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Specification of asynchronous circuit behaviour becomes more complex as the
complexity of today’s System-On-a-Chip (SOC) design increases. This also causes
the Signal Transition Graphs (STGs) – interpreted Petri nets for the specification
of asynchronous circuit behaviour – to become bigger and more complex, which
makes it more difficult, sometimes even impossible, to synthesize an asynchronous
circuit from an STG with a tool like petrify [CKK+96] or CASCADE [BEW00].
It has, therefore, been suggested to decompose the STG as a first step; this
leads to a modular implementation [KWVB03] [KVWB05], which can reduce syn-
thesis effort by possibly avoiding state explosion or by allowing the use of library
elements. A decomposition approach for STGs was presented in [VW02] [KKT93]
[Chu87a]. The decomposition algorithm by Vogler and Wollowski [VW02] is based
on that of Chu [Chu87a] but is much more generally applicable than the one in
[KKT93] [Chu87a], and its correctness has been proved formally in [VW02].
This dissertation begins with Petri net background described in chapter 2.
It starts with a class of Petri nets called a place/transition (P/T) nets. Then
STGs, the subclass of P/T nets, is viewed. Background in net decomposition
is presented in chapter 3. It begins with the structural decomposition of P/T
nets for analysis purposes – liveness and boundedness of the net. Then STG
decomposition for synthesis from [VW02] is described.
The decomposition method from [VW02] still could be improved to deal with
STGs from real applications and to give better decomposition results. Some
improvements for [VW02] to improve decomposition result and increase algorithm
efficiency are discussed in chapter 4. These improvement ideas are suggested in
[KVWB04] and some of them are have been proved formally in [VK04].
The decomposition method from [VW02] is based on net reduction to find
an output block component. A large amount of work has to be done to reduce
an initial specification until the final component is found. This reduction is not
always possible, which causes input initially classified as irrelevant to become
relevant input for the component. But under certain conditions (e.g. if structural
auto-conflicts turn out to be non-dynamic) some of them could be reclassified as
irrelevant. If this is not done, the specifications become unnecessarily large, which
intern leads to unnecessarily large implemented circuits. Instead of reduction, a
new approach, presented in chapter 5, decomposes the original net into structural
components first. An initial output block component is found by composing the
structural components. Then, a final output block component is obtained by net
reduction.
As we cope with the structure of a net most of the time, it would be useful
to have a structural abstraction of the net. A structural abstraction algorithm
[Kan03] is presented in chapter 6. It can improve the performance in finding an
output block component in most of the cases [War05] [Taw04]. Also, the structure
net is in most cases smaller than the net itself. This increases the efficiency of the
decomposition algorithm because it allows the transitions contained in a node of
the structure graph to be contracted at the same time if the structure graph is
used as internal representation of the net.
Chapter 7 discusses the application of STG decomposition in asynchronous
circuit design. Application to speed independent circuits is discussed first. Af-
ter that 3D circuits synthesized from extended burst mode (XBM) specifications
are discussed. An algorithm for translating STG specifications to XBM specifi-
cations was first suggested by [BEW99]. This algorithm first derives the state
machine from the STG specification, then translates the state machine to XBM
specification. An XBM specification, though it is a state machine, allows some
concurrency. These concurrencies can be translated directly, without deriving
all of the possible states. An algorithm which directly translates STG to XBM
specifications, is presented in chapter 7.3.1. Finally DESI, a tool to decompose
STGs and its decomposition results are presented.