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Sorted by
State Size
Formula Length
Temporal Hierarchy
Spec Patterns
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NBW
DBW
NGBW
DGBW
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DCW
NMW
DMW
NRW
DRW
NSW
DSW
NPW
DPW
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1 state
2 states
3 states
4 states
5 states
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1 temporal operator
2 temporal operators
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4 temporal operators
More than 4 operators
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To Be Determined
SafeGuarantee
Safety
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/ 27
False
Equivalent:
False
•
Y p
•
Y ¬ p
•
¬ Z p
•
¬ Z ¬ p
•
Y p ∧ Z False
•
Z p ∧ Y True
•
¬ G (q → O p) ∧ p
•
¬ G (p → q U p)
Complement:
True
•
¬ Y p
•
¬ Y ¬ p
•
Z p
•
Z ¬ p
•
¬ (Y p ∧ Z False)
•
F p → F p
•
Y ¬ p ∨ Z False
•
¬ (Z p ∧ Y True)
•
Z ¬ p ∨ Y True
•
Z Z p
•
G (p → F (q → p))
•
G (p → q U p)
NBW
True
Equivalent:
True
•
¬ Y p
•
¬ Y ¬ p
•
Z p
•
Z ¬ p
•
¬ (Y p ∧ Z False)
•
F p → F p
•
Y ¬ p ∨ Z False
•
¬ (Z p ∧ Y True)
•
Z ¬ p ∨ Y True
•
Z Z p
•
G (p → F (q → p))
•
G (p → q U p)
Complement:
False
•
Y p
•
Y ¬ p
•
¬ Z p
•
¬ Z ¬ p
•
Y p ∧ Z False
•
Z p ∧ Y True
•
¬ G (q → O p) ∧ p
•
¬ G (p → q U p)
NBW
G (p ∨ q)
Equivalent:
G (p ∨ q)
•
G (p W (q ∧ ¬ p))
•
G (p W q)
Complement:
NBW
¬ F (p → Fq)
Equivalent:
¬ F (p → Fq)
Complement:
NBW
G (p ∨ ¬ q)
Equivalent:
G (p ∨ ¬ q)
Complement:
NBW
p → F p
Equivalent:
p → F p
Complement:
DBW
G (¬ p ∧ q)
Equivalent:
G (¬ p ∧ q)
Complement:
NBW
G (¬ p ∨ q ∧ r)
Equivalent:
G (¬ p ∨ q ∧ r)
Complement:
NBW
G (p → q ∧ ¬ r)
Equivalent:
G (p → q ∧ ¬ r)
Complement:
NBW
G (¬ p ∨ ¬ q)
Equivalent:
G (¬ p ∨ ¬ q)
Complement:
F (p ∧ q)
•
¬ G (¬ p ∨ ¬ q)
NBW
G ¬ p
Equivalent:
¬ (True U p)
•
¬ F p
•
False R ¬ p
•
¬ p W (False ∧ ¬ p)
•
G ¬ p
•
¬ (p ∨ X F p)
•
¬ O F p
•
¬ F (True S p)
•
¬ F O p
•
¬ F F p
•
H G ¬ p
•
¬ p ∧ X G ¬ p
•
G (¬ p B (False ∧ ¬ p))
•
G H ¬ p
•
G G ¬ p
•
F (G ¬ p ∧ H ¬ p)
•
F G H ¬ p
•
¬ F G O p
•
¬ G (F p ∨ O p)
•
¬ G F O p
•
G F H ¬ p
Complement:
F p
•
True U p
•
¬ G ¬ p
•
O F p
•
F (True S p)
•
F O p
•
F F p
•
p ∨ X F p
•
F G O p
•
G (F p ∨ O p)
•
G F O p
NBW
G (¬ p ∧ ¬ q)
Equivalent:
¬ F (p ∨ q)
•
G (¬ p ∧ ¬ q)
•
¬ (F p ∨ F q)
•
G ¬ p ∧ G ¬ q
Complement:
F (p ∨ q)
•
F p ∨ F q
NBW
G p
Equivalent:
¬ F ¬ p
•
False R p
•
G p
•
p W False
•
G (p B False)
•
G G p
•
p ∧ X G p
•
F G H p
•
G F H p
Complement:
¬ (False R p)
•
¬ (p W False)
•
F ¬ p
•
True U (¬ p ∧ True)
•
True U ¬ p
•
p U ¬ p
•
¬ G p
•
¬ (p ∧ X G p)
•
F (True S (¬ p ∧ True))
•
F F ¬ p
•
¬ G (p B False)
•
¬ G G p
•
¬ p ∨ X F ¬ p
•
F G O ¬ p
•
¬ F G H p
•
¬ G F H p
•
G F O ¬ p
NBW
G (p ∧ q)
Equivalent:
G (p ∧ q)
•
G p ∧ G q
Complement:
F (¬ p ∨ ¬ q)
•
¬ G (p ∧ q)
•
¬ (G p ∧ G q)
•
F ¬ p ∨ F ¬ q
NBW
G (p → ¬ p U q)
Equivalent:
G (p → ¬ p U q)
•
G (¬ p W q)
Complement:
NBW