Avishay Tal

Hi, I'm Avishay, an Assistant Professor at the Department of Electrical Engineering and Computer Sciences at UC Berkeley. I am honored to be part of Berkeley's Theory Group.

I received my Ph.D. in 2015 from the Weizmann Institute of Science, under the guidance of Ran Raz. Prior to that, I was an M.Sc. student at the Technion under the guidance of Amir Shpilka. I feel very fortunate to have had both Amir and Ran as my mentors.

I held postdoctoral appointments at the Institute for Advanced Study (hosted by Avi Wigderson), Simons Institute (as part of the Lower Bounds in Computational Complexity program), and Stanford University (hosted by Omer Reingold).

Main Research Interests

• • Computational Complexity, 

  • Analysis of Boolean Functions, 

  • Circuit and Formula Lower Bounds, 

  • Query Complexity, 

  • Pseudorandomness, 

  • Computational Learning Theory, 

  • Quantum Computing,

  • Combinatorics, and 

  • Connections between Algorithms and Lower Bounds. 

Motivating questions that guide my research:

• • What is the power and limitations of parallel computation?

  • What is the role of randomness in computation?

  • What is the role of memory in learning?

  • For which tasks do quantum algorithms outperform classical algorithms?

Contact Information

Address:

635 Soda Hall

Department of Electrical Engineering and Computer Sciences

University of California, Berkeley

Berkeley, CA, 94720

E-mail: atal "at" berkeley.edu

Events

Workshop on Derandomizing Space-Bounded Computation (Part of STOC 2020)

Advances in Boolean Function Analysis Lecture Series @ The Simons Institute (Summer 2020)

Program on Analysis and TCS : New Frontiers @ The Simons Institute (Summer 2023) -- we have a reunion coming up in July 2024

Teaching

CS 294-92 - Analysis of Boolean Functions - Spring 2020

CS 170 - Efficient Algorithms and Intractable Problems - Fall 2020

CS 278 - Computational Complexity Theory - Spring 2021

CS 294-202 - Pseudorandomness - Fall 2021

CS 172 - Computability and Complexity - Spring 2022

CS 172 - Computability and Complexity - Fall 2022

CS 294-92 - Analysis of Boolean Functions - Spring 2023

CS 70 - Discrete Mathematics and Probability Theory - Fall 2023

CS 278 - Computational Complexity Theory - Spring 2024

CS 172 - Computability and Complexity - Fall 2024

Program Committees

FOCS 2019,  SODA 2020,  CCC 2020,  RANDOM 2020,  ITCS 2021,  STOC 2021, ITCS 2023, STOC 2024

Group Information

Current Ph.D. Students

• Orr Paradise (co-advised with Shafi Goldwasser)

• Kewen Wu

• Zoë Bell (co-advised with Shafi Goldwasser)

• Xin Lyu (co-advised with Jelani Nelson)

• Hongxun Wu (co-advised with Jelani Nelson)

Current Postdocs

• Lijie Chen - Miller Fellow

Former Students

• Michael Whitmeyer - M.Sc.  (now a PhD student @ UW)

• Vishnu Iyer - Undergraduate researcher (now a PhD student @ UT Austin)

• Nagaganesh Jaladanki - M.Sc. (now Software Engineer @ Stripe)

Former Postdocs

• William M. Hoza - Simons-Berkeley postdoc (now Faculty at U Chicago)

• Makrand Sinha - Simons-Berkeley postdoc (now Faculty at UIUC)

Publications

1. The Power of Adaptivity in Quantum Query Algorithms
   PDF
   joint with Uma Girish, Makrand Sinha, and Kewen Wu
   Presented at the 27th Annual Conference on Quantum Information Processing (QIP 2024).
   STOC, 2024.
   
   

2. Tight Time-Space Lower Bounds for Constant-Pass Learning
   PDF
   joint with Xin Lyu, Hongxun Wu, and Junzhao Yang
   FOCS, 2023.
   
   

3. Weighted Pseudorandom Generators via Inverse Analysis of Random Walks and Shortcutting
   PDF
   joint with Lijie Chen, William Hoza, Xin Lyu, and Hongxun Wu
   FOCS, 2023.
   
   

4. Fourier Growth of Communication Protocols for XOR Functions
   PDF
   joint with Uma Girish, Makrand Sinha, and Kewen Wu
   FOCS, 2023.
   
   

5. New PRGs for Unbounded-Width/Adaptive-Order Read-Once Branching Programs
   PDF
   Lijie Chen, Xin Lyu,  and Hongxun Wu
   ICALP, 2023.
   
