Programming Mini-Project 2

Max possible score:


Complete Task 1 and either Task 2-A or 2-B (Complete both for 50 Points Extra Credit)

Task 1:

Max: [4308: 50 Points, 5360: 50 Points]

The task in this programming assignment is to design appropriate descriptions of facts, actions, and goals, using the PDDL language, for two planning problems: the Tower of Hanoi problem, and the 7-puzzle problem (a variation of the 8-puzzle problem where two squares are clear instead of one). You will use your descriptions as inputs to a Graphplan implementation. If your descriptions are correct, Graphplan will produce appropriate plans.

Compiling and Running the Software

The Graphplan software can be downloaded from graphplan.zip. See the README file in that package for additional information. To compile the software on omega, unzip the directory, and, from that directory, type 
make graphplan
Once the program compiles, it can be invoked from the commandline as follows: 
graphplan -o [operators_file] -f [facts_file]
For example: 
graphplan -o block_ops.txt -f block_facts3.txt
Once you start running the software, it will ask you three questions. Just hit enter for each question, so as to use the default settings. If your descriptions of actions and facts are correct, the program will print out a plan achieving the stated goal.

Note that the preconds in each fact file will contain both statements that are always true in that domain (i.e., in the Tower of Hanoi domain or the 7-puzzle domain), and statements that simply describe the initial state for that specific planning problem. In addition to the facts files for the specific planning problems you are given, you will have to create a separate text file that includes all the statements that must be present in ANY facts file for that domain.

Tower of Hanoi Description

A description of the Tower of Hanoi domain can be found at Wikipedia. In all problems that your program will be tested with there will be five discs (called disk1, disk2, disk3, disk4, disk5) and three pegs (called A, B, C). In all your facts files you will have to include both a common part (defining objects and relations among objects) and a plan-specific part (describing the initial state and goal for each plan). Note that some of the five disks may not appear in some of the planning problems.

The two planning problems you have to solve are:

Problem 1

initial state:
(on disk1 disk2)
(on disk2 A) 
(clear disk1)
(clear B)
(clear C) 

goal:
(on disk1 B)
(on disk2 C)
Problem 2 
initial state:
(on disk1 disk2) 
(on disk2 disk3)
(on disk3 disk4)
(on disk4 disk5)
(on disk5 C) 
(clear disk1) 
(clear A) 
(clear B)

goal:
(on disk1 disk2) 
(on disk2 disk3)
(on disk3 disk4)
(on disk4 disk5)
(on disk5 A)

7-puzzle Description

7-puzzle is like 8-puzzle, except that there are only pieces numbered from 1 to 7 (not from 1 to 8), and there are two clear squares on the board. At any move, we can move a numbered piece to an adjacent clear square.

The two planning problems you have to solve are (X indicates a clear square):

Problem 1

initial state:
123
456
7XX

goal:
123
X56
4X7
Problem 2 
initial state:
XX7
654
321

goal:
123
456
7XX

Grading

This task will be graded for 50 points. Half the points will correspond to your solutions for the Tower of Hanoi world, and the rest will correspond to your solutions for the 7-puzzle problem. Specifically, the point allocation is:

Task 2-A:

Max: [4308: 50 Points, 5360: 50 Points]

The task in this part is to implement a system that: As in the slides that we saw in class, there are five types of bags of candies. Each bag has an infinite amount of candies. We have one of those bags, and we are picking candies out of it. We don't know what type of bag we have, so we want to figure out the probability of each type based on the candies that we have picked.

The five possible hypotheses for our bag are:

Command Line arguments:

The program takes a single command line argument, which is a string, for example CLLCCCLLL. This string represents a sequence of observations, i.e., a sequence of candies that we have already picked. Each character is C if we picked a cherry candy, and L if we picked a lime candy. Assuming that characters in the string are numbered starting with 1, the i-th character of the string corresponds to the i-th observation. The program should be invoked from the commandline as follows: 
compute_a_posteriori observations
For example: 
compute_a_posteriori CLLCCLLLCCL
We also allow the case of not having a command line argument at all, this represents the case where we have made no observations yet.

Output:

Your program should create a text file called "result.txt", that is formatted exactly as shown below. ??? is used where your program should print values that depend on its command line argument. Atleast five decimal points should appear for any floating point number. 
Observation sequence Q: ???
Length of Q: ???

After Observation ??? = ???: (This and all remaining lines are repeated for every observation)

P(h1 | Q) = ???
P(h2 | Q) = ???
P(h3 | Q) = ???
P(h4 | Q) = ???
P(h5 | Q) = ???

Probability that the next candy we pick will be C, given Q: ???
Probability that the next candy we pick will be L, given Q: ???

Task 2-B:

Max: [4308: 50 Points, 5360: 50 Points]


Earthquake_Burglary Net as discussed in Class

Figure 1: A Bayesian network establishing relations between events on the burglary-earthquake-alarm domain, together with complete specifications of all probability distributions.

For the Bayesian network of Figure 1, implement a program that computes and prints out the probability of any combination of events given any other combination of events. If the executable is called bnet, here are some example invocations of the program
  1. To print out the probability P(Burglary=true and Alarm=false | MaryCalls=false). 
    bnet Bt Af given Mf
  2. To print out the probability P(Alarm=false and Earthquake=true). 
    bnet Af Et
  3. To print out the probability P(JohnCalls=true and Alarm=false | Burglary=true and Earthquake=false). 
    bnet Jt Af given Bt Ef
  4. To print out the probability P(Burglary=true and Alarm=false and MaryCalls=false and JohnCalls=true and Earthquake=true). 
    bnet Bt Af Mf Jt Et
In general, bnet takes 1 to 6(no more, no fewer) command line arguments, as follows: The implementation should not contain hardcoded values for all combinations of arguments. Instead, your code should use the tables shown on Figure 1 and the appropriate formulas to evaluate the probability of the specified event. It is OK to hardcode values from the tables on Figure 1 in your code, but it is not OK to hard code values for all possible command arguments, or probability values for all possible atomic events. More specifically, for full credit, the code should include and use a Bayesian network class. The class should include a member function called computeProbability(b, e, a, j, m), where each argument is a boolean, specifying if the corresponding event (burglary, earthquake, alarm, john-calls, mary-calls) is true or false. This function should return the joint probability of the five events.

Sample output for both Task 2-A and 2-B are given here.

How to submit

For each part: Implementations in C, C++, Java, and Python will be accepted. Points will be taken off for failure to comply with this requirement.

Create a ZIPPED directory called <net-id>_proj2.zip (no other forms of compression accepted, contact the instructor or TA if you do not know how to produce .zip files). The zip file should contain: