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<title> Architectural and Logic Synthesis </title>

<h1>Architectural and Logic Synthesis</h1>

<img  src="synthesis.gif" ><p>

The abstracts of papers by members of this group in the above area are 
listed below. Please use the email addresses at the end of each
abstract to get further details.

<ul>


<li>Y.P. Chen and D.F. Wong
<b> On Retiming for FPGA Logic Module Minimization</b>. In
<cite>Proceedings of the IEEE International Conference on Computer Design</cite>,
October 1994. <p>

<blockquote>
We consider the problem of minimizing the number of logic 
modules for  Actel 2  or Actel 3 sequential circuits.
We make use of the fact that if a flip-flop is the only destination 
of its driving combinational block, then both the flip-flop and the 
combinational block can be put in a sequential module.  Retiming technique is
applied to minimize the number of registers that can not be merged with 
combinational blocks.  We formulate the problem as
an integer linear program.  We show that the constraint matrix of the integer
program is totally unimodular.  As a result, we can solve our logic
module minimization problem optimally by solving the linear relaxation 
of the integer program.
</blockquote>
<b>Contact:</b> <i>[e-mail]</i><p>

<li> Honghua Yang and D. F. Wong.
<b> Edge-Map: Optimal Performance Driven Technology Mapping for
                 Iterative LUT Based FPGA Designs</b>. In
<cite>Proceedings of the IEEE International Conference on 
       Computer-Aided Design</cite>, Nov. 1994. <p>

<blockquote>
We consider the problem of performance driven lookup-table (LUT) based 
technology mapping for FPGAs using a general delay model.  In the general 
delay model, each interconnection edge has a weight representing the delay
of the interconnection.  This model is particularly useful when combined with
an iterative re-technology mapping process where the actual delays of the
placed and routed circuit are fed-back to the technology mapping phase to
improve the mapping based on the more realistic delay estimation.
Well known technology mappers such as FlowMap and Chortle-d only minimize
the number of levels in the technology mapped circuit and hence are not
suitable for such an iterative re-technology mapping process.
Recently, Mathur and Liu  studied the performance driven
technology mapping problem using the general delay model and presented
an effective heuristic algorithm for the problem. In this paper,
we present an efficient technology mapping algorithm that achieves 
provably optimal delay in the technology mapped circuit using the general 
delay model.  Our algorithm is a non-trivial generalization of FlowMap.
A key problem in our algorithm is to compute a K-feasible network cut
such that the circuit delay on every cut edge is upper-bounded by a specific 
value.  We implemented our algorithm in a LUT based FPGA technology mapping 
package called Edge-Map, and tested Edge-Map on a set of benchmark circuits.
</blockquote>

<b>Contact:</b> <i>[e-mail]</i><p>

<li> Yung-Ming Fang and D.F. Wong.
<b> Simultaneous Functional-Unit Binding and Floorplanning</b>.
<cite> Proceedings of the IEEE International Conference on
       Computer-Aided Design</cite>, November 1994. <p>

<blockquote>
As device feature size decreases,
interconnection delay becomes the dominating factor of system performance.
Thus it is important that accurate physical information is used
during high level synthesis.
In this paper, we consider the problem of
simultaneously performing functional-unit binding and floorplanning.
Experimental results indicate that
our approach to combine binding and floorplanning is superior to
the traditional approach of separating the two tasks.
</blockquote>

<b>Contact:</b> <i>[e-mail]</i><p>


<li> Shashidhar Thakur, D.F. Wong, Shankar Krishnamoorthy, and P. Moceyunas.</li>
<b>Delay Minimal Decomposition of Multiplexers in Technology Mapping</b>
<cite> International Workshop on Logic Synthesis, </cite>May 1995. <p>

<blockquote>
Technology mapping requires the unmapped
logic network to be represented in terms of base
functions. Technology decomposition is the step that
transforms arbitrary networks to this form. Typically such
decomposition schemes ignore the fact that certain circuit
elements can be mapped more efficiently by treating them
separately during decomposition. Multiplexers are in one such
category of circuit elements. They appear very naturally in
circuits, in the form of datapath elements, and as a result of
synthesis of CASE statements in HDL specifications of
control logic. Mapping them using multiplexers in technology
libraries has many advantages. In this paper, we 
give an algorithm for
optimally decomposing multiplexers, so as to minimize the
delay of the network.  We present the results of mapping 
networks, decomposed by such a scheme, to Actel2 and lsi_10K
libraries, which are rich in multiplexers. Experimental
results indicate that the quality of the mapped circuits,
measured in terms of area, delay, and routability, is
greatly improved,
when compared to a Huffman tree based AND-OR decomposition
scheme.
</blockquote>

<b>Contact:</b> <i>[e-mail]</i><p>

<li>Shashidhar Thakur and D.F. Wong.</li>
<b>Simultaneous Area and Delay Minimum K-LUT
Mapping for K-Exact Networks</b>
<cite>International Conference on Computer Design, </cite>October 1995.</a><p>
<blockquote>
We address the technology mapping problem for 
lookup table FPGAs. The area minimization problem, for mapping
K-bounded networks, consisting of nodes with 
at most K inputs, using K-input lookup tables, is known to
be NP-complete for
K>=5. The complexity was unknown for K=2,3, and 4. The
corresponding delay minimization problem (under the constant
delay model) was solved in
polynomial time by the flow-map algorithm, for
arbitrary values of K. We study the class of K-bounded networks,
where all nodes have exactly K inputs. We call such
networks K-exact. We give a
characterization of mapping solutions for such
networks. This leads to a polynomial time algorithm for
computing the simultaneous area and delay minimum mapping
for such networks 
using K-input lookup tables. We 
also show that the 
flow-map algorithm minimizes the area of the mapped network
as well, for K-exact networks. We then show that for
K=2 the mapping solution 
for a 2-bounded network, minimizing the area and delay
simultaneously, can be easily obtained from that of a 2-exact
network derived from it by eliminating single input
nodes. Thus the area minimization problem 
for 2-input lookup tables can be solved in polynomial time,
resolving an open problem.
</blockquote>
<b>Contact:</b> <i>[e-mail]</i><p>
</ul>