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CSCI-561 - Fall 2023 - Foundations of Artificial Intelligence
Homework 3
Due Time: Monday, November 20th, 2023, 23:59:59 PST
Overview
This homework explores the applications of Temporal Reasoning in Artificial Intelligence. In general, the
solution for a temporal reasoning task involves taking a sequence of actions/observations on an Partially
Observable Markov Decision Process (POMDP Environment) , applying a temporal-reasoning algorithm
that you learned from this class, and returning the most probable sequence of the hidden states that the
POMDP most-likely went through when experiencing the given sequence of actions/observations.
More specifically, this assignment provides you with two versions of temporal data: a base version
involving the “Little Prince” Environment and an advanced version that revolves around speech
recognition and text prediction.
Scenario 1 : Little Prince Model
The setup in this version is very similar to the “Little Prince” environment shown in Figure 1, presented in
the lecture notes and in the optional reading textbook (ALFE).
Figure 1: The Little Prince POMDP (lecture 08-09 and 22).
You will be given a list of available percepts, actions and states and the corresponding initial state
weightages, transition and observation weight values in that environment (More on the input structure will
be covered in the sections below) . Your task is to design and implement a temporal-reasoning algorithm,
that will take a sequence of actions/observations and determine the most-likely sequence of states that this
POMDP has gone through, as shown in Figure 2. For example, if the Little Prince’s experience is given as

Then, your program should return a sequence of hidden-states that this POMDP is most-likely going
through (The following sequence is an example of the final state sequence that one might encounter):

Figure 2: The inputs and outputs of a temporal-reasoning task (lecture 22).
More Details on solving this state sequence prediction problem can be found in the lecture slides. The
input file format for this environment will be the same as the Speech Recognition environment. You will
be given weight values instead of probabilities and the process of converting weights to probabilities is
explained in detail in the following sections.
Scenario 2 : Simplified Speech Recognition
This scenario deals with a more sophisticated environment of speech recognition - without the hassle of
going through audio signal processing. This model will primarily focus on resolving the ambiguity
introduced by multiple plausible texts that could correspond to a single spoken utterance. For every word
pronunciation, instead of dealing with audio signals, you will be given a set of phonemes which
phonetically represent the word, and will produce a series of text fragments the same length as the
sequence of phonemes. The following table provides some sample words and their phoneme / fragment
mapping for better understanding.
Example Words Phoneme Mapping Fragment Mapping
water W | AO1 | T | ER0 w | a | t | er
human Y | UW1 | M | AH0 | N h | u | m | a | n
ocean OW1 | SH | AH0 | N o | c | ea | n
As evident in the table, there is a 1:1 correspondence with phoneme and fragment for a given word. For
the word water, fragment “A” corresponds to the phoneme “AO1” and fragment “er” corresponds to
“ER0”.
Because this project builds off prior work from the CMU Pronouncing Dictionary, we use a dialect of
English known as North American English, where e.g. human is pronounced with a “Y” sound at the start.
The ultimate goal of this environment is to find the best sequence of text fragments for a given sequence
of phonemes. Formally, we will represent the process as a POMDP, with the text fragments corresponding
to states and the phonemes corresponding to observations. For convenience, we will use a single null
action “N”. This will ensure that we are using a Partially Observable Markov Decision Process instead of
just a Partially Observable Markov Process. This will also allow you to re-use parsing code between the
Little Prince environment and the Speech Recognition environment.
As part of the input, you will be provided with a dataset containing a list of fragment to phoneme pairs,
along with a weight value for each pair. You will also be given fragment-to-fragment transition pairs with
their weight values. The following example explains the procedure to compute the probability tables in
more detail. These weights correspond to un-normalized total probabilities P(o, s) and P(s, s’) (using the
null action “N”), which were computed by counting (observation, state) and (state, state) pairs from a set
of approximately 300k Wikipedia articles. Note that you will need to normalize these weights into the
appropriate probability distributions P(o | s) and P(s’ | s, N).
Consider the following dataset:
Fragment to Phoneme Mapping
Fragment Phoneme Weight
s S 100
s Z 50
er ER0 10
o AH0 10
e AH0 20
Fragment to Fragment Transition Mapping
Fragment Fragment Weight
s er 80
s o 10
s e 10
er o 5
o e 8
Construction of Probability Tables :
● Initial State Probability: Computing the initial state / prior state distribution only involves
dividing each weight in the state probability table by the total weight in the table.
Given a state table as follows:
State s er o e
Weight 1 1 1 1
The initial probability P(s) is:
State s er o e
Prob 0.25 0.25 0.25 0.25
● State Transition Probability: This can be determined by looking at the weights of the transitions
from one fragment to another and calculating the probability through normalization for each
(state, action) pair. This produces P(s|s,a). In this example, there is only a single valid action, so
we don’t show it in the table.
The state transition probability for the sample dataset would be:
States s er o e
s 0.0 0.8 0.1 0.1
er 0 0 1 0
o 0 0 0 1
e 0 0 0 0
● Appearance Probabilities: This can be inferred from the fragment-phoneme pairs through
normalization over all weights for a given state, producing the conditional distribution P(o|s). The
appearance probability for the above example would be as follows:
S Z ER0 AH0
s 0.667 0.333 0 0
er 0 0 1 0
o 0 0 0 1
e 0 0 0 1
Note how the row for state “s” sums to 1 over the different possible observations / phonemes “S”
and “Z”.
Your algorithm will be tested on a list of phonemes for which it should provide the most probable
sequence of fragments.
Input / Output Format
As mentioned in the problem statement above, there will be two types of input to indicate two modes /
stages : Little Prince environment and Simplified Speech Recognition.
In both cases, you will be given a set of input files, containing the table of weights described above. You
will need to parse and normalize these tables into the appropriate conditional probabilities.
These input files all contain a similar format, that begins with a one line file type, then a header that
describes the number of entries, as well as a default weight. Then, each file contains a sequence of entries,
where states, observations, and actions are wrapped in double quotes, and the weights are specified as
integers. At the end of the file, there will be one final newline.
There are three weight table files:
The first of these files contains weights for every state, and describes the prior probability of each state
P(s). (The default weight value is present in this file just to ensure format consistency across all weight
files - this will not be required to be used, as all states will be present in the state weights file)
state_weights.txt:
state_weights

