A Tableau for the Combination of CTL and BCTL

It is known that there is an exponential decision procedure for CTL. Given that important properties cannot be expressed in CTL, we seek a pure tableau based decision procedure (that does not rely on translations into automata) that is exponential for formulas that have only a bounded number of non-CTL properties. In this paper we present such a tableau for a combination of CTL and a bundled variant(BCTL*) of CTL* that is singly exponential for formulae with abounded number of path-sub formulae. The existing pure tableau for CTL* was built upon the pure tableau for BCTL*, so this paper is also a natural first step towards a pure tableau technique for CTL* that is singly exponential when similarly restricted.