Publications and Presentations
On this webpage you find my
research papers,
survey papers,
PhD thesis,
Master's thesis,
slides for
some presentations
and
miscellaneous other stuff.
Research Papers

Massimo Lauria and Jakob Nordström.
Graph Colouring is Hard for Algorithms Based on
Hilbert's Nullstellensatz and Gröbner Bases.
Submitted, 2017.

Joël Alwen, Susanna F. de Rezende, Jakob Nordström, and Marc Vinyals.
Cumulative Space in BlackWhite Pebbling and Resolution.
In
Proceedings of the 8th Innovations in
Theoretical Computer Science Conference (ITCS '17),
January 2017.

Christoph Berkholz and Jakob Nordström.
Supercritical SpaceWidth Tradeoffs for Resolution.
Technical Report TR16203,
Electronic Colloquium on Computational Complexity (ECCC),
December 2016.

Susanna F. de Rezende, Jakob Nordström, and Marc Vinyals.
How Limited Interaction Hinders Real Communication
(and What It Means for Proof and Circuit Complexity).
In
Proceedings of the 57th Annual IEEE Symposium on
Foundations of Computer Science (FOCS '16),
pages 295304, October 2016.

Christoph Berkholz and Jakob Nordström.
NearOptimal Lower Bounds on Quantifier Depth and
WeisfeilerLeman Refinement Steps.
Technical Report TR16135,
Electronic Colloquium on Computational Complexity (ECCC),
August 2016.

Christoph Berkholz and Jakob Nordström.
Supercritical SpaceWidth Tradeoffs for Resolution.
In
Proceedings of the 43rd International Colloquium on
Automata, Languages and Programming (ICALP '16),
Leibniz International Proceedings in Informatics (LIPIcs),
volume 55, pages 57:157:14, July 2016.

Jan Elffers, Jan Johannsen, Massimo Lauria, Thomas Magnard,
Jakob Nordström, and Marc Vinyals.
Tradeoffs Between Time and Memory in a Tighter Model of CDCL SAT Solvers.
In
Proceedings of the 19th International Conference on
Theory and Applications of Satisfiability Testing (SAT '16),
Lecture Notes in Computer Science, volume 9710,
pages 160176, July 2016.

Christoph Berkholz and Jakob Nordström.
NearOptimal Lower Bounds on Quantifier Depth and
WeisfeilerLeman Refinement Steps.
In
Proceedings of the 31st Annual ACM/IEEE Symposium on
Logic in Computer Science (LICS '16),
July 2016.

Albert Atserias, Massimo Lauria, and Jakob Nordström.
Narrow Proofs May Be Maximally Long.
In
ACM Transactions on Computational Logic,
volume 17, issue 3, article 19, May 2016.

Siu Man Chan, Massimo Lauria, Jakob Nordström, and Marc Vinyals.
Hardness of Approximation in PSPACE and Separation
Results for Pebble Games (Extended Abstract).
In
Proceedings of the 56th Annual IEEE Symposium on
Foundations of Computer Science (FOCS '15),
pages 466485,
October 2015.

Yuval Filmus, Massimo Lauria, Jakob Nordström, Noga RonZewi, and Neil Thapen.
Space Complexity in Polynomial Calculus.
SIAM Journal on Computing,
volume 44, issue 4, pages 11191153, August 2015.

Yuval Filmus, Massimo Lauria, Mladen Mikša, Jakob Nordström, and Marc Vinyals.
From Small Space to Small Width in Resolution.
ACM Transactions on Computational Logic,
volume 16, issue 4, article 28, July 2015.

Massimo Lauria and Jakob Nordström.
Tight SizeDegree Bounds for SumsofSquares Proofs.
In
Proceedings of the 30th Annual
Computational Complexity Conference (CCC '15),
Leibniz International Proceedings in Informatics (LIPIcs),
volume 33, pages 448466,
June 2015.

Mladen Mikša and Jakob Nordström.
A Generalized Method for Proving
Polynomial Calculus Degree Lower Bounds.
In
Proceedings of the 30th Annual
Computational Complexity Conference (CCC '15),
Leibniz International Proceedings in Informatics (LIPIcs),
volume 33, pages 467487,
June 2015.

Mladen Mikša and Jakob Nordström.
A Generalized Method for Proving
Polynomial Calculus Degree Lower Bounds.
Technical Report TR15078,
Electronic Colloquium on Computational Complexity (ECCC),
May 2015.

Massimo Lauria and Jakob Nordström.
Tight SizeDegree Bounds for
SumsofSquares Proofs.
Technical Report TR15053,
Electronic Colloquium on Computational Complexity (ECCC),
April 2015.

