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

Table 3

Prospec's original LTL formulas for pattern and scope.

Pattern	Scope	LTL Formula
Absence	Global	¬(⋄𝑃)
	Before 𝑅	⋄𝑅→¬(¬(𝑅)𝑈𝑃)
	After 𝐿	¬(𝐿)𝑊(𝐿∧¬(⋄𝑃))
	Between 𝐿 and 𝑅	[]((𝐿∧¬(𝑅)∧⋄𝑅)→¬(¬(𝑅)𝑈𝑃))
	After 𝐿 Until 𝑅	[](𝐿∧¬(𝑅)→¬(¬(𝑅)𝑈𝑃))
Existence	Global	(⋄𝑃)
	Before 𝑅	⋄𝑅→(¬(𝑅)𝑈(𝑃∧¬(𝑅)))
	After 𝐿	¬(𝐿)𝑊(𝐿∧(⋄𝑃))
	Between 𝐿 and 𝑅	[]((𝐿∧¬(𝑅)∧⋄𝑅)→(¬(𝑅)𝑈(𝑃∧¬(𝑅))))
	After 𝐿 Until 𝑅	[]((𝐿∧¬(𝑅))→(¬(𝑅)𝑈(𝑃∧¬(𝑅))))
Universality	Global	[]𝑃
	Before 𝑅	⋄𝑅→(𝑃𝑈𝑅)
	After 𝐿	¬(𝐿)𝑊(𝐿∧[]𝑃)
	Between 𝐿 and 𝑅	[]((𝐿∧¬(𝑅)∧⋄𝑅)→(𝑃𝑈𝑅))
	After 𝐿 Until 𝑅	[]((𝐿∧¬(𝑅))→(𝑃𝑊𝑅))
Precedence	Global	¬(𝑃)𝑊𝑇
	Before 𝑅	⋄𝑅→(¬(𝑃)𝑈(𝑇∨𝑅))
	After 𝐿	¬(𝐿)𝑊(𝐿∧(¬(𝑃)𝑊(𝑇)))
	Between 𝐿 and 𝑅	[]((𝐿∧¬(𝑅)∧⋄𝑅)→(¬(𝑃)𝑈((𝑇∨𝑅))))
	After 𝐿 Until 𝑅	[](𝐿∧¬(𝑅)→(¬(𝑃)𝑊(𝑇∨𝑅)))
Response	Global	[](𝑃→⋄𝑇)
	Before 𝑅	⋄𝑅→((𝑃→(¬(𝑅)𝑈(𝑇∧¬(𝑅))))𝑈𝑅)
	After 𝐿	(¬𝐿)𝑊(𝐿∧[](𝑃→⋄𝑇))
	Between 𝐿 and 𝑅	[]((𝐿∧¬(𝑅)∧⋄𝑅)→(𝑃→(¬(𝑅)𝑈(𝑇∧¬(𝑅))))𝑈𝑅
	After 𝐿 Until 𝑅	[]((𝐿∧¬(𝑅)→(𝑃→(¬(𝑅)𝑈(𝑇∧¬(𝑅))))𝑊𝑅)
Strict Precedence	Global	¬(𝑃)𝑊(𝑇∧¬(𝑃))
	Before 𝑅	⋄𝑅→(¬(𝑃)𝑈((𝑇∧¬(𝑃))∨𝑅))
	After 𝐿	¬(𝐿)𝑊(𝐿∧(¬(𝑃)𝑊(𝑇∧¬(𝑃))))
	Between 𝐿 and 𝑅	[]((𝐿∧¬(𝑅)∧⋄𝑅)→(¬(𝑃)𝑈((𝑇∧¬(𝑃))∨𝑅)))
	After 𝐿 Until 𝑅	[](𝐿∧¬(𝑅)→(¬(𝑃)𝑊((𝑇∧¬(𝑃))∨𝑅)))