Counterexample-Preserving Reduction for Symbolic Model Checking

Table 7

Reduction rules for formulae involving adjacent 𝐔 operators.

𝜌⊢𝜃1→𝜃2 ⊳ 𝜃1𝐔𝜃2≈𝜃2	(U[1→2])
𝜌⊢𝜃1→𝜃3 ⊳ (𝜃1𝐔𝜑2)𝐔𝜃3≈𝜑2𝐔𝜃3	(U^U[1→3])
𝜌⊢𝜃2→𝜃3 ⊳ (𝜑1𝐔𝜃2)𝐔𝜃3≈𝜃3∨(𝜑1𝐔𝜃2)	(U^U[2→3])
𝜌⊢𝜃3→𝜃2 ⊳ (𝜑1𝐔𝜃2)𝐔𝜃3≈(𝜑1∨𝜃2)𝐔𝜃3	(U^U[3→2])
𝜌⊢𝜃2→𝜃^′3 ⊳ (𝜑1𝐔𝜃2)𝐔𝜃3≈(𝜑1∨𝜃2)𝐔𝜃3	(U^U[2→3^′])
𝜌⊢¬𝜃2→𝜃3 ⊳ (𝜑1𝐔𝜃2)𝐔𝜃3≈𝐅𝜃3	(U^U[¬2→3])
𝜌⊢𝜃1→𝜃2 ⊳ 𝜃1𝐔(𝜃2𝐔𝜑3)≈𝜃2𝐔𝜑3	(UU[1→2])
𝜌⊢𝜃1→𝜃3 ⊳ 𝜃1𝐔(𝜑2𝐔𝜃3)≈𝜑2𝐔𝜃3	(UU[1→3])
𝜌⊢𝜃2→𝜃1 ⊳ 𝜃1𝐔(𝜃2𝐔𝜑3)≈𝜃1𝐔𝜑3	(UU[2→1])