Papers on Relations among Complexity Classes


Parting Thoughts and Parting Shots (Read On for Details on How to Win Valuable Prizes!) ,
Guest Piece for the Complexity Theory Column, edited by Lane Hemaspaandra, SIGACT NEWS 54 March, 2023, pp. 63--81.

Robustness for Space-Bounded Statistical Zero Knowledge ,
(with Jacob Gray, Saachi Mutreja, Harsha Tirumala, and Pengxiang Wang) ECCC Report TR22-138, 2022. Submitted for publication.

Kolmogorov Complexity Characterizes Statistical Zero Knowledge ,
(with Shuichi Hirahara and Harsha Tirumala), Proc. 14th Innovations in Theoretical Computer Science (ITCS'23) 2023, Leibniz International Proceedings in Informatics (LIPIcs) 251, pp. 3:1--3:19. There is a video of a Princeton Theory Lunch talk on this paper (Sept. 30, 2022). It's a blackboard talk, and the writing on the blackboard is hard to read in the video.

On the Complexity of Algebraic Numbers, and the Bit-Complexity of Straight-Line Programs ,
(with Nikhil Balaji, Samir Datta, and Rameshwar Pratap) Computability (The Journal of the Association Computability in Europe) 12 (2023) pp. 145-173. Some of this work appeared in preliminary form as Low-Depth Uniform Threshold Circuits and the Bit-Complexity of Straight Line Programs,
(with Nikhil Balaji and Samir Datta), in Proc. 39th International Symposium on Mathematical Foundations of Computer Science (MFCS '14), Lecture Notes in Computer Science 8635, pp. 13-24, 2014.

Depth-First Search in Directed Planar Graphs, Revisited,
(with Archit Chauhan and Samir Datta), Acta Informatica, 59 (2022) 289-319; special issue for Klaus-Jörn Lange. (An earlier version appeared in preliminary form in 46th International Symposium on Mathematical Foundations of Computer Science (MFCS '21), Leibniz International Proceedings in Informatics (LIPIcs) 202, pp. 7:1 -- 7:22. See also ECCC Report TR20-074, 2020.

One-way Functions and a Conditional Variant of MKTP ,
(with Mahdi Cheraghchi, Dimitrios Myrisiotis, Harsha Tirumala, and Ilya Volkovich ), Proc. 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs) 213, pp. 7:1--7:19. See also ECCC Report TR21-009, 2021.

Cryptographic Hardness under Projections for Time-Bounded Kolmogorov Complexity ,
(with John Gouwar, Shuichi Hirahara, and Caleb Robelle ), Theoretical Computer Science 940(B), 2023, 206-224; special issue for Péter Gács. (An earlier version appeared in preliminary form in Proc. 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs) 212, pp. 54:1--54:17.) See also ECCC Report TR21-010, 2021.

A Note on Hardness under Projections for Graph Isomorphism and Time-Bounded Kolmogorov Complexity,
(with Azucena Garvìa Bosshard and Amulya Musipatla), ECCC Report TR20-158, 2020.

Syntactic Separation of Subset Satisfiability Problems,
(with Martin Farach-Colton and Meng-Tsung Tsai), Proc. 22nd International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX 2019), Leibniz International Proceedings in Informatics (LIPIcs) 145, pp. 16:1--16:23.

New Insights on the (Non-)Hardness of Circuit Minimization and Related Problems,
(with Shuichi Hirahara), ACM Transactions on Computation Theory (ToCT), 11,4 (2019) 27:1-27:27. An earlier version appeared in Proc. 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS '17), Leibniz International Proceedings in Informatics (LIPIcs) 83, pp. 54:1--54:14.

Better Complexity Bounds for Cost Register Automata,
(with Andreas Krebs and Pierre McKenzie ), Theory of Computing Systems 63(3), 2019, 367-385. An earlier version appeared in Proc. 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS '17), Leibniz International Proceedings in Informatics (LIPIcs) 83, pp. 24:1--24:14.

Minimum Circuit Size, Graph Isomorphism and Related Problems,
(with Joshua A. Grochow, Dieter van Melkebeek, Cristopher Moore, and Andrew Morgan), SIAM J. Comp., Vol. 47(4), 2018, 1339-1372. An earlier version appeared in Proc. 9th Innovations in Theoretical Computer Science (ITCS '18), Leibniz International Proceedings in Informatics (LIPIcs) 94, pp. 20:1--20:20. (See the Presentation at the Simons Institute.)

A note on Graph Automorphism and Smart Reductions,
(with Joshua A. Grochow, Dieter van Melkebeek, Cristopher Moore, and Andrew Morgan), ECCC Technical Report TR15-162, 2018.

Zero Knowledge and Circuit Minimization,
(with Bireswar Das), Information and Computation, 256 (2017) 2-8. (Special issue on MFCS 2014.) An earlier version appeared in Proc. 39th International Symposium on Mathematical Foundations of Computer Science (MFCS '14), Lecture Notes in Computer Science 8635, pp. 25-32, 2014. (Presentation available on-line.)

The Minimum Oracle Circuit Size Problem,
(with Dhiraj Holden and Valentine Kabanets), Computational Complexity 26 (2017) 469-496. Springer provides free read-only access to this publication. An earlier version appeared in Proc. 32nd International Symposium on Theoretical Aspects of Computer Science (STACS), 2015, pp. 21-33.

Dual VP Classes,
(with Anna Gál and Ian Mertz), Computational Complexity 26 (2017) 583-625. Springer provides free read-only access to this publication. An earlier version appeared in Proc. 40th International Symposium on Mathematical Foundations of Computer Science (MFCS '15), Lecture Notes in Computer Science 9235, pp. 14-25, 2015. (Presentation available on-line.) (A companion paper is Arithmetic Circuit Classes over Zm (with Asa Goodwillie), ECCC Technical Report TR15-145, 2015.)

