SIGACT News Complexity Theory Column 111

This issue's complexity theory column is by Ben Lee Volk on algebraic natural proofs. My warmest thanks to Ben Lee for his terri c article.

Technical Report Column

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.

Distributed Computing Column 84

Overview. In this column, we combine traditional content for the December edition, namely a perspective on the paper which received the 2021 Dijkstra Award, but we also depart of from tradition, by not having our traditional articles covering the PODC and/or DISC proceedings.

Review of The Age of Algorithms by Serge Abiteboul and Gilles Dowek

This book is about algorithms and their enormous influence on people in the current age. Algorithms are precise sets of rules to solve problems. They are ubiquitous and have a great effect on the lives of contemporary people, primarily due to technological advancement. A common example is searching for information using an Internet search engine such as Google. This book is not technical in nature and was first published in French as Le Temps des Algorithmes, by ´ Editions Le Pommier in 2020. The authors Serge Abiteboul and Gilles Dowek are computer scientists, with Institut National de Recherche en Informatique et en Automatique (INRIA), Rocquencourt and ´ Ecole Normale Sup´erieure, Paris respectively. They believe that algorithms have made life easier, nevertheless, they dread that algorithms may subjugate humans. This book is intended to serve as an eye-opener on the impact of algorithms on daily life.

SIGACT News Online Algorithms Column 38

In this column, we will discuss some papers in online algorithms that appeared in 2021. 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!

27 Open Problems in Kolmogorov Complexity

This formula can be informally read as follows: the ith messagemi brings us log(1=pi) "bits of information" (whatever this means), and appears with frequency pi, so H is the expected amount of information provided by one random message (one sample of the random variable). Moreover, we can construct an optimal uniquely decodable code that requires about H (at most H + 1, to be exact) bits per message on average, and it encodes the ith message by approximately log(1=pi) bits, following the natural idea to use short codewords for frequent messages. This fits well the informal reading of the formula given above, and it is tempting to say that the ith message "contains log(1=pi) bits of information." Shannon himself succumbed to this temptation [46, p. 399] when he wrote about entropy estimates and considers Basic English and James Joyces's book "Finnegan's Wake" as two extreme examples of high and low redundancy in English texts. But, strictly speaking, one can speak only of entropies of random variables, not of their individual values, and "Finnegan's Wake" is not a random variable, just a specific string. Can we define the amount of information in individual objects?

Review of A Short Course in Computational Geometry and Topology by Herbert Edelsbrunner

Computational geometry and topology are huge branches of mathematics. Focussing on concepts that lead to computation is one strategy to provide a concrete conceptual basis for ideas that hold in a more general context. Indeed, this short book gives an introduction to a surprisingly broad range of ideas that can serve as a good introduction to geometry and topology (even broadly conceived) for undergraduates.

The Book Review Column

The first two reviews in this column draw from the "SpringerBriefs" series, dedicated to compact summaries of cutting-edge research in a variety of fields. The first is from SpringerBriefs in Physics, the second from SpringerBriefs in Applied Sciences and Technology. We close with a review about algorithms in the context of the modern world.

Guest Column

Algebraic Natural Proofs is a recent framework which formalizes the type of reasoning used for proving most lower bounds on algebraic computational models. This concept is similar to and inspired by the famous natural proofs notion of Razborov and Rudich [RR97] for boolean circuit lower bounds, but, unlike in the boolean case, it is an open problem whether this constitutes a barrier for proving super-polynomial lower bounds for strong models of algebraic computation. From an algebraic-geometric viewpoint, it is also related to basic questions in Geometric Complexity Theory (GCT), and from a meta-complexity theoretic viewpoint, it can be seen as an algebraic version of the MCSP problem. We survey the recent work around this concept which provides some evidence both for and against the existence of an algebraic natural proofs barrier, with an emphasis on the di erent viewpoints and the connections to other areas.

A Perspective on "CCS Expressions, Finite State Processes, and Three Problems of Equivalence"

With the publication of the Kannellakis-Smolka 1983 PODC paper, Kanellakis and Smolka pioneered the development of efficient algorithms for deciding behavioral equivalence of concurrent and distributed processes, especially bisimulation equivalence. Bisimulation is the cornerstone of the process-algebraic approach to modeling and verifying concurrent and distributed systems. They also presented complexity results that showed certain behavioral equivalences are computationally intractable. Collectively, their results founded the subdiscipline of algorithmic process theory, and established the associated bridges between the European research community, whose focus at the time was on process theory, and that of the US, with a rich tradition in algorithm design and computational complexity, but to whom process theory was largely unknown.