   

6. Quantum Cryptography in Algorithmica
   PDF
   joint with William Kretschmer, Luowen Qian, and Makrand Sinha.
   Presented at the 26th Annual Conference on Quantum Information Processing (QIP 2023).
   STOC, 2023.
   
   

7. Depth-d Threshold Circuits vs. Depth-(d+1) AND-OR Trees
   PDF
   joint with Pooya Hatami, William Hoza, and Roei Tell.
   STOC, 2023.
   
   

8. On Certified Randomness from Quantum Advantage Experiments
   PDF
   joint with Roozbeh Bassirian, Adam Bouland, Bill Fefferman, and Sam Gunn.
   
   

9. Fourier Growth of Parity Decision Trees
   PDF
   joint with Uma Girish and Kewen Wu.
   CCC, 2021.
   
   

10. Pseudorandom Generators for Read-Once Monotone Branching Programs
    PDF
    joint with Dean Doron, Raghu Meka, Omer Reingold, and Salil Vadhan.
    RANDOM, 2021.
    
    

11. Fooling Constant-Depth Threshold Circuits
    PDF
    joint with Pooya Hatami, William Hoza, and Roei Tell.
    FOCS, 2021.
    
    

12. Junta Distance Approximation with Sub-Exponential Queries
    PDF
    joint with Vishnu Iyer and Michael Whitmeyer.
    CCC, 2021.
    
    

13. Shrinkage under Random Projections, and Cubic Formula Lower Bounds for AC0
    PDF
    joint with Yuval Filmus and Or Meir.
    ITCS, 2021.
    
    

14. Degree vs. Approximate Degree and Quantum Implications of Huang's Sensitivity Theorem
    PDF
    joint with Scott Aaronson, Shalev Ben-David, Robin Kothari, and Shravas Rao.
    (Subsumes an earlier version named "Quantum Implications of Huang's Sensitivity Theorem")
    Presented at the 24th Annual Conference on Quantum Information Processing (QIP 2021) as a short plenary talk.
    STOC, 2021.
    
    

15. Rigid Matrices From Rectangular PCPs
    PDF
    joint with Amey Bhangale, Prahladh Harsha, and Orr Paradise.
    FOCS, 2020. SICOMP, 2024.
    
    

16. Towards Optimal Separations between Quantum and Randomized Query Complexities
    PDF FOCS Long Talk
    FOCS, 2020.
    
    

17. Quantum versus Randomized Communication Complexity, with Efficient Players
    PDF
    joint with Uma Girish and Ran Raz.
    Presented at the 23rd Annual Conference on Quantum Information Processing (QIP 2020).
    ITCS, 2021. Computational Complexity Journal 2022.
    
    

18. On the Computational Power of Radio Channels
    PDF
    joint with Mark Braverman, Gillat Kol, and Rotem Oshman.
    DISC, 2019.
    
    

19. Time-Space Lower Bounds for Two-Pass Learning
    PDF
    joint with Sumegha Garg and Ran Raz.
    CCC, 2019.
    
    

20. AC0[p] Lower Bounds against MCSP via the Coin Problem
    PDF
    joint with Alexander Golovnev, Rahul Ilango, Russell Impagliazzo, Valentine Kabanets, and Antonina Kolokolova.
    ICALP, 2019.
    
    

21. Oracle Separation of BQP and PH
    PDF
    joint with Ran Raz.
    STOC, 2019. (Best Paper Award). JACM, 2022.
    Presented at the 22nd Annual Conference on Quantum Information Processing (QIP 2019) as a plenary talk.
    [Computational Complexity Blog] [Shtetl-Optimized] [Windows on Theory]
    [New Scientist] [Quanta] [The Hindu] [CACM] [Nature]
    Video (CMO Oaxaca) Video (IAS)
    
    

22. Exponential separation between shallow quantum circuits and unbounded fan-in shallow classical circuits
    PDF
    joint with Adam Bene Watts, Robin Kothari, and Luke Schaeffer.
    STOC, 2019.
    Presented at the 22nd Annual Conference on Quantum Information Processing (QIP 2019).
    
    

23. Pseudorandom Generators for Width-3 Branching Programs
    PDF
    joint with Raghu Meka and Omer Reingold.
    STOC, 2019.
    [Oded's choices]
    
    

24. Pseudorandom generators from the second Fourier level and applications to AC0 with parity gates
    PDF
    joint with Eshan Chattopadhyay, Pooya Hatami, and Shachar Lovett.
    ITCS, 2019.
    
