Hubie (Hubert) Chen
Department of Informatics
King’s College London
London, United Kingdom
E-mail address: (five-letter first name)(dot)(last name) plus (at)(kcl)(dot)(ac)(dot)(uk)
Computability and Complexity, by Hubie Chen. MIT Press,
2023.
MIT
Press website for book
This initiation to the theory of computation has been praised as a “beautifully comprehensive introduction to automata, computability, and complexity theory” that “discusses the landmark theorems very carefully” and is “presented with a high level of mathematical rigor.” This book combines intuitive discussion—backed by numerous diagrams and examples—with a precise mathematical treatment that includes comprehensive proofs.
Topics covered by this book include:
Automata theory – deterministic and nondeterministic finite automata, regular expressions, proving non-regularity via Myhill-Nerode theory, DFA minimization;
Computability theory – deterministic and nondeterministic Turing machines, universal Turing machines, diagonalization and non-computable languages, reductions, Rice’s theorem;
Complexity theory – time complexity classes (P, NP, and coNP), the P versus NP question, the theories of NP-completeness and of coNP-completeness, numerous completeness proofs, the space complexity class PSPACE, hierarchy theorems, parameterized complexity.
Numerous exercises and notes expand upon the main presentation and cover topics such as Gödel incompleteness, counting complexity, logarithmic space complexity, and treewidth.
An excerpt of this book is freely useable and freely distributable under a Creative Commons CC-BY-NC-ND license.
Hubie Chen and Stefan Mengel.
Optimally
Rewriting Formulas and Database Queries: A Confluence of Term Rewriting,
Structural Decomposition, and Complexity.
ICDT 2024. Invited to LMCS special issue of ICDT 2024.
Hubie Chen, Gianluigi Greco, Stefan Mengel, and Francesco
Scarcello.
Counting Solutions to
Conjunctive Queries: Structural and Hybrid Tractability.
arXiv:2311.14579.
Hubie Chen.
Algebraic Global
Gadgetry for Surjective Constraint Satisfaction.
Computational Complexity (33) 7, 2024.
Hubie Chen, Bart M. P. Jansen, Karolina Okrasa, Astrid Pieterse,
and Paweł Rzążewski.
Sparsification Lower
Bounds for List H-Coloring.
ACM Transactions on Computation Theory (15) 3-4: 8:1-8:23,
2023.
Hubie Chen, Georg Gottlob, Matthias Lanzinger, and Reinhard
Pichler.
Semantic Width and
the Fixed-Parameter Tractability of Constraint Satisfaction
Problems.
International Joint Conference on Artificial Intelligence (IJCAI), pp
1726–1733, 2020.
Hubie Chen and Yuichi Yoshida.
Testability of Homomorphism Inadmissibility: Property Testing Meets
Database Theory.
Symposium on Principles of Database Systems (PODS), Amsterdam, The
Netherlands, pp 365–382, 2019.
Hubie Chen.
The Selfish Models Property: Bounding the Complexity of Query
Containment and Entailment Problems.
Symposium on Principles of Database Systems (PODS), Amsterdam, The
Netherlands, pp 383–398, 2019.
Christoph Berkholz and Hubie Chen.
Compiling Existential Positive Queries to Bounded-Variable
Fragments.
Symposium on Principles of Database Systems (PODS), Amsterdam, The
Netherlands, pp 353–364, 2019.
Simone Bova and Hubie Chen.
How Many Variables are Needed to Express an Existential Positive
Query?.
Theory of Computing Systems 63(7): 1573–1594, 2019. Conference version
appeared in: International Conference on Database Theory (ICDT), Venice,
Italy, pp 9:1–9:16, 2017. ICDT 2017 Best Paper Award.
Note: H. Andréka, J. van Benthem, and I. Németi point out (in their Section 2) that this article settles a “long-standing open problem”.
Hubie Chen and Matthew Valeriote.
Learnability of
Solutions to Conjunctive Queries.
Journal of Machine Learning Research 20: 67:1–67:28, 2019. Conference
version appeared in: Conference on Learning Theory (COLT), Paris,
France, pp 326–337, 2015.
Hubie Chen and Stefan Mengel.
The logic of counting query
answers.
Symposium on Logic in Computer Science (LICS), Reykjavik, Iceland, pp
1–12, 2017.
Hubie Chen and Benoît Larose.
Asking the Metaquestions in
Constraint Tractability.
ACM Transactions on Computation Theory 9(3): 11:1–11:27, 2017.
Hubie Chen and Stefan Mengel.
Counting Answers to
Existential Positive Queries: A Complexity Classification.
Symposium on Principles of Database Systems (PODS), San Francisco, USA,
pp 315–326, 2016.
Hubie Chen, Matthew Valeriote, and Yuichi Yoshida.
Testing Assignments to Constraint Satisfaction Problems.
Symposium on Foundations of Computer Science (FOCS), New Brunswick, New
Jersey, USA, pp 525–534, 2016.