Duration Calculus

Undecidability
Even small extensions give undecidable subsets
RDC1 cont. time RDC2 RDC3
• ℓ = r, ⌈S ⌉
• ¬φ, φ∨ψ, φ ⌢ ψ
• S1 = S2
• ¬φ, φ∨ψ, φ ⌢ ψ
• ℓ = x, ⌈S ⌉
• ¬φ, φ∨ψ, φ ⌢ ψ, (∃x)φ
Reduce halting problem (2-counter machines) to satisfiability
RDC 2: c1 encoded by C + 1 − C − 1 , where C+ 1 , C − 1 : Time → {0, 1}
In qi decrement c1 (if c1 > 0) and go to qj:
Tallinn, November 17- 21, Michael R. Hansen – p.15/29