Mladen Mikša and Jakob Nordström.
Long Proofs of (Seemingly) Simple Formulas.
In
Proceedings of the 17th International Conference on
Theory and Applications of Satisfiability Testing (SAT '14),
Lecture Notes in Computer Science, volume 8561,
pages 121137, July 2014.

Albert Atserias, Massimo Lauria, and Jakob Nordström.
Narrow Proofs May Be Maximally Long (Extended Abstract).
In
Proceedings of the 29th Annual IEEE Conference on Computational Complexity (CCC '14),
pages 286297, June 2014.

Yuval Filmus, Massimo Lauria, Mladen Mikša, Jakob Nordström, and Marc Vinyals.
From Small Space to Small Width in Resolution.
In
Proceedings of the 31st Symposium on Theoretical Aspects of Computer Science
(STACS '14),
pages 300311, March 2014.

Yuval Filmus, Massimo Lauria, Mladen Mikša, Jakob Nordström, and Marc Vinyals.
Towards an Understanding of Polynomial Calculus: New Separations and
Lower Bounds (Extended Abstract).
In
Proceedings of the 40th International Colloquium on
Automata, Languages and Programming (ICALP '13),
Lecture Notes in Computer Science, volume 7965,
pages 437448, July 2013.

Chris Beck, Jakob Nordström, and Bangsheng Tang.
Some Tradeoff Results for Polynomial Calculus (Extended Abstract).
In
Proceedings of the 45th Annual ACM Symposium on Theory of Computing (STOC '13),
pages 813822,
June 2013.

Jakob Nordström and Johan Håstad.
Towards an Optimal Separation of Space and Length in Resolution.
Theory of Computing,
volume 9, article 14, pages 471557, May 2013.

Matti Järvisalo, Arie Matsliah, Jakob Nordström, and Stanislav Živný.
Relating Proof Complexity Measures and Practical Hardness of SAT.
In
Proceedings of the 18th International Conference on
Principles and Practice of Constraint Programming (CP '12),
Lecture Notes in Computer Science,
volume 7514, pages 316331, October 2012.

Yuval Filmus, Massimo Lauria, Jakob Nordström, Neil Thapen, and Noga RonZewi.
Space Complexity in Polynomial Calculus (Extended Abstract).
In
Proceedings of the 27th Annual IEEE Conference on Computational Complexity (CCC '12),
pages 334344, June 2012.

Trinh Huynh and Jakob Nordström.
On the Virtue of Succinct Proofs:
Amplifying Communication Complexity Hardness to
TimeSpace Tradeoffs in Proof Complexity (Extended Abstract).
In
Proceedings of the 44th Annual ACM Symposium on Theory of Computing (STOC '12),
pages 233248, May 2012.

Jakob Nordström.
On the Relative Strength of Pebbling and Resolution.
ACM Transactions on Computational Logic,
volume 13, issue 2, article 16, April 2012.

Arnab Bhattacharyya, Elena Grigorescu, Jakob Nordström, and Ning Xie.
On the Semantics of Local Characterizations for LinearInvariant Properties.
Manuscript, 2011.

Jakob Nordström and Alexander Razborov.
On Minimal Unsatisfiability and
TimeSpace Tradeoffs for kDNF Resolution.
In
Proceedings of the 38th International Colloquium on
Automata, Languages and Programming (ICALP '11),
Lecture Notes in Computer Science,
volume 6755, pages 642653, July 2011.

Eli BenSasson and Jakob Nordström.
Understanding Space in Proof Complexity: Separations and Tradeoffs via Substitutions (Extended Abstract).
In
Proceedings of the 2nd Symposium on Innovations in Computer Science (ICS '11),
pages 401416, January 2011.

Eli BenSasson and Jakob Nordström.
Understanding Space in Proof Complexity: Separations and Tradeoffs via Substitutions.
Technical Report TR10125,
Electronic Colloquium on Computational Complexity (ECCC),
August 2010.
This is a merged and updated version of the two ECCC technical reports
TR09034
and
TR09047,
which two papers it subsumes.

Jakob Nordström.
On the Relative Strength of Pebbling and Resolution (Extended Abstract).
In
Proceedings of the 25th Annual IEEE Conference on
Computational Complexity (CCC '10),
pages 151162, June 2010.

Jakob Nordström.
A Simplified Way of Proving Tradeoff Results for Resolution.
Information Processing Letters,
volume 109, number 18, pages 10301035, August 2009.

Jakob Nordström.
Narrow Proofs May Be Spacious: Separating Space and Width in Resolution.
SIAM Journal on Computing,
volume 39, issue 1, pages 59121, May 2009.
(Special issue on STOC '06.)

