@article(ajtaifagin1990, author = {Miklos Ajtai and Ronald Fagin}, year = {1990}, title = {Reachability is harder for directed than for undirected finite graphs}, journal = {Journal of Symbolic Logic}, volume = {55}, number = {1}, pages = {113–150}, doi = {10.2307/2274958}, ) @article(ARORA199797, author = {Sanjeev Arora and Ronald Fagin}, year = {1997}, title = {On winning strategies in {Ehrenfeucht--Fra\"{i}ss\'{e}} games}, journal = {Theoretical Computer Science}, volume = {174}, number = {1}, pages = {97--121}, doi = {10.1016/S0304-3975(96)00015-1}, ) @article(ArvindKurur, author = {V. Arvind and Piyush P. Kurur}, year = {2006}, title = {Graph Isomorphism is in {SPP}}, journal = {Information and Computation}, volume = {204}, number = {5}, pages = {835--852}, doi = {10.1016/j.ic.2006.02.002}, ) @inproceedings(BabaiGraphIso, author = {L\'{a}szl\'{o} Babai}, year = {2016}, title = {Graph isomorphism in quasipolynomial time [extended abstract]}, booktitle = {S{TOC}'16---{P}roceedings of the 48th {A}nnual {ACM} {SIGACT} {S}ymposium on {T}heory of {C}omputing}, publisher = {ACM, New York}, pages = {684--697}, doi = {10.1145/2897518.2897542}, note = {Preprint of full version at \href{https://arxiv.org/abs/1512.03547v2}{arXiv:1512.03547v2 [cs.DS]}}, ) @inproceedings(Babai1999GroupsSA, author = {L{\'a}szl{\'o} Babai and Robert Beals}, year = {1999}, title = {A polynomial-time theory of black box groups {I}}, booktitle = {Groups {S}t {A}ndrews 1997 in {B}ath, {I}}, doi = {10.1017/CBO9781107360228.004}, ) @inproceedings(BabaiBealsSeress, author = {L\'{a}szl\'{o} Babai and Robert Beals and \'{A}kos Seress}, year = {2009}, title = {Polynomial-Time Theory of Matrix Groups}, booktitle = {Proceedings of the Forty-First Annual ACM Symposium on Theory of Computing}, series = {STOC '09}, publisher = {Association for Computing Machinery}, pages = {55–64}, doi = {10.1145/1536414.1536425}, ) @inproceedings(BCGQ, author = {L{\'a}szl{\'o} Babai and Paolo Codenotti and Joshua A. Grochow and Youming Qiao}, year = {2011}, title = {Code equivalence and group isomorphism}, booktitle = {Proceedings of the {Twenty-Second} {Annual} {ACM--SIAM} {Symposium} on {Discrete} {Algorithms} ({SODA11})}, publisher = {SIAM}, address = {Philadelphia, PA}, pages = {1395--1408}, doi = {10.1137/1.9781611973082.107}, ) @inproceedings(BCQ, author = {L{\'a}szl{\'o} Babai and Paolo Codenotti and Youming Qiao}, year = {2012}, title = {Polynomial-Time Isomorphism Test for Groups with No Abelian Normal Subgroups - (Extended Abstract)}, booktitle = {International Colloquium on Automata, Languages, and Programming (ICALP)}, pages = {51--62}, doi = {10.1007/978-3-642-31594-7_5}, ) @inproceedings(BQ, author = {L\'aszl\'o Babai and Youming Qiao}, year = {2012}, title = {Polynomial-time Isomorphism Test for Groups with {Abelian} {Sylow} Towers}, booktitle = {29th STACS}, publisher = {Springer LNCS 6651}, pages = {453 -- 464}, doi = {10.4230/LIPIcs.STACS.2012.453}, ) @article(BE99, author = {Hans Ulrich Besche and Bettina Eick}, year = {1999}, title = {Construction of finite groups}, journal = {J. Symb. Comput.