Hardware Reference
In-Depth Information
Chapter 19
Conclusions and Open Problems
The problem of finding an unknown component in a network of components in
order to satisfy a global system specification was addressed. Abstract language
equations of the type
A X C
and
A ˘ X C
were investigated, where
are operators of language composition. The most general solution was
computed and various types of constrained solutions were studied. Then specialized
language equations were introduced, such as regular and FSM language equations.
The maximum subsets of them, closed with respect to various language properties,
were studied; in particular the largest compositional solutions were studied.
This approach unifies, in a seamless frame, previously reported techniques and
appears capable of modeling problems with various notions of language acceptance,
composition and conformance relations.
Examples were discussed, such as a classical synthesis problem of a converter
between a given mismatched pair of protocols, given their specifications, as well as
those of the channel and of the required service. This problem was also addressed
in the literature with supervisory control techniques. We were able to derive the
largest solution, and the largest compositionally progressive solution, which were
not previously reported in the literature.
We applied this theory to sequential logic synthesis in order to derive results for
some commonly studied topologies of networks of FSMs.
A prototype software package - BALM - has been built to compute the solutions
automatically. To assess the practical relevance of the method, we tested it in
different applicative domains. We also investigated approximations of the exact
solutions, to trade off flexibility vs. computational effort.
A number of open problems have been mentioned already throughout the text,
here are some open problems of a more general nature:
and
˘
1. How to make the computations to solve language equations more scalable. In ap-
plicative domains like synthesis of sequential circuits, one can choose state-based
representations vs. structural-based representations; the former are exponentially
related to the latter. Language equations require state-based representations,
which bounds the size of the problem instances that can be treated. It would
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