Seminar announcement:This seminar will cover topics in propositional and algebraic proof systems, and algorithms for satisfiability (SAT solvers). The seminar organizers are Sam Buss, Sicun Gao, Noah Fleming, and Russell Impagliazzo. We encourage participants to volunteer to speak! Student participants may receive credit for Math 199, CSE 199, or Math 268 depending on their standing.

Meetings The usual meeting times are Thursdays at 3:00-4:00, online only for Winter 2022 (at least initially). Individual meetings are announced via piazza. The meetings currently only on zoom:

Zoom Room ID is 996 9789 0444.

All seminar announcements will be made on piazza (Math 268, Fall 2021). Please email Sam Buss, sbuss@ucsd.edu, to join the piazza web page.

Lecture archive: (Talk titles link to videos.)

Thursday
Oct. 21, 2021
Speaker: Noah Fleming
Title: A Gentle Introduction to modern SAT Solving
Abstract: While SAT is the canonical NP-complete problem, and believed to be intractable in the worst case, there has been significant success in designing highly efficient algorithms which are capable of solving instances of SAT that occur in practice. These so-called SAT solvers are now routinely used in many areas. In the first talk of the SAT seminar, I will give a gentle introduction to CDCL algorithms, which are the most prevalent algorithms for solving SAT in practice. As well, I will describe how proof complexity -- the study of propositional proofs -- gives a convenient framework for studying these algorithms. I will begin by describing the simple DPLL algorithm on which CDCL SAT solvers are based. Then, I will show how DPLL can be analyzed through the lens of proof complexity. Following this, I will show how to extend DPLL to standard CDCL algorithms.
Thursday
Oct. 28, 2021
Speaker: Noah Fleming
Title: A Gentle Introduction to Modern SAT Solving Part 2: Analyzing CDCL and Resolution Lower Bounds.
Abstract: Last week we discussed the conflict driven clause learning paradigm which underlies modern algorithms for solving SAT by building up from the simple DPLL algorithm. As well, we showed that DPLL is captured by the tree Resolution proof system, which allowed us to analyze this class of algorithms. In this lecture I will talk about how we can analyze CDCL. I will show that the run of a CDCL algorithm gives rise to a (dag) Resolution proof. I will then discuss the storied history of resolution lower bounds and show how to obtain a simple lower bound on the size of Resolution proofs (and therefore a lower bound on CDCL runtime) via composition.
Thursday
Nov. 4, 2021
Speaker: Noah Fleming
Title: A Gentle Introduction to Modern SAT Solving Part 3: The width lower bound
Abstract: In the previous lecture we reduced the task of proving CDCL runtime lower bounds to Resolution size lower bounds, and then to width lower bounds. In this seminar we finish the proof that CDCL does not solve SAT in polytime by proving a width lower bound on resolution proofs of a CNF formula encoding of the pigeonhole principle. Finally, in the last part of the lecture, we will take a step and describe proof complexity and its connections to algorithm design and analysis.
Thursday
Nov. 18, 2021
Speaker: Russell Impagliazzo
Title: Introduction to Algebraic Proof Systems
Abstract: An introduction to the Nullstellensatz and Polynomial Calculus+Resolution proof systems.
Thursday
Dec. 3, 2021
Speaker: Russell Impagliazzo
Title: Second talk on Algebraic Proof Systems: PCR, resolution and automatizability
Abstract: Polynomial Calculus Resolution (PCR). Simulation of resolution. Size/degree bounds. Proof search.
Thursday
Jan. 6, 2022
Speaker: Russell Impagliazzo
Title: Third talk on Algebraic Proof Systems: PCR, resolution and automatizability
Abstract: Polynomial Calculus Resolution (PCR). Size versus degree bounds. Lower bounds for Tseitin tautologies.
Thursday
Jan. 13, 2022
Speaker: Noah Fleming
Title: Integer programming
Abstract: Branch and cut. Cutting planes. Stabbing planes. Upper bounds for Tseitin tautologies.