}, volume = {27}, number = {4}, pages = {387--404}, doi = {10.1006/jsco.1998.0258}, ) @article(BEO02, author = {Hans Ulrich Besche and Bettina Eick and E.A. O'Brien}, year = {2002}, title = {A Millennium Project: Constructing Small Groups}, journal = {Intern. J. Alg. and Comput}, volume = {12}, pages = {623--644}, doi = {10.1142/S0218196702001115}, ) @inproceedings(WLGroups, author = {Jendrik Brachter and Pascal Schweitzer}, year = {2020}, title = {On the {Weisfeiler--Leman} Dimension of Finite Groups}, editor = {Holger Hermanns and Lijun Zhang and Naoki Kobayashi and Dale Miller}, booktitle = {{LICS} '20: 35th Annual {ACM/IEEE} Symposium on Logic in Computer Science, Saarbr{\"{u}}cken, Germany, July 8-11, 2020}, publisher = {{ACM}}, pages = {287--300}, doi = {10.1145/3373718.3394786}, ) @misc(BrachterSchweitzerWLLibrary, author = {Jendrik Brachter and Pascal Schweitzer}, year = {2021}, title = {A Systematic Study of Isomorphism Invariants of Finite Groups via the {Weisfeiler--Leman} Dimension}, howpublished = {\href{https://arxiv.org/abs/2111.11908}{arXiv:2111.11908 [math.GR]}}, ) @misc(BGLQW, author = {Peter A. Brooksbank and Joshua A. Grochow and Yinan Li and Youming Qiao and James B. Wilson}, year = {2019}, title = {Incorporating {Weisfeiler}--{Leman} into algorithms for group isomorphism}, howpublished = {\href{https://arxiv.org/abs/1905.02518}{arXiv:1905.02518 [cs.CC]}}, ) @article(BMWGenus2, author = {Peter A. Brooksbank and Joshua Maglione and James B. Wilson}, year = {2017}, title = {A fast isomorphism test for groups whose {Lie} algebra has genus 2}, journal = {Journal of Algebra}, volume = {473}, pages = {545--590}, doi = {10.1016/j.jalgebra.2016.12.007}, ) @inproceedings(BuhrmanHomer, author = {Harry Buhrman and Steven Homer}, year = {1992}, title = {Superpolynomial Circuits, Almost Sparse Oracles and the Exponential Hierarchy}, editor = {R. K. Shyamasundar}, booktitle = {Foundations of Software Technology and Theoretical Computer Science, 12th Conference, New Delhi, India, December 18-20, 1992, Proceedings}, series = {Lecture Notes in Computer Science}, volume = {652}, publisher = {Springer}, pages = {116--127}, doi = {10.1007/3-540-56287-7\_99}, ) @article(CFI, author = {Jin-Yi Cai and Martin F\"{u}rer and Neil Immerman}, year = {1992}, title = {An optimal lower bound on the number of variables for graph identification}, journal = {Combinatorica}, volume = {12}, number = {4}, pages = {389--410}, doi = {10.1007/BF01305232}, note = {Originally appeared in SFCS '89}, ) @article(CH03, author = {John J. Cannon and Derek F. Holt}, year = {2003}, title = {Automorphism group computation and isomorphism testing in finite groups}, journal = {J. Symb. Comput.}, volume = {35}, pages = {241--267}, doi = {10.1016/S0747-7171(02)00133-5}, ) @article(ChattopadhyayToranWagner, author = {Arkadev Chattopadhyay and Jacobo Tor\'{a}n and Fabian Wagner}, year = {2013}, title = {Graph isomorphism is not {$\rm AC^0$}-reducible to group isomorphism}, journal = {ACM Trans. Comput. Theory}, volume = {5}, number = {4}, pages = {Art. 13, 13}, doi = {10.1145/2540088}, note = {Preliminary version appeared in FSTTCS '10; ECCC Tech. Report TR10-117}, ) @inproceedings(DasSharma, author = {Bireswar Das and Shivdutt Sharma}, year = {2019}, title = {Nearly Linear Time Isomorphism Algorithms for Some Nonabelian Group Classes}, editor = {Ren{\'e} van Bevern and Gregory Kucherov}, booktitle = {Computer Science -- Theory and Applications}, publisher = {Springer International Publishing}, address = {Cham}, pages = {80--92}, doi = {10.1007/s00224-020-10010-z}, ) @inproceedings(DawarHolm, author = {Anuj Dawar and Bjarki Holm}, year = {2012}, title = {Pebble Games with Algebraic Rules}, editor = {Artur Czumaj and Kurt Mehlhorn and Andrew Pitts and Roger Wattenhofer}, booktitle = {Automata, Languages, and Programming}, publisher = {Springer Berlin Heidelberg}, address = {Berlin, Heidelberg}, pages = {251--262}, doi = {10.1007/978-3-642-31585-5_25}, ) @article(DawarVagnozzi, author = {Anuj Dawar and Danny Vagnozzi}, year = {2020}, title = {Generalizations of