About Me

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Basic information

I am Jiatu Li (李嘉图), a first-year graduate student at MIT theory group, advised by Prof. Ryan Williams. I obtained my Bachelor’s degree from ``Yao Class”, Institute for Interdisciplinary Information Science (IIIS), Tsinghua University.

My research interests are about circuit complexity, proof complexity, and cryptography. Recently, I am interested in the following concrete directions:

  • The strength of Bounded Arithmetic, the fragments of Peano that capture the complexity of reasoning (see, e.g., Youtube Talk by Sam Buss). Can we prove strong lower bounds in Cook’s theory PV$_1$ or Buss’s theory $S^1_2$? Can we separate Jerabek’s theory APC$_1$ and Cook’s PV$_1$? Can we identify the relative strengths of combinatorial principles and theorems as a feasible analogy of the program of Reverse Mathematics?
  • The complexity of the Range Avoidance Problem (see Kor21, RSW22). What is the computational complexity of finding a non-output of an $n$-input $(n+1)$-output circuit? What if the circuit is a restricted one, say, an AC$_0$ circuit?
  • Proving unconditional complexity lower bounds (e.g. MW18, Chen23, CHR23, Li23) and derandomization results (e.g. CLORS23).

As complexity theorists, our mission is to liberate the warriors trying to solve inherently hard problems and use their stories to alleviate insomnia for cryptographers (see, e.g., Cryptographers Seldom Sleep Well).

I am also interested in writing formal (i.e. computer verified) mathematical proofs in Coq and Lean. Although it seems to be incredible nowadays, I believe that proof assistants will eventually be able to help mathematicians in their research (if mathematicians are not completely replaced by something like GPT-256, see, e.g., ChatGPT).

Experience

  • PhD Student: MIT (2023-)
  • Undergraduate Student: Tsinghua University (2019-2023)
    • Undergraduate Research Intern: University of Warwick (2022.3-2022.7), Advised by Dr. Igor Carboni Oliveira
    • Undergraduate Research Intern: Shanghai Qi Zhi Institute (2022.8-2022.9), Advised by Dr. Yilei Chen

How to contact me?

If you have any questions or comments about my papers, essays, and any other projects, please feel free to contact me. I will be more than happy to hear from anyone interested in my work.

Publications

In theoretical computer science, the authors are usually listed in alphabetical order.

Hardness of Range Avoidance and Remote Point for Restricted Circuits via Cryptography. STOC 2024. Yilei Chen and Jiatu Li.
View Paper. Preliminary Version.
Summary. Under a strong but plausible LWE-like assumption, we proved that the range avoidance problem is extremely hard: there is no efficient algorithm even if the circuit is of constant depth and the algorithm is allowed to use nondeterministic guesses. The main technical contribution is a generic construction of witness encryption for certain (possibly not NP-complete) hard languages from public-key encryption that has certain structures, and a Regev-style PKE that is plausibly hard against nondeterministic adversaries.

Indistinguishability Obfuscation, Range Avoidance, and Bounded Arithmetic. STOC 2023. Rahul Ilango, Jiatu Li, R. Ryan Williams.
View Paper. Full Version. Conference Version.
Summary. We showed that the range avoidance problem has no deterministic polynomial-time algorithm assuming $\mathsf{NP}\ne\mathsf{coNP}$ and indistinguishability obfuscation. Under similar assumptions, we proved that Cook’s theory $\mathsf{PV}$ cannot prove the dual weak pigeonhole principle, i.e., Jerabek’s $\mathsf{APC}_1$ is a strict extension of $\mathsf{PV}$.

Range Avoidance, Remote Point, and Hard Partial Truth Table via Satisfying-Pairs Algorithms. STOC 2023. Yeyuan Chen, Yizhi Huang, Jiatu Li, Hanlin Ren.
View Paper. Full Version. Conference Version.
Summary. We proposed a framework that solves the range avoidance problem, remote point problem, and hard partial truth-table for restricted circuit classes by non-trivial algorithms that solve satisfying pairs for the circuit class. This generalizes Williams’s algorithmic approach in circuit lower bounds. In particular, we construct unconditional $\mathsf{FP}^{\mathsf{NP}}$ algorithms of these problems for $\mathsf{ACC}^0$ circuits that recover the best-known (almost-everywhere) lower bound against $\mathsf{ACC}^0$.

