The complexity class QMA(2), featuring two unentangled quantum provers, occupies a central yet poorly understood position in quantum complexity theory. While superficially a modest extension of QMA, unentanglement fundamentally changes both the algorithmic and complexitytheoretic landscape, connecting QMA(2) to deep questions in separability testing, polynomial optimization, and hardness of approximation. Over the past two decades, QMA(2) has inspired a rich body of work spanning restricted verification models, semidefinite and Sum-of-Squares hierarchies, and surprising links to classical problems such as the Unique Games Conjecture. This survey provides an overview of these developments, emphasizing structural insights, algorithmic techniques, and known barriers, while highlighting how progress on QMA(2) continues to illuminate the interplay between quantum information, convex optimization, and classical complexity theory.
The PCP theorem [AS98, ALM + 98, Din07] is a breakthrough in theoretical CS with a wide range of applications. In this article, we discuss the work of [BMVY25] that constructs improved probabilistically checkable proofs (PCPs) from high-dimensional expanders (HDX). Our goal is to explain the main components of their construction, while also giving historical context for how the key ideas emerged across the PCP, HDX and routing literature. We aim for a largely self-contained overview, with additional pointers for technical details. We focus on the following ingredients: PCPs from expanders [Din07]; the abstraction of direct product testing [GS00]; recent constructions of linear size direct product testers with small soundness [BM24, BLM24, DD24a, DD24c, DDL24], and the role of high-dimensional expansion in enabling these results. We then explain how [BMVY25] turned such direct product testers into PCPs via a new connection to fault-tolerant routing, and a construction of such algorithms for HDX. Finally, we conclude with some other applications that these techniques have found and future directions.
This Issue's Column! This issue's Open Problem Column is by William Gasarch and is Relationships Between the Busy Beaver Function and Mathematics I: What is the Smallest n such that BB(n) > ... Request for Columns! I invite any reader who has knowledge of some area to contact me and arrange to write a column about open problems in that area. That area can be (1) broad or narrow or anywhere in between, and (2) really important or really unimportant or anywhere in between.
''Laplacian'' is one of those buzzwords that can stop a conversation. Algebraic techniques in a distributed setting can be frightening: they feel complicated, definition-heavy, and out of reach for the ordinary distributed computing researcher. I am here to tell you that it is not so bad. In this survey, I will outline the main ideas and techniques in the field, while simplifying to the level that you do not even need to remember much from your linear algebra classes.
Dear Readers, For this issue, Geoffroy Couteau contributed a wonderful guest column on the cryptographic problem of ''compressing'' correlated randomness and its surprising applications to cooking Chicken Tikka Masala (please do read the column for more details!). In the upcoming issues of SIGACT News, we expect to feature columns by Jesse Goodman (on seedless extractors); Davi Castro-Silva, Arkopal Dutt, and Tom Gur (on connections between additive combinatorics and quantum complexity theory); Debarati Das; and Jeroen Zuiddam (on matrix multiplication, moment polytopes and asymptotic spectra).
The Joy of Cryptography: An Undergraduate Course in Provable Security (MIT Press, 2026), by Mike Rosulek (Oregon State University), is a comprehensive introduction to the fundamentals of provable security for advanced undergraduates. Introduction to String Algorithms (Princeton University Press, 2026), by Carl Kingsford (Carnegie Mellon University), provides a guide to modern data structures and algorithms for large-scale string processing. The book is suitable for advanced undergraduates, graduate students, researchers, and practitioners in this field. Basic Graph Theory (Cambridge University Press, 2026), by Béla Bollobàs (University of Cambridge) and Robert Morris (IMPA, Rio de Janeiro), is a gentle introduction to graph theory, focusing on beautiful questions, ideas, and proofs, as well as illustrating powerful techniques such as the probabilistic method. Discrete Mathematics: A Combinatorial Approach (Springer, 2026), by Christos A. Athanasiadis (University of Athens), is an undergraduate textbook that provides a concise introduction to combinatorial and discrete mathematics, with an emphasis on enumeration and generating functions.
