Normed Simulations

W.O.D. Griffioen
and F.W. Vaandrager.
A Theory of Normed simulations.
ACM Transactions on Computational Logic (TOCL) 5(4):577-610, October 2004.
Abstract

In existing simulation proof techniques, a single step in a lower-level
specification may be simulated by an extended execution fragment in a
higher-level one.
As a result, it is cumbersome to mechanize these techniques using
general purpose theorem provers.
Moreover, it is undecidable whether a given relation is a simulation,
even if tautology checking is decidable for the underlying specification logic.
This paper studies various types of *normed simulations*.
In a normed simulation, each step in a lower-level specification can be
simulated by at most one step in the higher-level one, for any related
pair of states.
In earlier work we demonstrated that normed simulations are quite useful
as a vehicle for the formalization of refinement proofs via theorem provers.
Here we show that normed simulations also have
pleasant theoretical properties:
(1) under some reasonable assumptions, it is decidable whether a
given relation is a normed forward simulation,
provided tautology checking is decidable for the underlying logic;
(2) at the semantic level, normed forward and backward
simulations together form a complete proof method for establishing behavior
inclusion, provided that the higher-level specification has finite
invisible nondeterminism.
Postscript