Unprovability of Strong Complexity Lower Bounds in Bounded Arithmetic. STOC 2023. Jiatu Li, Igor C. Oliveira.
View Paper. Full Version. Conference Version.
Summary. We showed that strong average-case separation in the third level of polynomial-time hierarchy cannot be proved in $\mathsf{APC}_1$. This is a corollary of a general result that applies to the $i$-th level of polynomial-time hierarchy. We demonstrated a convenient game-theoretic witnessing theorem to develop unprovability results.

Extremely Efficient Constructions of Hash Functions, with Applications to Hardness Magnification and PRFs. CCC 2022. Lijie Chen, Jiatu Li, Tianqi Yang.
View Paper. Full Version. Conference Version.
Summary. We constructed an explicit, uniform, randomness efficient, and low-complexity hash function. It is used to prove the following hardness magnification result: if there is a sparse language in NP that is not computable by $2.01n$ size probabilistic circuits, then NP is not contained in SIZE$[n^k]$.

The Exact Complexity of Pseudorandom Functions and the Black-Box Natural Proof Barrier for Bootstrapping Results in Computational Complexity. STOC 2022. Zhiyuan Fan, Jiatu Li, Tianqi Yang.
View Paper. Full Version. Conference Version. Online Talk.
Summary. We gave tight bounds to compute PRFs in general $\mathsf{B}_2$ circuit (in size), $\mathsf{NC}_1$ circuits (in size and depth) and $\mathsf{TC}_0$ circuits (in wire). Inspired by the natural proof barrier and our results, we demonstrated a barrier for bootstrapping results (e.g. hardness magnification) in complexity theory.

$3.1n−o(n)$ Circuit Lower Bounds for Explicit Functions. STOC 2022. Jiatu Li, Tianqi Yang.
View Paper. Full Version. Conference Version. Online Talk.
Summary. We improved the $(3 + 1/86)n + o(n)$ unconditional circuit lower bound (for explicit function in $\mathsf{P}$ to $3.1n + o(n)$ with a more clever choice of complexity measure and a more careful case analysis (plus some combinatorial tricks).

Other projects

  • Formalization of PAL·S5 in Proof Assistant.
  • Formalization of a theorem in a competitive programming problem.
  • Cutepiler: A Compiler for a C-like Language.
  • Hyper OS: An Operating System Simulator in C++.
    • Github: https://github.com/tqyaaaaang/Hyper-OS
    • A joint work with Tianqi Yang.
    • Summary. An operating system simulator for teaching and research use in C++. It contains basic virtual hardware (such as CPU, APIC, MMU, etc) and a tiny kernel (including process scheduling and paging).
  • A Quick Introduction to Mathematical Logic.
    • Note: https://ljt12138.github.io/2020/05/05/logic-note/
    • Summary. A note on classical results about propositional logic, first-order logic, proof system and (basic) model theory. It covers completeness theorem of first-order logic, the compactness theorem and G¨odel’s incompleteness theorem.
  • The Application of Non-Programming Problems in Competitive Programming Training (in Chinese).

Interesting facts about me

  • My name, Li Jiatu, is the same as the Chinese translation of Ricardo. My parents chose the name when they were reading The Capital of Karl Marx, in which the name David Ricardo occurs constantly.
  • I learned Go (the chess game, not the programming language) when I was a kid and achieved amateur four-dan. Inspired by recent Livestreams of professional Go players in China, I’m now interested in playing go again. My ID on Fox Weiqi is jiatu1li (6d). I am a member of the MIT Go Club and you could probably catch me in the meetings (check https://www.meetup.com/massgo/ for the schedule).