We give an optimal (
), sound and complete tableau-based algorithm for deciding satisfiability for propositional dynamic logic with converse (CPDL) which does not require the use of analytic cut. Our main contribution is a sound method to combine our previous optimal method for tracking least fix-points in PDL with our previous optimal method for handling converse in the description logic
. The extension is non-trivial as the two methods cannot be combined naively. We give sufficient details to enable an implementation by others. Our OCaml implementation seems to be the first theorem prover for CPDL.