k-dimensional Weisfeiler–Leman stabilization}, journal = {Moscow Journal of Combinatorics and Number Theory}, volume = {9}, pages = {229--252}, doi = {10.2140/moscow.2020.9.229}, ) @misc(DietrichWilson, author = {Heiko Dietrich and James B. Wilson}, year = {2022}, title = {Polynomial-time isomorphism testing for groups of most finite orders}, doi = {10.1109/FOCS52979.2021.00053}, ) @article(Ehrenfeucht, author = {A. Ehrenfeucht}, year = {1960/61}, title = {An application of games to the completeness problem for formalized theories}, journal = {Fund. Math.}, volume = {49}, pages = {129--141}, doi = {10.4064/fm-49-2-129-141}, ) @article(ELGO02, author = {Bettina Eick and Leedham-Green, C. R. and E. A. O'Brien}, year = {2002}, title = {Constructing automorphism groups of {$p$}-groups}, journal = {Comm. Algebra}, volume = {30}, number = {5}, pages = {2271--2295}, doi = {10.1081/AGB-120003468}, ) @article(GroheFlum, author = {Jörg Flum and Martin Grohe}, year = {2000}, title = {On Fixed-Point Logic with Counting}, journal = {The Journal of Symbolic Logic}, volume = {65}, number = {2}, pages = {777--787}, doi = {10.2307/2586569}, ) @article(Fraisse, author = {Fra\"{\i}ss\'{e}, Roland}, year = {1954}, title = {Sur quelques classifications des syst\`emes de relations}, journal = {Publ. Sci. Univ. Alger. S\'{e}r. A}, volume = {1}, pages = {35--182 (1955)}, ) @article(DescriptiveComplexityAbelianGroups, author = {Walid Gomaa}, year = {2010}, title = {Descriptive Complexity of Finite Abelian Groups.}, journal = {IJAC}, volume = {20}, pages = {1087--1116}, doi = {10.1142/S0218196710006047}, ) @misc(grochow2022descriptive, author = {Joshua A. Grochow and Michael Levet}, year = {2022}, title = {On the Descriptive Complexity of Groups without Abelian Normal Subgroups}, eprint = {2209.13725}, ) @misc(GrochowLevetWL, author = {Joshua A. Grochow and Michael Levet}, year = {2022}, title = {On the parallel complexity of Group Isomorphism and canonization via {Weisfeiler--Leman}}, howpublished = {\href{https://arxiv.org/abs/2112.11487}{arXiv:2112.11487 [cs.DS]}}, ) @inproceedings(GQ15, author = {Joshua A. Grochow and Youming Qiao}, year = {2015}, title = {Polynomial-Time Isomorphism Test of Groups that are Tame Extensions - (Extended Abstract)}, booktitle = {Algorithms and Computation - 26th International Symposium, {ISAAC} 2015, Nagoya, Japan, December 9-11, 2015, Proceedings}, pages = {578--589}, doi = {10.1007/978-3-662-48971-0_49}, ) @book(GroheBook, author = {Martin Grohe}, year = {2017}, title = {Descriptive complexity, canonisation, and definable graph structure theory}, series = {Lecture Notes in Logic}, volume = {47}, publisher = {Association for Symbolic Logic, Ithaca, NY; Cambridge University Press, Cambridge}, doi = {10.1017/9781139028868}, ) @inproceedings(grohe, author = {Martin Grohe}, year = {2021}, title = {The logic of graph neural networks}, booktitle = {LICS '21: Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science}, doi = {10.1109/LICS52264.2021.9470677}, note = {Preprint arXiv:2104.14624 [cs.LG]}, ) @misc(grohe2019linear, author = {Martin Grohe and Sandra Kiefer}, year = {2019}, title = {A Linear Upper Bound on the {W}eisfeiler--{L}eman Dimension of Graphs of Bounded Genus}, eprint = {1904.07216}, ) @misc(grohe2021logarithmic, author = {Martin Grohe and Sandra Kiefer}, year = {2021}, title = {Logarithmic {W}eisfeiler--{L}eman Identifies All Planar Graphs}, eprint = {2106.16218}, ) @misc(grohe2019rankwidth, author = {Martin Grohe and Daniel Neuen}, year = {2019}, title = {Canonisation and Definability for Graphs of Bounded Rank Width}, eprint = {1901.10330}, ) @article(GroheOttoLinearEquations, author = {Martin Grohe and Martin Otto}, year = {2015}, title = {Pebble Games and linear equations}, journal = {J. Symb. Log.