“Simulation preorder”的意思、由来-开放百科全书

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Simulation preorder

释义

Formal definition
Similarity of separate transition systems
See also
References

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 (i.e. R ⊆ S × S) such that for every pair of elements (p,q) ∈ R, 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.

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.

References

{{Cite conference

| first = David
| last = Park
| year = 1981
| title = Concurrency and Automata on Infinite Sequences
| booktitle = Proceedings of the 5th GI-Conference, Karlsruhe
| series = Lecture Notes in Computer Science
| editor = Deussen, Peter
| pages = 167–183
| volume = 104
| publisher = Springer-Verlag
| isbn = 978-3-540-10576-3
| doi = 10.1007/BFb0017309
}}

{{Cite book

| last = Milner
| first = Robin
| title = Communication and Concurrency
| year = 1989
| publisher = Prentice Hall
| isbn = 0-13-114984-9
}}

{{Cite conference

| last = van Glabbeek
| first = R. J.
| title = The Linear Time – Branching Time Spectrum I: The Semantics of Concrete, Sequential Processes
| booktitle = Handbook of Process Algebra
| url = http://boole.stanford.edu/pub/spectrum1.pdf.gz
| chapter = 1
| pages = 3–99
| year = 2001
| publisher = Elsevier
}}{{DEFAULTSORT:Simulation Preorder}}

1 : Theoretical computer science

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Formal definition

Similarity of separate transition systems

See also

References