PPT-Unprovability of strong complexity lower bounds in bounded arithmetic

Dagstuhl Workshop March 2023 Igor Carboni Oliveira University of Warwick 1 Join work with Jiatu Li Tsinghua 2 Context Goals of Complexity Theory include separating complexity classes. The heart of this technique is a complex ity measure for multivariate polynomials based on the linear span of their partial derivatives We use the technique to obtain new lower bounds for computing sym metric polynomials which hold over 64257elds of and Circuits. Lecture . 5. Binary Arithmetic. let’s. . look . at the procedures for performing the four basic arithmetic functions: . addition,. subtraction, multiplication, and division. Addition. Program Analysis and Verification . Nikolaj Bj. ø. rner. Microsoft Research. Lecture 3. Overview of the lectures. Day. Topics. Lab. 1. Overview of SMT and applications. . SAT solving,. Z3. Encoding combinatorial problems with Z3. CS1313 Spring 2016. 1. Arithmetic Expressions Lesson #2 Outline. Arithmetic Expressions Lesson #2 Outline. Named Constant & Variable Operands #1. Named Constant & Variable Operands #2. Named Constant & Variable Operands #2. Section 8.2 beginning on page 417. Identifying Arithmetic Sequences. In an . arithmetic sequence. , the difference of consecutive terms is constant. This constant difference Is called . common difference. Shubhangi. . Saraf. Rutgers University. Based on joint works with . Albert Ai, . Zeev. . Dvir. , . Avi. . Wigderson. Sylvester-. Gallai. Theorem (1893). v. v. v. v. Suppose that every line through . unseen problems. David . Corne. , Alan Reynolds. My wonderful new algorithm, . Bee-inspired Orthogonal Local Linear Optimal . Covariance . K. inetics . Solver. Beats CMA-ES on 7 out of 10 test problems !!. approximate membership. dynamic data structures. Shachar. Lovett. IAS. Ely . Porat. Bar-. Ilan. University. Synergies in lower bounds, June 2011. Information theoretic lower bounds. Information theory. A combinatorial approach to P . vs. NP. Shachar. Lovett. Computation. Input. Memory. Program . Code. Program code is . constant. Input has . variable length (n). Run time, memory – grow with input length. Hrubeš . &. . Iddo Tzameret. Proofs of Polynomial Identities . 1. IAS, Princeton. ASCR, Prague. The Problem. How . to solve it by hand . ?. Use the . polynomial-ring axioms . !. associativity. , . Ben Braun, Joe Rogers. The University of Texas at Austin. November 28, 2012. Why primitive recursive arithmetic?. Primitive recursive arithmetic is consistent.. Many functions over natural numbers are primitive recursive:. Toniann. . Pitassi. University of Toronto. 2-Party Communication Complexity. [Yao]. 2-party communication: . each party has a dataset. . Goal . is to compute a function f(D. A. ,D. B. ). m. 1. m. 2. 2, 4, 6, 8, . …. The . first term in a sequence is denoted as . a. 1. , . the second term is . a. 2. , . and so on up to the nth term . a. n. .. Each number in the list called a . term. .. a. 1. , a. Specifications. Will Klieber . (presenting). Will Snavely. Software Engineering Institute. Carnegie Mellon University. Pittsburgh. , PA. IEEE SecDev Conference. Nov . 3. –. 4, 2016. Copyright 2016 Carnegie Mellon University.