Formal Definition
Given a labelled state transition system (S, Λ, →), a simulation relation is a binary relation R over S (i.e. 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,
implies that there is a q' ∈ S such that
and (p',q') ∈ R.
Equivalently, in terms of relational composition:
Given two states p and q in S, q simulates p, written p ≤ q if there is a simulation R such that (p, q) ∈ R. The relation ≤ is a preorder, and is usually called the simulation preorder. It is the largest simulation relation over a given transition system.
Two states p and q are said to be similar, written p ≤≥ q, if p simulates q and q simulates p. Similarity is an equivalence relation, but it is coarser than bisimilarity.
Read more about this topic: Simulation Preorder
Famous quotes containing the words formal and/or definition:
“The bed is now as public as the dinner table and governed by the same rules of formal confrontation.”
—Angela Carter (1940–1992)
“Perhaps the best definition of progress would be the continuing efforts of men and women to narrow the gap between the convenience of the powers that be and the unwritten charter.”
—Nadine Gordimer (b. 1923)