A Rooted Tableau for BCTL*

The existing pure tableau technique for satisfiability checking BCTL* [Reynolds, M., A Tableau for Bundled CTL*, J Logic Computation 17 (2007), pp. 117–132. URL http://logcom.oxfordjournals.org/cgi/content/abstract/17/1/117] begins by constructing all possible colours. Traditional tableaux begin with a single root node, and only construct formulae that are derived from that root. These rooted tableaux provide much better performance on most real world formulae, as they only need to construct a fraction of the possible nodes. We present a rooted variant of this tableau for BCTL*, together with an implementation demonstrating the performance of our rooted variant is superior to the original; this implementation is made available as a Java applet. We discuss further possible optimisations. This research will be useful in finding an optimised rooted tableau for CTL*.