Branching time regular temporal logic for model checking with linear time complexity

Firstly in this paper, we propose a branching time logic BRTL (Branching time Regular Temporal Logic) which has automata connectives as temporal operators. BRTL is more expressive than CTL proposed by Clarke et.al. and it is modest in terms of model checking, i.e. it has a model checking algorithm which runs in time proportional both to the size of a given Kripke structure and to the length of a given formula, as shown in the paper. Secondly, in order to improve the succinctness of the temporal logic formulas, we introduce the mechanism of substitutions to Boolean variables and references to the Boolean variables. We propose EBRTL(Extended BRTL), i.e. BRTL with the substitution mechanism, and show examples of descriptions of some temporal properties. We develop its model checking algorithm whose time complexity is linear both in the size of a given Kripke structure and in the length of a given formula and exponential in the number of the Boolean variables used in the formula.