Hi everyone! As promised in the previous issue, I will also use this column to highlight exciting, broadly accessible workshop talks. In this issue, we get to read Tijn de Vos's gentle introduction to distributed Laplacian techniques, based on his talk at ADGA 2025, colocated with DISC 2025 in Berlin. I was very happy to see the talk, read the survey, and finally come away with the feeling that all this scary Laplacian stuff is actually easy, natural, and good for all of us. I hope you, dear reader, will experience the same revelation. If you have any feedback or ideas for future contributions to this column, please drop me an email, or ping me on social media or instant messaging, wherever you see me. I will be at SIROCCO 2026 this summer, and I will do my best to also take part in PODC/SPAA/ICALP 2026 at Royal Holloway. See you!
Is it possible to emulate sampling from an arbitrary efficiently-samplable distribution using an efficient deterministic procedure which is initially fed with a short random seed and increments a counter after each query? Yes, under minimal cryptographic assumptions (the existence of one-way functions) as shown by a sequence of celebrated results in the 80s. Equivalently, one can view this problem as the goal to compress a large number of (seemingly) random samples into a short random seed. But what happens when multiple parties want, given short correlated random seeds distributed in a one-time initialization step, to deterministically and non-interactively obtain correlated samples that cannot be distinguished (even by a subset of the participants themselves) from random samples from a joint distribution? In other words, can cryptography help us compress (seemingly) random correlated samples? Our knowledge of this natural generalization of the problem is considerably more limited, and there is much more that we don't know than we know! Nevertheless, many special cases of this question have been explored in recent (and not so recent) works, motivated in part by numerous applications to other cryptographic tasks. In this article, I provide an introductory exposition of the topic, recasting a number of results originally introduced using various formalisms, under the lens of compressed samplers for multiple parties.
1 This is the first of (hopefully only) two papers In this paper we ask the following question: for a variety of computable functions f, what is the smallest n such that BB(n) > f(n). In the sequel, we will ask questions such as: What is the smallest Turing machine M such that Goldbach's conjecture is true iff M never halts? In both papers all concepts and definitions are due to others unless otherwise noted. For example, if I wrote We define a hierarchy similar to the Wainer hierarchy the definition we give is already known.
1 This Issue's Column! Luca Trevisan passed away on June 19, 2024 at the age of 52, of cancer. He worked on randomness, approximation, and many other topics in theory. My last column consisted of open problems by Lance Fortnow, Oded Goldreich, Johan H˚astad, Salil Vadhan, and David P. Williamson that Luca was interested in. This column is also about a problem that Luca was interested in. The column is on Constructive Lower Bounds on Ramsey numbers and is by Rishi Cherukuri and William Gasarch. Extractors played a large part in that work, and one of Luca's biggest contributions was his papers on extractors. Request for Columns! I invite any reader who has knowledge of some area to contact me and arrange to write a column about open problems in that area. That area can be (1) broad or narrow or anywhere inbetween, and (2) really important or really unimportant or anywhere inbetween.
Approximation Algorithms for Traveling Salesman Problems (Cambridge University Press, 2024) by Vera Traub and Jens Vygen (both of University of Bonn) presents the state of the art of approximation algorithms for the Traveling Salesman Problem (TSP), covering both classic and recent results as well as outstanding open problems. Understanding Cryptography: From Established Symmetric and Asymmetric Ciphers to Post- Quantum Algorithms, Second Edition (Springer, 2024) by Christof Paar (Max Planck Institute), Jan Pelzl (Hamm-Lippstadt University) , Tim G¨uneysu (Ruhr University Bochum) focuses on modern applications of cryptography, with special emphasis on post-quantum methods. The Elements of Computing Systems: Building a Modern Computer from First Principles, Second Edition (The MIT Press, 2021) by Noam Nisan (Hebrew University of Jerusalem) and Shimon Schocken (Interdisciplinary Center Herzliya) updates the popular textbook that inspires Nand-to-Tetris courses on how to build a general-purpose computer system from scratch. This new edition is divided into two standalone parts, Hardware and Software, and features four new appendices. The Joy of Quantum Computing: A Concise Introduction (Princeton University Press, 2025) by Jed Brody (Emory University) is an accessible introduction to the subject requiring only calculus and no quantum mechanics background.