Investigations Concerning the Structure of Complete Sets,
in Perspectives in Computational Complexity: The Somenath Biswas Anniversary Volume, Progress in Computer Science and Applied Logic vol. 26, 2014, pp. 23-35.

Reductions to the set of random strings: The resource-bounded case,
(with Harry Buhrman, Luke Friedman, Bruno Loff), Logical Methods in Computer Science 10 (3:5) 2014, pp. 1-18. (Special issue on The Turing Centenary Conference: CiE 2012). An earlier version appeared in Proc. 37th International Symposium on Mathematical Foundations of Computer Science (MFCS '12), 2012, Lecture Notes in Computer Science 7464, pp. 88-99, 2012.

Width-parameterized SAT: time-space tradeoffs,
(with Shiteng Chen, Tiancheng Lou, Periklis Papakonstantinou, and Bangsheng Tang),
Theory of Computing 10(12), 2014, 297-339.

Symmetry Coincides with Nondeterminism for Time-Bounded Auxiliary Pushdown Automata,
(with Klaus-Jörn Lange). Theory of Computing 10(8), 2014, 199-215. An earlier version appeared in Proc. 25th Annual IEEE Conference on Computational Complexity, 2010, pp. 172-180.

Kolmogorov Complexity, Circuits, and the Strength of Formal Theories of Arithmetic,
(with George Davie, Luke Friedman, Samuel B. Hopkins, and Iddo Tzameret),
Chicago Journal of Theoretical Computer Science, 2013, article 5.

Limits on the Computational Power of Random Strings,
(with Luke Friedman and William Gasarch), Information and Computation, 222, 2013, 80-92. (Special issue on ICALP 2011). An earlier version appeared in Proc. 38th International Colloquium on Automata, Languages, and Programming (ICALP), 2011, Lecture Notes in Computer Science 6755, pp. 293-304. (A companion paper is Exposition of the Muchnik-Positselsky Construction of a Prefix Free Entropy Function that is not Complete under Truth-Table Reductions (with Luke Friedman and William Gasarch), ECCC Technical Report TR10-138, 2010.

Curiouser and Curiouser: The Link between Incompressibility and Complexity,
in Proc. Computability in Europe: (CiE 2012), Lecture Notes in Computer Science 7318, pp. 11-16, 2012.

Uniform Derandomization from Pathetic Lower Bounds,
(with V Arvind, Rahul Santhanam and Fengming Wang), . Philosophical Transactions of the Royal Society, Series A, 370, 2012, 3512-3535. Special issue on the Turing Centenary. See also the Comment on ECCC. An earlier version appeared in Proc. 14th International Workshop on Randomization and Computation (RANDOM/APPROX 2010), Lecture Notes in Computer Science 6302, pp. 380-393, 2010.

Avoiding Simplicity is Complex, (with Holger Spakowski),
Theory of Computing Systems 51, 2012, 282-296. Special issue on CiE 2010. An earlier version appeared in Proc. Computability in Europe: Programs, Proofs, Processes (CiE 2010), Lecture Notes in Computer Science 6158, pp. 1-10, 2010.

The Pervasive Reach of Resource-Bounded Kolmogorov Complexity in Computational Complexity Theory,
(with Michal Koucký, Detlef Ronneburger, and Sambuddha Roy), Journal of Computer and System Sciences 77, 2011, 14-40. (Some of this material appeared in preliminary form in the paper Derandomization and Distinguishing Complexity, Proc. 18th Annual IEEE Conference on Computational Complexity, 2003, pp. 209-220.)

Amplifying Lower Bounds by Means of Self-Reducibility,
(with Michal Koucký), Journal of the ACM 57,3 (2010) 14:1 - 14:36. An earlier version appeared in Proc. 23rd Annual IEEE Conference on Computational Complexity, 2008, pp. 31--40.

On the Complexity of Numerical Analysis,
(with Peter Bürgisser, Johan Kjeldgaard-Pedersen and Peter Bro Miltersen), SIAM J. Comp. Vol. 38, 2009, 1987-2006. An earlier version appeared in Proc. 21st Annual IEEE Conference on Computational Complexity, 2006, pp. 331--339.

Time-Space Tradeoffs in the Counting Hierarchy,
(with Michal Koucký, Detlef Ronneburger, Sambuddha Roy, and V. Vinay), in Proc. 16th Annual IEEE Conference on Computational Complexity, 2001, pp. 295-302.

Making nondeterminism unambiguous,
(with Klaus Reinhardt), SIAM J. Comp. Vol. 29, 2000, 1118-1131. An earlier version appeared in FOCS 1997, pp. 244-253.

RUSPACE(log n) is contained in DSPACE(log^2 n/loglog n),
(with Klaus-Jörn Lange). Theory of Computing Systems, Vol. 31, 1998, pp. 539-550. Special issue devoted to the 7th Annual International Symposium on Algorithms and Computation ( ISAAC '96).

Limitations of the Upward Separation Technique,
Mathematical Systems Theory 24 (1991) 53-67. An earlier version appeared in Proc. 16th International Colloquium on Automata, Languages, and Programming (ICALP 1989), Lecture Notes in Computer Science 372, pp. 18-30.

Oracles vs Proof techniques that do not relativize,
in Proc. SIGAL International Symposium on Algorithms, 1990, Lecture Notes in Computer Science 450, pp. 39-52.

Downward translations of equality
(with Chris Wilson), Theoretical Computer Science Vol. 75, 1990, pp. 335-346.