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32 CHAPTER 2. TOY(FD) Programming Examples

S5 == 7

S6 == 10

Elapsed time: 0 ms.

more solutions (y/n/d) [y]?

yes

S1 == 1

S2 == 4

S3 == 12

S4 == 1

S5 == 7

S6 == 11

Elapsed time: 0 ms.

more solutions (y/n/d) [y]? ; % Do not look for more solutions

2.3.2 A Hardware Design Problem

A more interesting example comes from the hardware area. In this setting, many

constrained optimization problems arise in the design of both sequential and combina-

tional circuits as well as the interconnection routing between components. Constraint

programming has been shown to eﬀectively attack these problems. In particular, the

interconnection routing problem (one of the major tasks in the physical design of very

large scale integration - VLSI - circuits) have been solved with constraint logic pro-

gramming Zhou, 1996.

For the sake of conciseness and clarity, we focus on a constraint combinational

hardware problem at the logical level but adding constraints about the physical factors

the circuit has to meet. This problem will show some of the nice features of TOY for

specifying issues such as behavior, topology and physical factors.

Our problem can be stated as follows. Given a set of gates and modules, a switching

function, and the problem parameters maximum circuit area, power dissipation, cost,

and delay (dynamic behavior), the problem consists of ﬁnding possible topologies based

on the given gates and modules so that a switching function and constraint physical

factors are met. In order to have a manageable example, we restrict ourselves to the

logical gates NOT, AND, and OR. We also consider circuits with three inputs and

one output, and the physical factors aforementioned. We suppose also the following

problem parameters:

Gate Area Power Cost Delay

NOT 1 1 1 1

AND 2 2 1 1

OR 2 2 2 2

In the sequel we will introduce the problem by ﬁrst considering the features TOY oﬀers

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