Homework 1 (based on Class of 1/21)

[[The homework will be due 1 week after the socket is closed]]

I. Consider a simple blocks world domain containing 2 blocks--A and
B. Each block  can be on table or on top of one of the blocks or be held by
the robot hand (1 hand). Assume that left/right position of the blocks 
on the table doesn't matter. Answer the following questions:

--How many distinct states are possible for this world? 

--Give an expression for the number of states if there are k blocks
instead of 2 blocks. 

--Assuming that there are four actions--pickup, putdown, stack and
unstack--show the transition diagram for the 2-block world

--If our initial state has A and B on table and hand empty, and we
want to be in a state where A is on B. Show how the plan for this
corresponds to a path in the transition graph. 

--show how the transition diagram will change (use a differnt color to 
show the changes) if the stack is an uncertain action which sometimes
winds up dropping the block on to the table rather than putting it
on. 


II. Give  example problems (domain, action, initial and goal state
descriptions in English) where

  (a) Only conformant plan is possible

  (b) Only conditional plan is possible

  (c) Both are possible 


Added on [Jan 28, 2003]

III. Consider a domain where states are represented in terms of 2
binary state variables--p1 and p2.

 --Give an example action (doesn't have to have any physical meaning)
   whose specification is no shorter in the factored representation
   than it is in the transition diagram representation.


IV. Consider a domain that contains 5 objects--A,B,C,D,E, and unary predicates P and
    Q.  We have the following single action:

    Action A
     precondition: 
       .exists. x P(x)
     Effects:
       .forall. x P(x) => Q(x)

    Convert A into a set of equivalent canonical actions--where the
preconditions and effects are all "propositional" (in that there is no 
disjunction,implication or quantification)


V. Consider the "register" domain. In this simple domain, all 
you can do is to write the contents of one register into another
register. Our problem is to swap the contents of two registers r1, and 
r2. There is a spare register--r3--that is available in the initial
state. 

 Write a PDDL specification of this domain and the problem. 


********CLosed. DUE 4th Feb. In class.