}, volume = {80}, number = {3}, pages = {797--844}, doi = {10.1017/jsl.2015.28}, ) @inproceedings(GroheVerbitsky, author = {Martin Grohe and Oleg Verbitsky}, year = {2006}, title = {Testing Graph Isomorphism in Parallel by Playing a Game}, editor = {Michele Bugliesi and Bart Preneel and Vladimiro Sassone and Ingo Wegener}, booktitle = {Automata, Languages and Programming, 33rd International Colloquium, {ICALP} 2006, Venice, Italy, July 10-14, 2006, Proceedings, Part {I}}, series = {Lecture Notes in Computer Science}, volume = {4051}, publisher = {Springer}, pages = {3--14}, doi = {10.1007/11786986_2}, ) @article(HeQiao, author = {Xiaoyu He and Youming Qiao}, year = {2021}, title = {On the {Baer--Lov\'{a}sz--Tutte} construction of groups from graphs: {Isomorphism} types and homomorphism notions}, journal = {Eur. J. Combin.}, volume = {98}, pages = {103404}, doi = {10.1016/j.ejc.2021.103404}, ) @article(Heineken1974TheOO, author = {Hermann Heineken and Hans Liebeck}, year = {1974}, title = {The occurrence of finite groups in the automorphism group of nilpotent groups of class {$2$}}, journal = {Arch. Math. (Basel)}, volume = {25}, pages = {8--16}, doi = {10.1007/BF01238631}, ) @article(Hella1989, author = {Lauri Hella}, year = {1989}, title = {Definability hierarchies of generalized quantifiers}, journal = {Annals of Pure and Applied Logic}, volume = {43}, number = {3}, pages = {235 -- 271}, doi = {10.1016/0168-0072(89)90070-5}, ) @article(Hella1993, author = {Lauri Hella}, year = {1996}, title = {Logical Hierarchies in {PTIME}}, journal = {Information and Computation}, volume = {129}, number = {1}, pages = {1--19}, doi = {10.1006/inco.1996.0070}, ) @article(ImmermanPTime, author = {Neil Immerman}, year = {1986}, title = {Relational Queries Computable in Polynomial Time}, journal = {Inf. Control.}, volume = {68}, number = {1-3}, pages = {86--104}, doi = {10.1016/S0019-9958(86)80029-8}, ) @incollection(ImmermanLander1990, author = {Neil Immerman and Eric Lander}, year = {1990}, title = {Describing Graphs: A First-Order Approach to Graph Canonization}, editor = {Alan L. Selman}, booktitle = {Complexity Theory Retrospective: In Honor of Juris Hartmanis on the Occasion of His Sixtieth Birthday, July 5, 1988}, publisher = {Springer New York}, address = {New York, NY}, pages = {59--81}, doi = {10.1007/978-1-4612-4478-3_5}, ) @article(ETH, author = {Russell Impagliazzo and Ramamohan Paturi and Francis Zane}, year = {2001}, title = {Which Problems Have Strongly Exponential Complexity?}, journal = {Journal of Computer and System Sciences}, volume = {63}, number = {4}, pages = {512--530}, doi = {10.1006/jcss.2001.1774}, ) @article(IvanyosQ19, author = {G{\'{a}}bor Ivanyos and Youming Qiao}, year = {2019}, title = {Algorithms Based on *-Algebras, and Their Applications to Isomorphism of Polynomials with One Secret, Group Isomorphism, and Polynomial Identity Testing}, journal = {{SIAM} J. Comput.