The Computer Always Wins: A Playful Introduction to Algorithms through Puzzles and Strategy Games (The MIT Press, 2025) by Elliot Lichtman (Yale University, '27) is an accessible introduction to advanced computing concepts for young coders. Quantum Algorithms: A Survey of Applications and End-to-End Complexities (Cambridge University Press, 2025) by Alexander M. Dalzell et al. (AWS Center for Quantum Computing) summarizes the most common quantum algorithmic primitives and demonstrates their various applications. Guide to Distributed Algorithms: Design, Analysis and Implementation Using Python (Springer, 2025) by K. Erciyes (Ya¸sar University, T¨urkiye) is a textbook on distributed algorithms with working Python implementations. Algorithm Design: A Methodological Approach - 150 Problems and Detailed Solutions (Routledge, 2023) by Patrick Bosc, Marc Guyomard, Laurent Miclet (all at Universit´e de Rennes, France) is the English edition of the French best-selling textbook that aims to teach algorithm design methodologies and analysis through examples.
Overview. In this column, we follow tradition and cover one of the two main conferences in our community this year, PODC 2025. One departure from our usual columns-co-written with participating students-is that the column is written from the perspective of the organizers, specifically Gilde Valeria Rodriguez, Armando Castañeda, and Sergio Rajsbaum. As such, the column includes the usual detailed overview of talks, but also some of the emotion of being an organizer of a conference that may be affected by a hurricane. I invite you to enjoy the column, and thank the authors for all their work!
In this column, we will discuss some papers in online algorithms that appeared in 2025. As usual, we make no claim at complete coverage here, and have instead made a selection. If we have unaccountably missed your favorite paper and you would like to write about it or about any other topic in online algorithms, please don't hesitate to contact us!
In this column, we overview recent progress by many authors on understanding the approximability of constraint satisfaction problems (CSPs) in low-space streaming models. Inspired by this recent progress, we collate nine conjectural lower bounds against streaming algorithms for CSPs, some of which appear here for the first time.
Local decoding enables fast recovery of individual symbols of a message, even in the presence of errors. Locally decodable codes that can withstand Hamming errors are foundational in theoretical computer science, with deep connections to program checking, probabilistically checkable proofs, private information retrieval, and data structures. More recently, the literature has expanded to address a much more challenging type of errors: insertions and deletions. These synchronization errors may cause misalignment in the data, and are especially relevant to emerging applications in DNA storage technologies. In this article, we survey recent advances on local decoding in the presence of synchronization errors, highlight key techniques, and state several open problems.
This article continues from Lecture One, where we introduced the basic ideas of quantum computing using intuitive examples aimed at college students. In this lecture, we focus on basic concepts from linear algebra and complex numbers that are essential for understanding quantum computing. We also demonstrate how these linear algebra operations relate to quantum computation. This chapter is designed to provide a smooth transition to Lecture Three, which will introduce the quantum gates.
I invite any reader who has knowledge of some area to contact me and arrange to write a column about open problems in that area. That area can be (1) broad or narrow or anywhere inbetween, and (2) really important or really unimportant or anywhere inbetween. A better, in color, and up-to-date version of this paper can be found at the following link: https://www.cs. umd.edu/~gasarch/open/MONOUNIT/monounit.pdf.
The 44th edition of the ACM Symposium on Principles of Database Systems (PODS) was held from June 23 to 25, 2025, in Berlin, Germany. As in previous years, the symposium was held jointly with the ACM International Conference on Management of Data (SIGMOD). PODS research aims to provide a solid scientific foundation for methods, techniques, and solutions to the data management challenges that continually arise in our data-driven society. Specifically, PODS calls for papers contributing principled approaches to modeling, application, system building, and both theoretical and experimental validation in the context of data management. Such papers may be based, among others, on establishing theoretical results, developing new concepts and frameworks that merit further exploration, providing experimental work that sheds light on the scientific foundations of the discipline, or conducting a rigorous analysis of widely used or recently developed industry artifacts.
Welcome to the Technical Reports Column. If your institution publishes technical reports that you'd like to have included here, please contact me at the email address above.
