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We introduce a general definition for a family of branching-time logics that extend CTL * by allowing constraints between variables at the atomic level. These constraints allow to compare values of variables at different states of the model. We define an automata-theoretic approach to solve verification problems for such extensions. Our method is based on a finite abstraction of the infinite state space and a symbolic representation of the models that generalizes several approaches used fordoi:10.1016/j.entcs.2009.05.040 fatcat:qgr2cwvolrbuzf6zyzbqjwbmwq