Today Adam Ó Conghaile will give a talk on “Games & Comonads in Finite Model Theory” as a part of our Theory Seminar Series.
Abstract. Model-comparison games (such as Ehrenfeucht-Fraïssé games, pebble games and modal bisimulation) capture various approximations to isomorphism and homomorphism between structures. These approximations are important and well-studied in computer science for their connections with logic and algorithms but their descriptions are often ad hoc and unified approach to these games is lacking in classical finite model theory. Game comonads, introduced by Abramsky, Dawar & Wang , provide a categorical semantics for these games which reveals connections between these games and relates them in a surprising and elegant way to structural parameters such as treewidth.
In my talk, I will survey the landscape of model-comparison games and developments in this new comonadic perspective to them, including contributions from my recent work with Anuj Dawar on game comonads for logics with generalised quantifiers. 
 – S. Abramsky, A. Dawar, P. Wang The pebbling comonad in finite model theory, LiCS 2017
 – A. Ó Conghaile, A. Dawar Game comonads & generalised quantifiers, CSL 2021
Adam Ó Conghaile
I am a PhD student at the Computer Lab of the University of Cambridge. With my supervisor, Prof Anuj Dawar, I’m researching a compositional approach to finite model theory and descriptive complexity.
Professor Moshe Vardi from Rice University, Texas, will give a talk on The Automated-Reasoning Revolution: From Theory to Practice and Back Wednesday 27th June, 12-1pm, Computational Foundry Seminar Room (Talbot 909).
For the past 40 years computer scientists generally believed that NP-complete problems are intractable. In particular, Boolean satisfiability (SAT), as a paradigmatic automated-reasoning problem, has been considered to be intractable. Over the past 20 years, however, there has been a quiet, but dramatic, revolution, and very large SAT instances are now being solved routinely as part of software and hardware design. In this talk I will review this amazing development and show how automated reasoning is now an industrial reality.
I will then describe how we can leverage SAT solving to accomplish other automated-reasoning tasks. Counting the number of satisfying truth assignments of a given Boolean formula or sampling such assignments uniformly at random are fundamental computational problems in computer science with applications in software testing, software synthesis, machine learning, personalized learning, and more. While the theory of these problems has been thoroughly investigated since the 1980s, approximation algorithms developed by theoreticians do not scale up to industrial-sized instances. Algorithms used by the industry offer better scalability, but give up certain correctness guarantees to achieve scalability. We describe a novel approach, based on universal hashing and Satisfiability Modulo Theory, that scales to formulas with hundreds of thousands of variables without giving up correctness guarantees.