Eli BenSasson and Jakob Nordström.
Short Proofs May Be Spacious: An Optimal Separation of Space and Length in Resolution.
Technical Report TR09002,
Electronic Colloquium on Computational Complexity (ECCC),
January 2009.

Eli BenSasson and Jakob Nordström.
Short Proofs May Be Spacious: An Optimal Separation of Space and Length in Resolution.
In
Proceedings of the 49th Annual IEEE Symposium on
Foundations of Computer Science (FOCS '08),
pages 709718,
October 2008.

Jakob Nordström and Johan Håstad.
Towards an Optimal Separation of Space and Length in Resolution (Extended Abstract).
In
Proceedings of the 40th Annual ACM Symposium on Theory of Computing (STOC '08),
pages 701710,
May 2008.

Jakob Nordström.
Narrow Proofs May Be Spacious: Separating Space and Width in Resolution (Extended Abstract).
In
Proceedings of the 38th Annual ACM Symposium on Theory of Computing (STOC '06),
pages 507516,
May 2006.
Cowinner of the Danny Lewin Best Student Paper Award.
Survey Papers

Jakob Nordström.
New Wine into Old Wineskins: A Survey of Some
Pebbling Classics with Supplemental Results.
Manuscript in preparation.
To appear in
Foundations and Trends in Theoretical Computer Science.
Current draft version available for download—comments are welcome.

Jakob Nordström.
On the Interplay Between Proof Complexity and SAT Solving.
ACM SIGLOG News,
volume 2, number 3, pages 1944, July 2015.
(Lightly edited version with some typos fixed.)

Jakob Nordström.
A (Biased) Proof Complexity Survey for SAT Practitioners.
In
Proceedings of the 17th International Conference on
Theory and Applications of Satisfiability Testing (SAT '14),
Lecture Notes in Computer Science, volume 8561,
pages 16, July 2014.

Jakob Nordström.
Pebble Games, Proof Complexity, and TimeSpace Tradeoffs.
Logical Methods in Computer Science,
volume 9, issue 3, article 15, September 2013.
PhD Thesis
Jakob Nordström.
Short Proofs May Be Spacious: Understanding Space in Resolution.
PhD thesis,
Royal Institute of Technology,
Stockholm, Sweden, May 2008.
Received the Ackermann Award 2009
for outstanding dissertations in
Logic in Computer Science from the
European Association for Computer Science Logic.
Master's Thesis
Jakob Nordström.
Stålmarck's Method Versus Resolution: A Comparative Theoretical Study.
Master's thesis TRITANAE0184,
Stockholm University,
Stockholm, Sweden,
2001.
Some Presentations

A Generalized Method for Resolution and Polynomial Calculus Lower Bounds.
Talk given at the Dagstuhl seminar
Computational Complexity of Discrete Problems,
March 2017.

Understanding ConflictDriven SAT Solving
Through the Lens of Proof Complexity.
Survey talk given at the workshop
Theoretical Foundations of SAT Solving
at the Fields Institute in Toronto, Canada,
August 2016,
and at IIT Bombay in Mumbai, India, February 2017.

A Generalized Method for Proving Polynomial Calculus Degree Lower Bounds.
Talk given at the workshop on proof complexity during the
Special Semester Program on Complexity Theory
in St. Petersburg, Russia, May 2016,
and at the Tata Institute of Fundamental Research, Mumbai, India,
February 2017.

Supercritical SpaceWidth Tradeoffs for Resolution.
Talk given at the Dagstuhl seminar
SAT and Interactions,
September 2016,
and at Rutgers University, New Jersey, USA,
October 2016.

Tradeoffs Between Time and Memory in a
Tighter Model of CDCL SAT Solvers.
Brief talk given at
SAT '16
in Bordeaux, France, July 2016.

Seeking Practical CDCL Insights from Theoretical SAT Benchmarks.
Brief talk given at the
7th Pragmatics of SAT Workshop
in Bordeaux, France, July 2016.

On the Interplay Between Proof Complexity and SAT Solving.
Tutorialstyle talk
given at the
International Summer School on Satisfiability, Satisfiability
Modulo Theories, and Automated Reasoning
in Lisbon, Portugal, June 2016.

How Limited Interaction Hinders Real Communication
(and What It Means for Proof and Circuit Complexity).
Brief talk given at the
CCC 2016 Satellite Kyoto Workshop
in Kyoto, Japan, June 2016.

How Limited Interaction Hinders Real Communication
(and What It Means for Proof and Circuit Complexity).
Talk given at the
Workshop on Algorithms in Communication Complexity, Property Testing
and Combinatorics
at the Skolkovo Institute of Science and Technology,
in Moscow, Russia, April 2016.

