Homework for Chapters 9 and 11, CMSC 421, Fall 2008
•There are 5 problems worth 10 points each, for a total of 50 points.
Chapter 9: Do problems 9.12 and 9.19 from Russell & Norvig.
Planning homework: Consider the following coffee-making domain. This is a planning domain
in which you have a coffee maker and several different kinds of coffee beans, and the coffee maker
can be used to make pots of coffee. There are three operators: load coffee into the machine, start
the machine running, and end the machine’s coffee-making cycle. Here is a classical representation
of them:
load(x)
precond: coffee(x), loaded(nil)
effects: loaded(x), ¬loaded(nil)
brew(x)
precond: loaded(x), ¬loaded(nil), ¬loaded(waste)
effects:¬loaded(x), loaded(waste), pot(x)
unload(x)
precond: loaded(x), ¬loaded(nil)
effects:¬loaded(x), loaded(nil)
Most of the questions in this homework assignment involve the following planning problem in
the coffee-making domain. We will call this problem P1. In P1, there are two kinds of coffee: caf
and decaf. The goal is to make one pot of each. Here are the initial state and the goal formula:
Initial state: {coffee(caf ), coffee(decaf), loaded(nil)}
Goal formula: {pot(caf ), pot(decaf)}
Problem 1 Suppose we do a backward state-space search on P1, without any loop-checking.
(a) How many execution traces lead to solutions?
(b) A solution is shortest if there is no other solution that contains fewer actions. What are all
of the shortest solutions?
(c) How many execution traces don’t lead to solutions? If any of these execution traces is finite,
then give an example—and if none of them is finite, then explain why not.
Problem 2 Suppose we run Graphplan on P1.
(a) Draw the planning graph after the first graph-expansion. Include all maintenance actions and
mutexes. For each mutex, tell what kind of mutex it is.
(b) At what level does Graphplan first call Extract?
