Abstract
Sequential synthesis offers a collection of problems that can be modeled by FSM equations under synchronous composition. Some have been addressed in the past with various techniques in different logic synthesis applications. In place of designing a huge monolithic FSM and then optimizing it by state reduction and encoding, it is convenient to work with a network of smaller FSMs. However, if each of them is optimized in isolation, part of the implementation flexibility is lost, because no use is made of the global network information. Hierarchical optimization calls for optimizing the FSMs of a network capturing the global network information by means of don’t care conditions. The goal of hierarchical optimization is to optimize the FSMs of a network capturing the global network information by means of don’t care conditions. This paradigm follows the approach taken in multi-level combinational synthesis since the beginning[29,27], where a lot of effort has been invested in capturing the don’t cares conditions and devising efficient algorithms to compute them or their subsets [95, 54, 44, 57].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
One has to take care of defining over the same alphabets both \({A}_{{M}_{A}}^{o}\) and M B , for instance turning \({A}_{{M}_{A}}^{o}\) into an FSM with don’t care outputs for each input combination of the automaton \({A}_{{M}_{A}}^{o}\).
- 2.
Consider a series composition M A → M B of two FSMs M A = (S A , I, U, δ A , λ A , r A ) and M B = (S B , U, O, δ B , λ B , r B ). The FSM representing all behaviors that can be realized at the head component is given by the NDFSM M D = (S A ×S B ×S B , I, U, T, (r A , r B , r B )), where \((({s}_{A},\hat{{s}}_{B},\tilde{{s}}_{B}),i,u, ({s^{\prime}}_{A},\hat{{s}^{\prime}}_{B},\tilde{{s}^{\prime}}_{B}))\) ∈ T iff the output of M A → M B at state (s A , s B ) under input i is equal to the output of M B at state \(\tilde{{s}}_{B}\) under input u, and \(({s^{\prime}}_{A},\hat{{s}^{\prime}}_{B},\tilde{{s}^{\prime}}_{B})\) are the successor states respectively in M A → M B and M B .
Theorem 5.4.
[111] M C → M B = M A → M B iff M C is a reduction of M D .
.
- 3.
ψ ⊆ S 1 ×S 2 is a simulation relation from an FSM M 1 = ⟨S 1, I, O, T 1, r 1⟩ to an FSM M 2 = ⟨S 2, I, O, T 2, r 2⟩ if:
-
1.
(r 1, r 2) ∈ ψ, and
-
2.
\(({s}_{1},{s}_{2}) \in \psi \Rightarrow \{\ \forall i\ \forall o\ \forall {s}_{1}^{^{\prime}}\ [\ ({s}_{1}{{{i/o}\atop{\rightarrow }}}_{{M}_{1}}\ {s}_{1}^{^{\prime}}) \Rightarrow \exists {s}_{2}^{^{\prime}}\ [({s}_{2}\ {{{i/o}\atop{\rightarrow }}}_{{M}_{2}}\ {s}_{2}^{^{\prime}})\ \wedge \ ({s}_{1}^{^{\prime}},{s}_{2}^{^{\prime}}) \in \psi ]\ ]\ \}\).
If such a ψ exists, we say that M 2 simulates M 1, or that M 1 has a simulation into M 2, and denote it by M 1 ≼ sim M 2.
-
1.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2012 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Villa, T., Yevtushenko, N., Brayton, R.K., Mishchenko, A., Petrenko, A., Sangiovanni-Vincentelli, A. (2012). A Survey of Relevant Literature. In: The Unknown Component Problem. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-68759-9_5
Download citation
DOI: https://doi.org/10.1007/978-0-387-68759-9_5
Published:
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-34532-1
Online ISBN: 978-0-387-68759-9
eBook Packages: EngineeringEngineering (R0)