You can find a general discussion of cheating, plagiarism, and the like on the university's web page and on the CS department's page.
In this class, you are explicitly allowed to work on homework problems in small groups (2-3 people). Therefore, it's likely that everyone in the group will submit solutions that use a similar approach and share key technical details. However, you must write up your final solution yourself, in your own words. Among other things, this helps you ensure that you do understand all the details and it gives you practice composing mathematical English. If you don't understand your group's solution well enough to write it out by yourself, you will do badly on the exams.
To keep everyone honest, you must note the names or netids of the other group members on your homework. Clearly distinguish whose submission this is, e.g. write their names under yours and/or label them as "collaborators" or something similar.
If you don't understand these guidelines, please talk to us. If something unusual happens (e.g. a roommate blurts out advice that you didn't ask for), consult with us and also write an explanation on your homework. If you clearly acknowledge all help you received, you might lose points but it won't be considered cheating.
If we do catch someone cheating, we will apply the following penalties for a first offense:
For a second cheating offense of any kind, you will fail this course.