research area, where bisimulation is the main tool for describing process equivalence, and in the model checking area, where bisimulation serves as a means to reduce state explosion.