ECE598HZ: Advanced Topics in Machine Learning and Formal Methods

ECE598HZ: Advanced Topics in Machine Learning and Formal Methods

Fall 2024

Homework 1

Due Sep 23 11:59pm CT

Typeset your solutions using LATEX, create a single zip file including your solutions (in a single

PDF file), your code, and instructions to run your code. Name your zip file as netid-598-F24 . zip and upload this file through Canvas.

Problem 1: Boolean Satisfiability Problem and DPLL (30pts)

Suppose you are working as an intern in an e-commerce company. You are building a machine learning model to predict whether a customer will buy a product based on a very large datasest with six features: A,B,C,D,E, and F. However, due to computational constraints, your manager asks you to only use three features in your final model.

You have the following information about the features:

• If feature A is selected, theneither feature B or feature C must also be selected.

• Feature C and feature D cannot be selected together.

• If feature E is selected, then feature F must not be selected.

• At least one of features B,C, or D must be selected.

• If feature F is selected, theneither feature A or feature E must also be selected.

1. Formulate this feature selection problem as a Boolean satisfiability problem. (15pts)

2. Use the DPLL algorithm to find a satisfying assignment that represents a valid selection of three features. If such an assignment does not exist, report that the solution does not exist. Show your steps. (15pts)

Problem 2: 4-SAT, 3-SAT, and 2-SAT problems (20pts)

1. A 4-SAT problem inCNF form. has 4 literals in each clause. An example 4-SAT problem is given below:

φ4-SAT  := (x1∨ x2∨ x3∨ x4) Λ (¬x1∨ ¬x2∨ x3∨ ¬x4) Λ (x1∨ ¬x2∨ ¬x3∨ x4)

Convert this 4-SAT problem to an equivalent 3-SAT problem, i.e., find a 3-SAT&n