}, volume = {48}, number = {3}, pages = {926--963}, doi = {10.1137/18M1165682}, ) @article(Kavitha, author = {T. Kavitha}, year = {2007}, title = {Linear time algorithms for Abelian group isomorphism and related problems}, journal = {Journal of Computer and System Sciences}, volume = {73}, number = {6}, pages = {986 -- 996}, doi = {10.1016/j.jcss.2007.03.013}, ) @inproceedings(KayalNezhmetdinov, author = {Neeraj Kayal and Timur Nezhmetdinov}, year = {2009}, title = {Factoring Groups Efficiently}, editor = {Susanne Albers and Marchetti-Spaccamela, Alberto and Yossi Matias and Sotiris Nikoletseas and Wolfgang Thomas}, booktitle = {Automata, Languages and Programming}, publisher = {Springer Berlin Heidelberg}, address = {Berlin, Heidelberg}, pages = {585--596}, doi = {10.1007/978-3-642-02927-1_49}, ) @inproceedings(KieferMcKay, author = {Sandra Kiefer and Brendan D. McKay}, year = {2020}, title = {The Iteration Number of Colour Refinement}, editor = {Artur Czumaj and Anuj Dawar and Emanuela Merelli}, booktitle = {47th International Colloquium on Automata, Languages, and Programming, {ICALP} 2020, July 8-11, 2020, Saarbr{\"{u}}cken, Germany (Virtual Conference)}, series = {LIPIcs}, volume = {168}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum f{\"{u}}r Informatik}, pages = {73:1--73:19}, doi = {10.4230/LIPIcs.ICALP.2020.73}, ) @article(KieferPonomarenkoSchweitzer, author = {Sandra Kiefer and Ilia Ponomarenko and Pascal Schweitzer}, year = {2019}, title = {The {Weisfeiler--Leman} Dimension of Planar Graphs Is at Most 3}, journal = {J. ACM}, volume = {66}, number = {6}, doi = {10.1145/3333003}, ) @article(KieferSchweitzerSelman, author = {Sandra Kiefer and Pascal Schweitzer and Erkal Selman}, year = {2022}, title = {Graphs Identified by Logics with Counting}, journal = {{ACM} Trans. Comput. Log.}, volume = {23}, number = {1}, pages = {1:1--1:31}, doi = {10.1145/3417515}, ) @article(GILowPP, author = {Johannes K{\"{o}}bler and Uwe Sch{\"{o}}ning and Jacobo Tor{\'{a}}n}, year = {1992}, title = {Graph Isomorphism is Low for {PP}}, journal = {Comput. Complex.}, volume = {2}, pages = {301--330}, doi = {10.1007/BF01200427}, ) @article(Ladner, author = {Richard E. Ladner}, year = {1975}, title = {On the Structure of Polynomial Time Reducibility}, journal = {J. ACM}, volume = {22}, number = {1}, pages = {155–171}, doi = {10.1145/321864.321877}, ) @inproceedings(Gal09, author = {Le Gall, Fran\c{c}ois}, year = {2009}, title = {Efficient Isomorphism Testing for a Class of Group Extensions}, booktitle = {Proc. 26th STACS}, pages = {625--636}, doi = {10.4230/LIPIcs.STACS.2009.1830}, ) @misc(GR16, author = {Le Gall, Fran{\c{c}}ois and David J. Rosenbaum}, year = {2016}, title = {On the Group and Color Isomorphism Problems}, howpublished = {\href{https://arxiv.org/abs/1609.08253}{arXiv:1609.08253 [cs.CC]}}, ) @article(LW12, author = {Mark L. Lewis and James B. Wilson}, year = {2012}, title = {Isomorphism in expanding families of indistinguishable groups}, journal = {Groups - Complexity - Cryptology}, volume = {4}, number = {1}, pages = {73--110}, doi = {10.1515/gcc-2012-0008}, ) @article(Lindstrom, author = {P. Lindstrom}, year = {1966}, title = {First Order Predicate Logic with Generalized Quantifiers}, journal = {Theoria}, volume = {32}, number = {3}, pages = {186--195}, doi = {10.1111/j.1755-2567.1966.tb00600.x}, ) @article(Mekler, author = {Alan H. Mekler}, year = {1981}, title = {Stability of Nilpotent Groups of Class 2 and Prime Exponent}, journal = {The Journal of Symbolic Logic}, volume = {46}, number = {4}, pages = {781--788}, doi = {10.2307/2273227}, url = {http://www.jstor.org/stable/2273227}, ) @inproceedings(MillerTarjan, author = {Gary L. Miller}, year = {1978}, title = {On the {$n^{\qopname\relax o{log}n}$} Isomorphism Technique (A Preliminary Report)}, booktitle = {Proceedings of the Tenth Annual ACM Symposium on Theory of Computing}, series = {STOC '78}, publisher = {Association for Computing Machinery}, address = {New York, NY, USA}, pages = {51--58}, doi = {10.1145/800133.804331}, ) @article(Mostowski1957, author = {Andrzej Mostowski}, year = {1957}, title = {On a generalization of quantifiers}, journal = {Fundamenta Mathematicae}, volume = {44}, number = {1}, pages = {12--36}, doi = {10.4064/fm-44-1-12-36}, url = {http://eudml.org/doc/213418}, ) @article(FiniteGroupsFOL, author = {Andr\'{e} Nies and Katrin Tent}, year = {2017}, title = {Describing finite groups by short first-order sentences}, journal = {Israel J. Math.