“state1”
“state2”
etc…
The second of these files contains weights for (state, action, state) triples, and describes the probability of
state transitions P(s, a, s). Triples not specified in the table should be given the weight default weight
specified on the second line. Note that you will need to normalize these weights into the appropriate
probability distribution P(s’ | a, s).
state_action_state_weights.txt:
state_action_state_weights
actions>
“state1” “action1” “next state1”
“state2” “action2” “next state2”
etc…
The third of these files contains weights for every (state, observation) pair, and describes the probability
of each state observation pair P(s, o). Pairs not specified in the table should be given the default weight
specified on the second line. Note that you will need to normalize these weights into the appropriate
probability distribution P(o | s).
state_observation_weights.txt:
state_observation_weights
observations>
“state1” “observation1”
“state2” “observation2”
etc…
Lastly, you will receive a file containing the sequence of (observation, action) pairs, on which you should
run the Viterbi algorithm.
observation_actions.txt:
observation_actions

“observation1” “action1”
“observation2” “action2”
etc…
Your code will be expected to produce a file containing the predicted state sequence.
states.txt:
states

“state1”
“state2”
etc…
Sample Test Case
The following sample test case corresponds to the Little Prince Environment (The format matches that
used for Simplified Speech Recognition Environment)
Little Prince Environment Test case:
state_weights.txt
state_weights
3 0
"S0" 2
"S1" 5
"S2" 5
state_observation_weights.txt
state_observation_weights
9 3 3 0
"S0" "Volcano" 3
"S0" "Grass" 3
"S0" "Apple" 2
"S1" "Volcano" 5
"S1" "Grass" 5
"S1" "Apple" 2
"S2" "Volcano" 3
"S2" "Grass" 5
"S2" "Apple" 2
state_action_state_weights.txt
state_action_state_weights
27 3 3 0
"S0" "Forward" "S0" 3
"S0" "Forward" "S1" 3
"S0" "Forward" "S2" 2
"S1" "Forward" "S0" 4
"S1" "Forward" "S1" 5
"S1" "Forward" "S2" 1
"S2" "Forward" "S0" 1
"S2" "Forward" "S1" 5
"S2" "Forward" "S2" 4
"S0" "Backward" "S0" 5
"S0" "Backward" "S1" 5
"S0" "Backward" "S2" 5
"S1" "Backward" "S0" 3
"S1" "Backward" "S1" 4
"S1" "Backward" "S2" 1
"S2" "Backward" "S0" 2
"S2" "Backward" "S1" 3
"S2" "Backward" "S2" 3
"S0" "Turnaround" "S0" 5
"S0" "Turnaround" "S1" 3
"S0" "Turnaround" "S2" 5
"S1" "Turnaround" "S0" 3
"S1" "Turnaround" "S1" 4
"S1" "Turnaround" "S2" 2
"S2" "Turnaround" "S0" 1
"S2" "Turnaround" "S1" 2
"S2" "Turnaround" "S2" 2
observation_actions.txt
observation_actions
4
"Apple" "Turnaround"
"Apple" "Backward"
"Apple" "Forward"
"Volcano"
Output:
states.txt
states
4
"S2"
"S2"
"S2"
"S1"
Input Constraints & Time Limits
Little Prince Environment:
Maximum Number of States in the Environment 10 states
Maximum Number of Percepts in the Environment 10 percepts
Number of Actions Possible in the Environment (Fixed) 3 (“Forward”, “Backward”, “Turnaround”)
Maximum Length of Observation Action Sequence 20
Time Limit allowed per test case 1 second
Number of test cases 20 ( 5 Preliminary and 15 hidden)
Simplified Speech Recognition Environment:
Maximum Number of States in the Environment 682
Maximum Number of Observations in the Environment 69
Number of Actions Possible in the Environment (Fixed) “N” ( Indicates Null Action, Refer Scenario
Description )
Maximum Length of Observation Action Sequence 100 steps
Time Limit allowed per test case 1 minute
Number of test cases 30 ( 5 Preliminary and 25 hidden)
Grading Criteria
There will be 50 test cases in total : 20 cases with the Little Prince environment and 30 cases with Speech
Recognition. Each test case is worth 2 points. On clicking the submit button in Vocareum, Your solution
will be run on preliminary test cases. Your code will be evaluated on the hidden test cases after the
assignment deadline.
The performance of your program will be computed automatically by comparing your output sequence
with the most-likely known sequence, and the matching percentage will determine the grade of your
submissions.More specifically, the probability of the hidden state sequence that your solution has
