Logical Analysis and Verification of Cryptographic Protocols - Loria

4.4. DECIDABILITY RESULTS 97
Figure 4.1 System of saturation rules
Input:
The intruder deduction rules LI.
Initialisation:
Let I ′ = 〈F, LI ′, ∅〉 be the variant of the intruder deduction system I (Definition
19, Chapter 2). We recall that
LI ′ =
�
x1, . . . , xn → f(x1, . . . , xn) ∈ LI
θ variant substitution of f(x1, . . . , xn)
x1θ, . . . , xnθ → (f(x1, . . . , xn)θ)↓
Step 1. Start with LI” = LI ′. Apply on LI” the rules below until any added rule is
subsumed by a rule already present in LI”.
Subsumption :
Closure :
Output:
Output LI”.
�l1 → r ∈ LI” � l2 → r ∈ LI”
�
LI” ← LI” \ �l2 → r
�l1 → r1 ∈ LI”, t, � l2 → r2 ∈ LI”
�
LI” ← LI” ∪ ( � l1, � �
l2 → r2)σ
� � l1 ⊆ � l2
t /∈ X
σ = mgu ∅(r1, t)