1. Introduction to Debates CS5800 Algorithms Instructor: Karl Lieberherr Teaching Assistant: Zhengxing Chen Based on Ahmed Abdelmeged’s Dissertation

2. Approach We introduce debates with two sets of slides –The first set covers debates between two students, based on semantic games. Logical formulas Games based on logical formulas Evaluation based on merit graphs –The second set (these slides) extends debates to involve the entire class.

3. Review Semantic games for interpreted logical formulas

4. 4 Semantic Games (SGs) for interpreted formulas A semantic game for a given claimφ, A is a game played by a verifier and a falsifier, denoted SG(φ, A, verifier, falsifier), such that: –A |= φ the verifier has a winning strategy for φ.

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6. Introduction 3 students form a team –Teams will be carefully selected –In first class we have ad-hoc teams. 2 forms of debates - Intra-team - Inter-team

7. Intra-team Debate In a team, every 2 team members have one debate. So there are only 3 debates for each small round-robin tournament. Forced players are chosen randomly/ Team member with fewest number of losses wins. –It is possible that all three team members win!

8. Intra-team Debate Two sides for any given claim: - Verifier (believes claim is true) - Falsifier (believes claim is false) 2 engaged team members choose sides, while the 3 rd team member plays as an admin (checking the game rules) One must be the forced falsifier/verifier if two choose the same side

9. Inter-team Debate After intra-team debate, every team may find a better combined algorithm. 3 teams form a group. Each team stays together and plays now against 2 other teams of 3 students. Every team will have a debate with two other teams in the group. Team plays by consensus against other teams.

10. Count losses Nobody drops out but we count losses in non-forced position, first individually then per team. When a team loses, loss is added to all team members.

11. Time Debate could be going on Piazza or in class. In class: - each intra-team debate: 10min - each inter-team debate: 12min Piazza: - each intra-team debate: 720min - each inter-team debate: 720min

12. Translating debates into grades Intra-team –Max. 2 losses in non-forced position Inter-team –Max. 2 losses in non-forced position Total: –0 losses: A –1 loss: A- –2 losses: B –3 losses: C+ –4 losses: C Remember: It is possible that all three team members get an A.

13. Debates Organization 27 students: S 1 … S27 9 teams: T1 … T9 of 3 students each Intra-team: choose sides –For i from 1 to 9 T i consists of S 3*i, S 3*i-1, S 3*i-2 1. round: S 3*i-2 – S 3*i-1 2. round: S 3*i-2 – S 3*i 3. round: S 3*i-1 – S 3*I –For each player: show number of losses in non-forced side.

14. Inter-team Choose sides (now as a team) –For j from 1 to 3 1.round: T 3*j-2 – T 3*j-1 2.round: T 3*j-2 – T 3*j 3. round: T 3*j-1 – T 3*j –For each team: show number of losses in non- forced side.

15. After each round Choose one game (debate) to show to the class. Choose a debate where ideally one of the players has 0 losses in non-forced side.