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:
“Two clergymen disputing whether ordination would be valid without the imposition of both hands, the more formal one said, “Do you think the Holy Dove could fly down with only one wing?””
—Horace Walpole (1717–1797)
“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)