How can I program a simple chat bot AI?

Folks have mentioned already that statefulness isn't a big component of typical chatbots:

• a pure Markov implementations may express a very loose sort of state if it is growing its lexicon and table in real time—earlier utterances by the human interlocutor may get regurgitated by chance later in the conversation—but the Markov model doesn't have any inherent mechanism for selecting or producing such responses.

• a parsing-based bot (e.g. ELIZA) generally attempts to respond to (some of the) semantic content of the most recent input from the user without significant regard for prior exchanges.

That said, you certainly can add some amount of state to a chatbot, regardless of the input-parsing and statement-synthesis model you're using. How to do that depends a lot on what you want to accomplish with your statefulness, and that's not really clear from your question. A couple general ideas, however:

• Create a keyword stack. As your human offers input, parse out keywords from their statements/questions and throw those keywords onto a stack of some sort. When your chatbot fails to come up with something compelling to respond to in the most recent input—or, perhaps, just at random, to mix things up—go back to your stack, grab a previous keyword, and use that to seed your next synthesis. For bonus points, have the bot explicitly acknowledge that it's going back to a previous subject, e.g. "Wait, HUMAN, earlier you mentioned foo. [Sentence seeded by foo]".

• Build RPG-like dialogue logic into the bot. As your parsing human input, toggle flags for specific conversational prompts or content from the user and conditionally alter what the chatbot can talk about, or how it communicates. For example, a chatbot bristling (or scolding, or laughing) at foul language is fairly common; a chatbot that will get het up, and conditionally remain so until apologized to, would be an interesting stateful variation on this. Switch output to ALL CAPS, throw in confrontational rhetoric or demands or sobbing, etc.

Can you clarify a little what you want the state to help you accomplish?

You probably want to look into Markov Chains as the basics for the bot AI. I wrote something a long time ago (the code to which I'm not proud of at all, and needs some mods to run on Python > 1.5) that may be a useful starting place for you: http://sourceforge.net/projects/benzo/

EDIT: Here's a minimal example in Python of a Markov Chain that accepts input from stdin and outputs text based on the probabilities of words succeeding one another in the input. It's optimized for IRC-style chat logs, but running any decent-sized text through it should demonstrate the concepts:

import random, sys

NONWORD = "\n"
STARTKEY = NONWORD, NONWORD
MAXGEN=1000

class MarkovChainer(object):
    def __init__(self):
        self.state = dict()

    def input(self, input):
        word1, word2 = STARTKEY
        for word3 in input.split():
            self.state.setdefault((word1, word2), list()).append(word3)
            word1, word2 = word2, word3 
        self.state.setdefault((word1, word2), list()).append(NONWORD)

    def output(self):
        output = list()
        word1, word2 = STARTKEY
        for i in range(MAXGEN):
            word3 = random.choice(self.state[(word1,word2)])
            if word3 == NONWORD: break
            output.append(word3)
            word1, word2 = word2, word3
        return " ".join(output)

if __name__ == "__main__":
    c = MarkovChainer()
    c.input(sys.stdin.read())
    print c.output()

It's pretty easy from here to plug in persistence and an IRC library and have the basis of the type of bot you're talking about.

I think you can look at the code for Kooky, and IIRC it also uses Markov Chains.

Also check out the kooky quotes, they were featured on Coding Horror not long ago and some are hilarious.

Imagine a neural network with parsing capabilities in each node or neuron. Depending on rules and parsing results, neurons fire. If certain neurons fire, you get a good idea about topic and semantic of the question and therefore can give a good answer.

Memory is done by keeping topics talked about in a session, adding to the firing for the next question, and therefore guiding the selection process of possible answers at the end.

Keep your rules and patterns in a knowledge base, but compile them into memory at start time, with a neuron per rule. You can engineer synapses using something like listeners or event functions.