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:
“It is in the nature of allegory, as opposed to symbolism, to beg the question of absolute reality. The allegorist avails himself of a formal correspondence between “ideas” and “things,” both of which he assumes as given; he need not inquire whether either sphere is “real” or whether, in the final analysis, reality consists in their interaction.”
—Charles, Jr. Feidelson, U.S. educator, critic. Symbolism and American Literature, ch. 1, University of Chicago Press (1953)
“The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.”
—Samuel Taylor Coleridge (1772–1834)