Efficient Semantics-Based Compliance Checking Using LTL Formulae and Unfolding

Table 1

LTL formulae in SPS.

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