On the Interplay Between Proof Complexity and SAT Solving.
Long survey talk given at the
National Research University Higher School of Economics
in Moscow, Russia, April 2016.

A Generalized Method for Proving Polynomial Calculus Degree Lower Bounds.
Talk given at the program
Semidefinite and Matrix Methods for Optimization and Communication
at the Institute for Mathematical Sciences in Singapore, February 2016.

A Survey of Proof Complexity from a SAT Solving Perspective.
Talk given at Uppsala University, November 2015.

I skärningspunkten mellan beviskomplexitet och SATlösning.
Docent (habilitation) lecture given at
KTH Royal Institute of Technology, November 2015.

A (Biased) Proof Complexity Survey for SAT Practitioners.
Talk given at Université d'Artois in Lens, France,
February 2015.

Exploring Connections Between Proof Complexity
and Practical Hardness of SAT.
Talk given at Université d'Artois in Lens, France,
February 2015.

TimeSpace Tradeoffs in Proof Complexity (and SAT Solving?).
Talk given at the workshop
Algorithms, Complexity and Machine Learning:
A Tribute to Kurt Mehlhorn
at Chalmers University of Technology, Göteborg, October 2014.

A (Biased) Proof Complexity Survey for SAT Practitioners.
Invited talk given at SAT '14
in Vienna, Austria, July 2014.

A (Biased) Survey of Space Complexity and
TimeSpace Tradeoffs in Proof Complexity.
Invited talk given at the proof complexity workshop at
FLoC '14
in Vienna, Austria, July 2014.

Narrow Proofs May Be Maximally Long.
Talk given at the University of Chicago, May 2014.

MiniTutorial on Weak Proof Systems and Connections to SAT Solving.
Talk given at the workshop
Theoretical Foundations of Applied SAT Solving
at the Banff International Research Station in Canada, January 2014.
(Also available in
video
from BIRS.)

Relating Proof Complexity Measures and Practical Hardness of SAT.
Talk given at the
First Symposium on Structure in Hard Combinatorial Problems
in Vienna, Austria, May 2013.

Rediscovering the Joys of Pebbling.
Talk given in the KTH Theory reading group,
April 2013.

Relating Proof Complexity Measures and Practical Hardness of SAT.
Talk given at the Dagstuhl seminar
SAT Interactions,
November 2012,
and at the University of Toronto, January 2013.

Relating Proof Complexity Measures and Practical Hardness of SAT.
Brief overview talk given at
CP '12, October 2012.

On the Virtue of Succinct Proofs:
Amplifying Communication Complexity Hardness to
TimeSpace Tradeoffs in Proof Complexity.
Talk given at the
Limits of Theorem Proving workshop in Rome, Italy, September 2012,
and (slightly modified) in the KTH Theory reading group, October 2012,
and at the Tata Institute of Fundamental Research in Mumbai, India, March 2013.

On the Virtue of Succinct Proofs:
Amplifying Communication Complexity Hardness to
TimeSpace Tradeoffs in Proof Complexity.
Brief overview talk given at
STOC '12, May 2012.

Understanding the Hardness of Proving Formulas in Propositional Logic.
Updated version of a
survey talk about SAT solving, proof complexity, and timespace tradeoffs in resolution and other proof systems
given at Stockholm University,
November 2011.

On Minimal Unsatisfiability and TimeSpace Tradeoffs for kDNF Resolution.
Brief talk given at
ICALP '11,
July 2011.

On Proof Complexity Lower Bounds and Possible Connections to SAT Solving.
Brief talk given at the
Synergies in Lower Bounds
workshop at Aarhus University, Denmark,
JuneJuly 2011,
and (slightly modified)
at the Oberwolfach workshop
Mathematical Logic: Proof Theory, Constructive Mathematics,
November 2011.

On the Semantics of Local Characterizations
for LinearInvariant Properties.
Brief talk given at the Dagstuhl seminar on
Computational Complexity of Discrete Problems,
March 2011.

On the Semantics of Local Characterizations
for LinearInvariant Properties.
Talk given
in the KTH Theory Group seminar series, November 2010,
and (slightly modified) at the
Technion – Israel Institute of Technology in Haifa, Israel,
December 2010.

Understanding the Hardness of Proving Formulas in Propositional Logic.
Survey talk about SAT solving, proof complexity, and resolution timespace tradeoffs
given at Lund University,
October 2010
and in a slightly expanded and more technical version at the
Complexity and Finite Models (CMF 2011) workshop
in Paris, June 2011.

