Research Article

Towards Support for Software Model Checking: Improving the Efficiency of Formal Specifications

Table 9

LTL formulas generated using the New Prospec's formulas.

Formulas

(1) ( ¬ ( ( ¬ 𝑙 ) 𝑈 ( 𝑙 ( ( ( ¬ 𝑝 ¬ 𝑝 𝑝 ¬ 𝑝 𝑝 𝑝 ) ( ( ¬ 𝑝 ¬ 𝑝 𝑝 ¬ 𝑝 𝑝 𝑝 ) 𝑈 ( 𝑝 𝑝 𝑝 𝑝 𝑝 𝑝 ) ) ) ) ) ) )
(2) ( ¬ ( ( ¬ 𝑙 ) 𝑈 ( 𝑙 ( ( 𝑝 ( ( ¬ 𝑝 𝑝 ) 𝑈 𝑝 𝑝 ) ) ) ) ) )
(3) ( ¬ ( ( ¬ 𝑙 ) 𝑈 ( 𝑙 ( ( 𝑝 𝑋 ( ¬ 𝑝 𝑝 𝑈 𝑝 𝑝 ) ) ) ) ) )
(4) ( ¬ ( ( ¬ ( ( ¬ 𝑙 ¬ 𝑙 𝑙 ) ( ( ¬ 𝑙 ¬ 𝑙 𝑙 ) 𝑈 ( 𝑙 𝑙 𝑙 ) ) ) ) 𝑈 ( ( ( ( ¬ 𝑙 ¬ 𝑙 𝑙 ) ( ( ¬ 𝑙 ¬ 𝑙 𝑙 ) 𝑈 ( ( 𝑙 𝑙 𝑙 ) 𝑝 ) ) ) ) ) ) )
(5) ( ¬ ( ( ¬ ( 𝑙 ( ( ¬ 𝑙 𝑙 ) 𝑈 𝑙 𝑙 ) ) ) 𝑈 ( ( ( 𝑙 ( ( ¬ 𝑙 𝑙 ) 𝑈 ( 𝑙 𝑙 𝑝 ) ) ) ) ) ) )
(6) ( ¬ ( ( ¬ ( 𝑙 𝑋 ( ¬ 𝑙 𝑙 𝑈 𝑙 𝑙 ) ) ) 𝑈 ( ( ( 𝑙 𝑋 ( ¬ 𝑙 𝑙 𝑈 ( 𝑙 𝑙 𝑝 ) ) ) ) ) ) )
(7) ( ¬ ( ( ¬ 𝑙 ) 𝑈 ( 𝑙 ¬ ( ( ( ¬ 𝑝 ¬ 𝑝 𝑝 ¬ 𝑝 𝑝 𝑝 ) ( ( ¬ 𝑝 ¬ 𝑝 𝑝 ¬ 𝑝 𝑝 𝑝 ) 𝑈 ( 𝑝 𝑝 𝑝 𝑝 𝑝 𝑝 ) ) ) ) ) ) )
(8) ( ¬ ( ( ¬ 𝑙 ) 𝑈 ( 𝑙 ¬ ( ( 𝑝 ( ( ¬ 𝑝 𝑝 ) 𝑈 ( 𝑝 𝑝 ( ( ¬ 𝑝 𝑝 𝑝 ) 𝑈 𝑝 𝑝 𝑝 ) ) ) ) ) ) ) )
(9) ( ¬ ( ( ¬ 𝑙 ) 𝑈 ( 𝑙 ¬ ( ( 𝑝 𝑋 ( ¬ 𝑝 𝑝 𝑈 ( 𝑝 𝑝 𝑋 ( ¬ 𝑝 𝑝 𝑝 𝑈 𝑝 𝑝 𝑝 ) ) ) ) ) ) ) )
(10) ( ¬ ( ( ¬ ( ( ¬ 𝑙 ¬ 𝑙 𝑙 ¬ 𝑙 𝑙 𝑙 ) ( ( ¬ 𝑙 ¬ 𝑙 𝑙 ¬ 𝑙 𝑙 𝑙 ) 𝑈 ( 𝑙 𝑙 𝑙 𝑙 𝑙 𝑙 ) ) ) ) 𝑈 ( ( ( ( ¬ 𝑙 ¬ 𝑙 𝑙 ¬ l 𝑙 𝑙 ) ( ( ¬ 𝑙 ¬ 𝑙 𝑙 ¬ 𝑙 𝑙 𝑙 ) 𝑈 ( ( 𝑙 𝑙 𝑙 𝑙 𝑙 𝑙 ) ¬ 𝑝 ) ) ) ) ) ) )
(11) ( ¬ ( ( ¬ ( 𝑙 ( ( ¬ 𝑙 𝑙 ) 𝑈 𝑙 𝑙 ) ) ) 𝑈 ( ( ( 𝑙 ( ( ¬ 𝑙 𝑙 ) 𝑈 ( 𝑙 𝑙 ¬ 𝑝 ) ) ) ) ) ) )
(12) ( ¬ ( ( ¬ ( 𝑙 𝑋 ( ¬ 𝑙 𝑙 𝑈 𝑙 𝑙 ) ) ) 𝑈 ( ( ( 𝑙 𝑋 ( ¬ 𝑙 𝑙 𝑈 ( 𝑙 𝑙 ¬ 𝑝 ) ) ) ) ) ) )
