 
Summary: Applying Genetic Algorithms to the
State Assignment Problem: A case Study
Jose Nelson Amaral, Kagan Tumer, and Joydeep Ghosh
Department of Electrical and Computer Engineering,
University of Texas at Austin,
Austin, Texas 78712
Abstract
Finding the best state assignment for implementing a synchronous sequential circuit is important for reducing
silicon area or chip count in many digital designs. This State Assignment Problem (SAP) belongs to a broader
class of combinatorial optimization problems than the well studied traveling salesman problem, which can be
formulated as a special case of SAP. The search for a good solution is considerably more involved for the SAP
than it is for the traveling salesman problem due to a much larger number of equivalent solutions, and no effective
heuristic has been found so far to cater to all types of circuits.
In this paper, a matrix representation is used as the genotype for a Genetic Algorithm (GA) approach to this
problem. A novel selection mechanism is introduced, and suitable genetic operators for crossover and mutation,
are constructed. The properties of each of these elements of the GA are discussed and an analysis of parameters
that influence the algorithm is given. A canonical form for a solution is defined to significantly reduce the search
space and number of local minima. Simulation results for scalable examples show that the GA approach yields
results that are comparable to those obtained using competing heuristics. Although a GA does not seems to be the
tool of choice for use in a sequential VonNeumann machine, the results obtained are good enough to encourage