Understanding Space in Proof Complexity: Separations and Tradeoffs via Substitutions.
Brief overview talk, with a slightly more applied angle, given at the
Propositional Proof Complexity: Theory and Practice workshop at
FLoC '10,
July 2010,
and (in a slightly shorter version) at
ICS '11,
January 2011.

Understanding Space in Proof Complexity: Separations and Tradeoffs via Substitutions.
Yet another survey talk
about my PhD thesis and some subsequent work,
but with a slightly more applied angle, given at the
International Workshop on Tractability
at Microsoft Research Cambridge, UK, July 2010.

On the Relative Strength of Pebbling and Resolution.
Brief overview talk given at
CCC '10,
June 2010,
and in the KTH Theory Group seminar series, October 2010.
(Also available in
video
from Harvard.)

Understanding Space in Proof Complexity: Separations and Tradeoffs via Substitutions.
Survey talk about my PhD thesis and some subsequent work given
in the CSAIL Theory of Computation Colloquium series,
April 2010 and then (slightly modified) at the University of Toronto and
at KTH, May 2010.
Yet another modified and updated version of this talk, but with the title
Understanding the Hardness of Proving Formulas in Propositional Logic,
was given at the proof complexity workshop
at the Banff International Research Station in Canada, October 2011.

Understanding Space in Proof Complexity.
Survey talk about my PhD thesis and some subsequent work given
at the Ackermann Award ceremony at
CSL '09,
September 2009.

Understanding Space in Proof Complexity: Separations and Tradeoffs via Substitutions.
Brief overwiev talk
about the ECCC reports
TR09034
and
TR09047
given at the Barriers in Computational Complexity workshop in Princeton, USA, August 2009.
(Also available in video
from the Center for Computational Intractability.)

Guest lectures about proof complexity in the MIT Advanced Complexity Theory course,
April 2009.
Handwritten
lecture notes
and (mostly accurate)
scribed notes for lecture 1
and
lecture 2.

Understanding Space in Resolution: Optimal Lower Bounds and Exponential Tradeoffs.
Talk
about our
FOCS '08 paper
and
ECCC report TR09034
given at the Dagstuhl seminar on
Computational Complexity of Discrete Problems,
September 2008,
and (slightly modified) in the MIT CSAIL Algorithms and Complexity Seminar series, October 2008.

Short Proofs May Be Spacious: An Optimal Separation of Space and Length in Resolution.
Brief overview talk given at
FOCS '08,
October 2008.

Towards an Optimal Separation of Space and Length in Resolution.
Brief overview talk given at
STOC '08
and at the NORDITA
Physics of distributed information systems (PhysDIS)
workshop in Stockholm, May 2008.

Towards an Optimal Separation of Space and Length in Resolution.
Talk given at
the Technion – Israel Institute of Technology in Haifa
and
the Weizmann Institute of Science in Rehovot,
Israel, March 2008.
Some technical slides in the appendix.

Narrow Proofs May Be Spacious: Separating Space and Width in Resolution.
Very detailed technical talk in the KTH Theory Group seminar series, June 2006.

Narrow Proofs May Be Spacious: Separating Space and Width in Resolution.
Brief overview talk given at
STOC '06,
May 2006.

Narrow Proofs May Be Spacious: Separating Space and Width in Resolution.
Somewhat detailed talk given at
the Dagstuhl seminar on
Complexity of Boolean Functions in March 2006
and (slightly modified) at the Isaac Newton Institute Workshop
New Directions in Proof Complexity in Cambridge, UK, in April 2006.
(Also available in
audio
from the Isaac Newton Institute)

Short Proofs Are Narrow (Well, Sort of), But Are They Tight?
Fairly technical talk about width and space in resolution
in the KTH Theory Group PhD student seminar series, April 2006.

Stålmarck's Method versus Resolution: A Comparative Theoretical Study.
Rather informal overview of the subject matter of my Master's thesis, November 2001.

Stålmarck's Method versus Resolution: A Comparative Theoretical Study.
More technical account of the most important results in my Master's thesis, November 2001.
Miscellaneous

[in Swedish] Jakob Nordström.
Kort populärvetenskaplig
sammanfattning av min doktorsavhandling.
Försök till kort (knappt 2 sidor)
sammanfattning av ungefär vad min doktorsavhandling handlar om
och varför man är intresserad av att undersöka
den typen av frågor,
september 2009.

[in Swedish] Jakob Nordström.
Om formler, bevis och andra komplexa saker.
Något förkortad och översatt version av inledningskapitlet
i min doktorsavhandling
Short Proofs May Be Spacious:
Understanding Space in Resolution,
maj 2008.