(13) ( ¬ ( ( ¬ ( ( ¬ 𝑙 ¬ 𝑙 𝑙 ¬ 𝑙 𝑙 𝑙 ) ( ( ¬ 𝑙 ¬ 𝑙 𝑙 ¬ 𝑙 𝑙 𝑙 ) 𝑈 ( 𝑙 𝑙 𝑙 𝑙 𝑙 𝑙 ) ) ) ) 𝑈 ( ( ( ( ¬ 𝑙 ¬ 𝑙 𝑙 ¬ 𝑙 𝑙 𝑙 ) ( ( ¬ 𝑙 ¬ 𝑙 𝑙 ¬ 𝑙 𝑙 𝑙 ) 𝑈 ( ( 𝑙 𝑙 𝑙 𝑙 𝑙 𝑙 ) ¬ 𝑝 ) ) ) ) ) ) )
(14) ( ¬ ( ( ¬ ( 𝑙 ( ( ¬ 𝑙 𝑙 ) 𝑈 𝑙 𝑙 ) ) ) 𝑈 ( ( ( 𝑙 ( ( ¬ 𝑙 𝑙 ) 𝑈 ( 𝑙 𝑙 ¬ 𝑝 ) ) ) ) ) ) )
(15) ( ¬ ( ( ¬ ( 𝑙 𝑋 ( ¬ 𝑙 𝑙 𝑈 𝑙 𝑙 ) ) ) 𝑈 ( ( ( 𝑙 𝑋 ( ¬ 𝑙 𝑙 𝑈 ( 𝑙 𝑙 ¬ 𝑝 ) ) ) ) ) ) )
(16) ( ¬ ( ( ¬ 𝑙 ) 𝑈 ( 𝑙 ¬ ( ( ( ( ¬ 𝑝 ) ( ¬ 𝑝 𝑝 ) ) ( ( ( ¬ 𝑝 ) ( ¬ 𝑝 𝑝 ) ) 𝑈 ( 𝑝 𝑝 𝑝 ) ) ) ( ( ( ¬ 𝑝 ) ( ¬ 𝑝 𝑝 ) ) ( ( ( ¬ 𝑝 ) ( ¬ 𝑝 𝑝 ) ) 𝑈 ( 𝑝 𝑝 𝑝 𝑞 ) ) ) ) ) ) )
(17) ( ¬ ( ( ¬ 𝑙 ) 𝑈 ( 𝑙 ¬ ( ( 𝑝 ( ( ¬ 𝑝 𝑝 ) 𝑈 ( 𝑝 𝑝 ) ) ) ) ( 𝑝 ( ( ¬ 𝑝 𝑝 ) 𝑈 ( 𝑝 𝑝 𝑞 ) ) ) ) ) )
(18) ( ¬ ( ( ¬ 𝑙 ) 𝑈 ( 𝑙 ¬ ( ( 𝑝 𝑋 ( ( ¬ 𝑝 𝑝 ) 𝑈 ( 𝑝 𝑝 ) ) ) ) ( 𝑝 𝑋 ( ( ¬ 𝑝 𝑝 ) 𝑈 ( 𝑝 𝑝 𝑞 ) ) ) ) ) )
(19) ( ¬ ( ( ¬ 𝑙 ) 𝑈 ( 𝑙 ¬ ( 𝑝 ( ( ( ¬ 𝑞 ) ( ¬ 𝑞 𝑞 ) ) ( ( ( ¬ 𝑞 ) ( ¬ 𝑞 𝑞 ) ) 𝑈 ( 𝑞 𝑞 𝑞 ) ) ) ) ) ) )
(20) ( ¬ ( ( ¬ 𝑙 ) 𝑈 ( 𝑙 ¬ ( 𝑝 ( 𝑞 ( ( ¬ 𝑞 𝑞 ) 𝑈 ( 𝑞 𝑞 ( ( ¬ 𝑞 𝑞 𝑞 ) 𝑈 𝑞 𝑞 𝑞 ) ) ) ) ) ) ) )
(21) ( ¬ ( ( ¬ 𝑙 ) 𝑈 ( 𝑙 ¬ ( p ( 𝑞 𝑋 ( ( ¬ 𝑞 𝑞 ) 𝑈 ( 𝑞 𝑞 𝑋 ( ( ¬ 𝑞 𝑞 𝑞 ) 𝑈 𝑞 𝑞 𝑞 ) ) ) ) ) ) ) )
(22) ( ¬ ( ( ¬ ( ( ( ¬ 𝑙 ) ( ¬ 𝑙 𝑙 ) ) ( ( ( ¬ 𝑙 ) ( ¬ 𝑙 𝑙 ) ) 𝑈 ( 𝑙 𝑙 𝑙 ) ) ) 𝑈 ( ( ( ( ¬ 𝑙 ) ( ¬ 𝑙 𝑙 ) ) ( ( ( ¬ 𝑙 ) ( ¬ 𝑙 𝑙 ) ) 𝑈 ( 𝑙 𝑙 𝑙 ¬ ( 𝑝 𝑞 ) ) ) ) ) ) ) )
(23) ( ¬ ( ( ¬ ( 𝑙 ( ( ¬ 𝑙 𝑙 ) 𝑈 ( 𝑙 𝑙 ) ) ) ) 𝑈 ( ( 𝑙 ( ( ¬ 𝑙 𝑙 ) 𝑈 ( 𝑙 𝑙 ¬ ( 𝑝 𝑞 ) ) ) ) ) ) )
(24) ( ¬ ( ( ¬ ( 𝑙 𝑋 ( ( ¬ 𝑙 𝑙 ) 𝑈 ( 𝑙 𝑙 ) ) ) ) 𝑈 ( ( 𝑙 𝑋 ( ( ¬ 𝑙 𝑙 ) 𝑈 ( 𝑙 𝑙 ¬ ( 𝑝 𝑞 ) ) ) ) ) ) )