An on-the-fly tableau construction for a real-time temporal logic

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4. The Tableau Algorithm L0 := {((s, Now, Next), TS(¯0)) | (TS, Now, Next) ∈ NFs({ϕ})} LNew := {(s, Now, Next) | ((s, Now, Next), TS) ∈ L0 } L := ∅, E := ∅ while LNew = ∅ do Let (it, Now, Next) ∈ LNew LNew := LNew\{(it, Now, Next)} L := L ∪ {(it, Now, Next)} for every (TS ′ , Now ′ , Next ′ ) ∈ NF it (Next) do E := E ∪ {((it, Now, Next), TS ′ , (it, Now ′ , Next ′ ))} if (it, Now ′ , Next ′ ) /∈ L then LNew := LNew ∪ {(it, Now ′ , Next ′ )} od od A 29
4. Example Tableau automaton of the formula ≤100♦≤5p © ¥ ¦ § ¡¢¤¨ ¥ ¥ ¡¢¤£ 0 § ¥ § ¥ ¥ § ¥ § ¥ § ¥ ¥ ¦ § ¥ ¥ § ¥ § singular open sing.+open A 30
Page 1 and 2: An on-the-fly tabl
Page 3 and 4: 1. Introduction: Real-time Systems
Page 5 and 6: 1. Introduction: Related Work • T
Page 7 and 8: 2. Modelling Timed Systems A 6
Page 9 and 10: 2. Exploring a Labelled Transition
Page 11 and 12: 3. Real-Time Temporal Logic A 10
Page 13 and 14: 3. Real-time Temporal Logic To deal
Page 15 and 16: 3. Real-time Temporal Logic To spec
Page 17 and 18: 4. On-the-fly tableau construction
Page 19 and 20: 4. Real-time On-the-fly Tableaux To
Page 21 and 22: 4. Real-time On-the-fly Tableaux x:
Page 23 and 24: 4. Real-time On-the-fly Tableaux TS
Page 25 and 26: 4. Real-time On-the-fly Tableaux Lo
Page 27 and 28: 4. Real-time On-the-fly Tableaux As
Page 29: 4. Real-time On-the-fly Tableaux TS
Page 33 and 34: 5. Constructing Monitors for Runtim
Page 35: 5. Conclusions and Future Work •

An on-the-fly tableau construction for a real-time temporal logic

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