Everything about Simulation Preorder totally explained
In
theoretical computer science a
simulation preorder is a
relation between
state transition systems associating systems which behave in the same way in the sense that one system
simulates the other.
Intuitively, a system simulates another system if it can match all of its moves.
The basic definition relates states within one transition system, but this is easily adapted to relate two separate transition systems by building a system consisting of the disjoint union of the corresponding components.
Formal definition
Given a
labelled state transition system (S, Λ, →), a
simulation relation is a
binary relation R over S (for example R ⊆ S × S) such that for every pair of elements p, q ∈ S, if (p,q)∈ R then for all α ∈ Λ, and for all p' ∈ S,
»
Given two states p and q in S, q
simulates p, written p ≤ q if there's a simulation R such that (p, q) ∈ R. In such a case, p and q are said to be
similar and ≤ is called the
similarity relation.
The similarity relation ≤ is a
preorder. Furthermore, it's the largest simulation relation over a given transition system.
Similarity of separate transition systems
When comparing two different transition systems (S', Λ', →') and (S' ', Λ' ', →' '), the basic notions of simulation and similarity can be used by forming the disjoint composition of the two machines, (S, Λ, →) with S = S' ∪ S' ', Λ = Λ' ∪ Λ' ' and → = →' ∪ →' ', where ∪ is the
disjoint union operator between sets.
Further Information
Get more info on 'Simulation Preorder'.
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