Verification of Rewrite Rules for Computation Tree Logics

Abstract

A number of procedures for checking the satisfiability of formulas in the important branching time temporal logic CTL* have recently been proposed. This paper instead focuses on automatic generation and verification of rewrite rules for computation tree logics; shows that non-local computation tree logics can be used to verify rewrite rules, including for CTL*; presents an efficient tableau for the non-local bundled variant NL-BCTL*; and shows that NL-BCTL* is 2EXPTIME-complete. We show that such rules can quickly simplify CTL* formulas. These simplified formulas are shorter and easier to reason with using existing decision procedures for CTL*, as demonstrated by significant speed-ups across a wide range of benchmark formulas. While CTL* is not widely used due to the complexity of its reasoning tasks, it is strictly more expressive than LTL or CTL. Furthermore, there are applications for theorem-proving and model-checking.