Genetic Algorithms, Historical Markers, and Finite State Automata
Complex Adaptive Systems
CS 591, Section 7
Assignment 1
February 19, 2003
1 Introduction
The basic idea of this assignment is to see how the genetic algorithm works on a language-induction problem. In
language induction, the learning system is presented with a set of symbol strings defined over a fixed-size alphabet.
These strings, known as sentences, are exemplars of a language (any set of legal sentences defines a language).
The induction problem is to figure out a minimal procedure for recognizing legal strings in the language (that is,
the set of exemplar sentences). In our assignment we will be using finite-state automata (FSA) to represent the
procedure.
A trivial solution to this problem would be simply to define the language of all possible strings over the
alphabet. Then, any possible set of exemplars would be recognized by our FSA. To make the problem more
interesting, we will supply exemplars of strings that are in the language (positive examples) and strings that are
not in the language (negative examples). Your GA should discover FSAs that recognize all the positive examples
and reject all the negative examples.
We will study two methods for representing FSAs using genetic algorithms: the fixed-size table method and
the variable-length genome method with historical markers. We will suggest the basic representation strategy
and you are welcome to use existing software, but you are expected to design and implement your own fitness
function.
2 Assignment
You are free to choose any publicly available genetic algorithm software or to write your own using the language
of your choice. One possible choice is a very simple genetic algorithm written in C by Gary Flake (see URLs
below) which generates FSAs for playing the Prisoner’s Dilemma.
1. Due: March 5 Modify an existing GA (or write your own) to learn FSAs (language acceptors) using a
simple rule-table representation. Test the GA on the sample data sets.
2. Due: March 12 Modify your GA to incorporate variable-length genomes and historical markers, as de-
scribed in the Stanley and Mikkulainen papers. It is recommended that you also use their idea of initializing
the population with a homogeneous set of minimal machines (we will discuss in class what the minimal
machine looks like). At least initially, it is recommended that you skip the other mechanisms such as
fitness-sharing.
3. Due: March 12 Apply the extended GA to the FSA examples from Parts 1 and 2 and compare the
performance of the two methods.
3 Details
3.1 Finite State Machines
If you have never heard of a finite-state automata, you can find a description and formal definition in any automata
theory book and in most compiler books (among other applications, finite-state machines are used for the lexical
analysis phase of compilers). Here are some materials we found on the web:
1. http://www.math.iastate.edu/danwell/ma378/chapter6.pdf
2. http://www.dcs.ed.ac.uk/teaching/cs1/CS1/Ah/Notes/FiniteStateMachines1.pdf
If there is sufficient interest, we can hold an extra discussion session to review the basics of FSAs.
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