T. Wilke, "CTL + is Exponentially More Succinct than CTL", Foundations of Software Technology and Theoretical Computer Science: 19th Conference, (1999), 110--121. A Background on CTL A popular and quite expressive language for Model  Home/Search   Document Details and Download   Summary   Related Articles

....says that there is a path along which the predicates p 1 through pn occur in some order, requires size n to express in CTL. Our lower bound is optimal. It follows that the succinctness of CTL with respect to CTL is exactly #(n) Wilke had shown that the succinctness was at least exponential [Wil99]. We also use our games to prove an optimal# n) lower bound on the number of boolean variables needed for a weak reachability logic (RL w ) to polynomially embed the language LTL. The number of booleans needed for full reachability logic RL and the transitive closure logic FO 2 (TC) ....

....path starting from the current point. F is the modal quantifier: somewhere now or in the future along the current path. This offers a quite different proof and improves the exponential lower bound on the succinctness of CTL compared # Research supported by NSF grant CCR 9877078. with CTL [Wil99]. We thus prove that the succinctness of CTL with respect to CTL is exactly #(n) We prove that the parse tree of any CTL formula expressing Occurn has at least n leaves. This bound is exactly optimal because the following formula expresses Occurn and has n leaves in its parse tree. Here ....

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T. Wilke, "CTL + is Exponentially More Succinct than CTL", Foundations of Software Technology and Theoretical Computer Science: 19th Conference, (1999), 110--121. A Background on CTL A popular and quite expressive language for Model

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