Model Checking CTL is Almost Always Inherently Sequential

Abstract

The model checking problem for CTL is known to be P-complete (Clarke,Emerson, and Sistla (1986), see Schnoebelen (2002)). We consider fragments ofCTL obtained by restricting the use of temporal modalities or the use ofnegations---restrictions already studied for LTL by Sistla and Clarke (1985)and Markey (2004). For all these fragments, except for the trivial case withoutany temporal operator, we systematically prove model checking to be eitherinherently sequential (P-complete) or very efficiently parallelizable(LOGCFL-complete). For most fragments, however, model checking for CTL isalready P-complete. Hence our results indicate that, in cases where thecombined complexity is of relevance, approaching CTL model checking byparallelism cannot be expected to result in any significant speedup. We alsocompletely determine the complexity of the model checking problem for allfragments of the extensions ECTL, CTL+, and ECTL+