}, volume = {221}, number = {1}, pages = {85--115}, doi = {10.1007/s11856-017-1563-2}, ) @inproceedings(QST11, author = {Youming Qiao and Jayalal M. N. Sarma and Bangsheng Tang}, year = {2011}, title = {On Isomorphism Testing of Groups with Normal {Hall} Subgroups}, booktitle = {Proc. 28th STACS}, pages = {567--578}, doi = {10.4230/LIPIcs.STACS.2011.567}, ) @misc(Rosenbaum2013BidirectionalCD, author = {David J. Rosenbaum}, year = {2013}, title = {Bidirectional Collision Detection and Faster Deterministic Isomorphism Testing}, howpublished = {\href{https://arxiv.org/abs/1304.3935}{arXiv:1304.3935 [cs.DS]}}, ) @inproceedings(Rossman2009EhrenfeuchtFrassGO, author = {Benjamin Rossman}, year = {2009}, title = {Ehrenfeucht--{F}ra{\"{\i}}ss{\'{e}} Games on Random Structures}, editor = {Hiroakira Ono and Makoto Kanazawa and Ruy J. G. B. de Queiroz}, booktitle = {Logic, Language, Information and Computation, 16th International Workshop, WoLLIC 2009, Tokyo, Japan, June 21-24, 2009. Proceedings}, series = {Lecture Notes in Computer Science}, volume = {5514}, publisher = {Springer}, pages = {350--364}, doi = {10.1007/978-3-642-02261-6_28}, ) @techreport(Savage, author = {C. Savage}, year = {1980}, title = {An {$O(n^2)$} Algorithm for Abelian Group Isomorphism}, type = {Technical Report}, institution = {North Carolina State University}, ) @article(Schoning, author = {Uwe Sch{\"{o}}ning}, year = {1988}, title = {Graph isomorphism is in the low hierarchy}, journal = {Journal of Computer and System Sciences}, volume = {37}, number = {3}, pages = {312 -- 323}, doi = {10.1016/0022-0000(88)90010-4}, ) @inproceedings(VardiPTime, author = {Moshe Y. Vardi}, year = {1982}, title = {The Complexity of Relational Query Languages (Extended Abstract)}, editor = {Harry R. Lewis and Barbara B. Simons and Walter A. Burkhard and Lawrence H. Landweber}, booktitle = {Proceedings of the 14th Annual {ACM} Symposium on Theory of Computing, May 5-7, 1982, San Francisco, California, {USA}}, publisher = {{ACM}}, pages = {137--146}, doi = {10.1145/800070.802186}, ) @article(Vikas, author = {Narayan Vikas}, year = {1996}, title = {An {$O(n)$} Algorithm for Abelian {$p$}-Group Isomorphism and an {$O(n \qopname\relax o{log}n)$} Algorithm for Abelian Group Isomorphism}, journal = {Journal of Computer and System Sciences}, volume = {53}, number = {1}, pages = {1--9}, doi = {10.1006/jcss.1996.0045}, ) @article(WilsonDirectProductsArxiv, author = {James B. Wilson}, year = {2012}, title = {Existence, algorithms, and asymptotics of direct product decompositions, {I}}, journal = {Groups - Complexity - Cryptology}, volume = {4}, number = {1}, doi = {10.1515/gcc-2012-0007}, ) @article(WilsonSubgroupProfiles, author = {James B. Wilson}, year = {2019}, title = {The Threshold for Subgroup Profiles to Agree is Logarithmic}, journal = {Theory of Computing}, volume = {15}, number = {19}, pages = {1--25}, doi = {10.4086/toc.2019.v015a019}, ) @article(ZKT, author = {V. N. Zemlyachenko and N. M. Korneenko and R. I. Tyshkevich}, year = {1985}, title = {Graph isomorphism problem}, journal = {J. Soviet Math.}, volume = {29}, number = {4}, pages = {1426--1481}, doi = {10.1007/BF02104746}, )