    

25. Cubic Formula Size Lower Bounds Based on Compositions with Majority
    PDF
    joint with Anna Gal and Adrian Trejo Nuñez.
    ITCS, 2019.
    
    

26. Improved Pseudorandomness for Unordered Branching Programs through Local Monotonicity
    PDF
    joint with Eshan Chattopadhyay, Pooya Hatami and Omer Reingold.
    STOC, 2018.
    
    

27. Extractor-Based Time-Space Lower Bounds for Learning
    PDF
    joint with Sumegha Garg and Ran Raz.
    STOC, 2018.
    
    

28. On Constant-Depth Canonical Boolean Circuits for Computing Multilinear Functions
    PDF
    joint with Oded Goldreich.
    Book chapter in "Computational Complexity and Property Testing", 2020.
    
    

29. The Choice and Agreement Problems of a Random Function
    PDF
    joint with Or Meir.
    Information Processing Letters, Volume 133, 2018.
    
    

30. Pseudorandom Generators for Low Sensitivity Functions
    PDF
    joint with Pooya Hatami.
    ITCS, 2018.
    
    

31. Robust Sensitivity
    PDF
    joint with Shachar Lovett and Jiapeng Zhang.
    SODA, 2018.
    
    

32. Lower Bounds for 2-Query LCCs over Large Alphabet
    PDF
    joint with Arnab Bhattacharyya and Sivakanth Gopi.
    RANDOM, 2017.
    
    

33. Tight Bounds on The Fourier Spectrum of AC0
    PDF Slides
    CCC, 2017.
    [Oded's choices]
    
    

34. The Bipartite Formula Complexity of Inner-Product is Quadratic
    PDF
    STOC, 2017 (merged with "Computing Requires Larger Formulas than Approximating").
    
    

35. Computing Requires Larger Formulas than Approximating
    PDF Slides TCS+ Talk
    STOC, 2017 (merged with "The Bipartite Formula Complexity of Inner-Product is Quadratic").
    [Oded's choices]
    
    

36. Time-Space Hardness of Learning Sparse Parities
    PDF Slides
    joint with Gillat Kol and Ran Raz.
    STOC, 2017.
    
    

37. Low-Sensitivity Functions from Unambiguous Certificates
    PDF
    joint with Shalev Ben-David and Pooya Hatami.
    ITCS, 2017.
    
    

38. Degree and Sensitivity: Tails of Two Distributions
    PDF
    joint with Parikshit Gopalan, Rocco Servedio, and Avi Wigderson.
    (a preliminary version of this paper by Gopalan, Servedio, and Wigderson appeared in CCC, 2016).
    
    

39. On the Sensitivity Conjecture
    PDF Slides
    ICALP, 2016.
    
    

40. #SAT Algorithms from Shrinkage
    PDF
    
    

41. Matrix Rigidity of Random Toeplitz Matrices
    PDF Journal-version Slides (STOC) Slides (longer version)
    joint with Oded Goldreich.
    STOC, 2016. Computational Complexity, 2016.
    
    

42. Shrinkage of De Morgan Formulae by Spectral Techniques
    PDF Slides
    FOCS, 2014.
    
    

43. On Fractional Block Sensitivity
    PDF Journal-version
    joint with Raghav Kulkarni.
    CJTCS, 2016.
    
    

44. Two Structural Results for Low Degree Polynomials and Applications
    PDF Video (IAS) Slides (RANDOM)
    joint with Gil Cohen.
    RANDOM, 2015.
    An implementation of the algorithm suggested in Theorem 4.1.
    
    

45. On the Structure of Boolean Functions with Small Spectral Norm
    PDF
    joint with Amir Shpilka and Ben lee Volk.
    ITCS, 2014. Computational Complexity Journal, 2015.
    
    

46. Improved Average-Case Lower Bounds for De Morgan Formula Size
    PDF Journal-version Slides
    joint with Ilan Komargodski and Ran Raz.
    FOCS, 2013. SICOMP, 2017.
    
    

47. Properties and Applications of Boolean Function Composition
    PDF Slides
    ITCS, 2013. (Best Student Paper)
    [Oded's choices]
    
    

48. On the Degree of Univariate Polynomials Over the Integers
    PDF Journal-version
    joint with Gil Cohen and Amir Shpilka.
    ITCS, 2012. Combinatorica, 2016
    
    

49. On The Minimal Fourier Degree of Symmetric Boolean Functions
    PDF Journal-version Slides Amir@MSR
    joint with Amir Shpilka.
    CCC, 2011. Combinatorica, 2014.
    [Richard Lipton's Blog Post] [2]