# The complexity of connectivity problems on context-free graph languages

## Abstract

We analyze the precise complexity of connectivity problems on graph languages generated by context-free graph rewriting systems under various restrictions. Let *L* be the family of all context-free graph rewriting systems that generate at least one disconnected resp. connected graph. We show that *L* is DEXPTIME-complete w.r.t. log-space reductions. If *L* is finite then *L* is PSPACE-complete w.r.t. log-space reductions. These results hold true for graph rewriting systems as for example boundary node label controlled (BNLC) graph grammars, hyper-edge replacement systems (HRS's), apex (APEX) graph grammars, simple context-free node label controlled (SNLC) graph grammars, and even for the simple context-free graph grammars introduced by Slisenko in [Sli82].

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