generated (p1), will be compared with the probability of the hidden state sequence proposed by TA agent
(p2) and p1/ p2 will be used as the final score for each test case.
Score for a single test case = 2 * Probability of student’s state sequence
Probability of TA agent’s state sequence
Final Score = Sum of scores across all test cases
NOTE : The Max Score for a single test case will be capped at 2 points.
The probability of the state sequence will be calculated based on the joint probability of the state
sequence, along with the action sequence and the observation sequence.
In the following example [used for calculation purposes only], the score will be calculated as follows:
States List = [S0, S1, S2], Actions Set= [N], Observations set= [A, B]
Initial State Probability
S0 S1 S2
0.5 0.25 0.25
Appearance Probability
A B
S0 0.9 0.1
S1 0.2 0.8
S2 0.5 0.5
Transition Probability
S0 S1 S2
S0 0.5 0.3 0.2
S1 0.9 0.1 0
S2 0.2 0.8 0
Observation Action Sequence = [A, , B,, B]
If the student’s predicted state sequence is [S0, S1, S1], then
Student’s Probability = π(𝑆0)*P(A|S0)*P(S1|S0,)*P(B|S1)*P(S1|S1,)*P(B|S1)
= 0.5*0.9*0.3*0.8*0.1*0.8
= 0.00864
If the TA’s predicted state sequence is [S0, S1, S0], then
TA’s Probability = π(𝑆0)*P(A|S0)*P(S1|S0,)*P(B|S1)*P(S0|S1,)*P(B|S0)
= 0.5 * 0.9 * 0.3 *0.8 * 0.9 * 0.1
= 0.00972
Your Score for this test case = 2 * 0.00864 / 0.00972 = 1.778
Notes
- Please name your program “my_solution.xxx” where ‘xxx’ is the extension for the
programming language you choose (“py” for python, “cpp” for C++, and “java” for Java). If you
are using C++11, then the name of your file should be “my_solution11.cpp” and if you are using
python3 then the name of your file should be “my_solution3.py”. Please use only the
programming languages mentioned above for this homework. Please Note the highest version of
Python that is offered is Python 3.7.5, hence the walrus operator and other features of higher
version Python are not supported.
- The time limit is the total combined CPU time as measured by the Unix time command. This
command measures pure computation time used by your program, and discards time taken by
the operating system, disk I/O, program loading, etc. Beware that it cumulates time spent in any
threads spawned by your agent (so if you run 4 threads and use 400% CPU for 10 seconds, this
will count as using 40 seconds of allocated time). Your local machine may be more powerful,
and thus faster than Vocareum.
- Please don't copy code from any website as our plagiarism agent will certainly flag that.
This includes Wikipedia.
- There may be a lot of Q&A on Piazza. Please always search for relevant questions before
posting a new one. Duplicate questions make everyone’s lives harder.
- Only submit the source code files (in .java, .py or .cpp). All other files should be excluded.
- Please submit your homework code through Vocareum (https://labs.vocareum.com/) under the
assignment HW3. Your username is your email address. Click “forgot password” for the first
time login. You should have been enrolled in this course on Vocareum. If not, please post a
private question with your email address and USC ID on Piazza so that we can invite you again.
- You can submit your homework code (by clicking the “submit” button on Vocareum) as many
times as you want. Only the latest submission will be considered for grading. After the initial
deadline, the submission window will still be open for 5 days. However, a late penalty will be
applied as 20% per day if your latest submission is later than the initial deadline.
- Every time you click the “submit” button, you can view your submission report to see if your
code works. The grading report will be released after the due date of the project.
- You don’t have to keep the page open on Vocareum while the scripts are running.
- Be careful and avoid multiple submissions of large files to Vocareum. Vocareum does not allow
students to delete old submissions, and in the past, students have run out of space and been
unable to use Vocareum until we got in touch with support and asked them to delete files.