CS533: Intelligent Agents and Decision Making

Homework 1

Due: Friday, January 15 

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Exercise 11.4 

Exercise 11.10

Ecercise 11.11
 
Exercise 11.13


Exercise A:

A standard propositional STRIPS planning problem (as described in
class) specifies: 1) a goal condition, 2) an initial state, and 3)
a set of propositional STRIPS actions with positive
preconditions. We will refer to the set of all standard STRIPS
problems as STANDARD.

   i) Let NEG-PRE be the class of problems that are specified as
      above, except that actions are allowed to have negative
      preconditions. (Note that NEG-PRE is a strict superset of
      STANDARD.) Show how to convert any problem p1 in NEG-PRE to a
      problem p2 in STANDARD such that p1 has a solution iff p2 has a
      solution. In other words, give a reduction from Plan-SAT for
      NEG-PRE to Plan-SAT for STANDARD. Prove your answer for full
      credit.

   ii) Let DISJ-GOAL be the class of problems that are standard STRIPS
       problems only they have disjunctive goals. A disjunctive goal is
       a disjunction of standard goals, where a standard goal is a set
       of propositions. For example, the following is a disjunctive
       goal:

            {on(a,b),on(b,c)} or {on(c,b),on(b,a)}

       We say that a problem in DISJ-GOAL is solvable iff there is an
       action sequence from the initial state to some state that
       satisfies at least one of the goal disjuncts. So in our example
       above we must reach a state with either the tower (a,b,c) or
       (c,b,a).

       Repeat part (i) for DISJ-GOAL.