Small dynamic complexity classes

[1]  Thomas Schwentick,et al.  Reachability Is in DynFO , 2015, ICALP.

[2]  P. Erdös,et al.  Combinatorial Theorems on Classifications of Subsets of a Given Set , 1952 .

[3]  Wim Martens,et al.  The complexity of regular expressions and property paths in SPARQL , 2013, TODS.

[4]  Peter Bro Miltersen.  Cell probe complexity-a survey , 1999 .

[5]  William Hesse,et al.  The dynamic complexity of transitive closure is in DynTC0 , 2001, Theor. Comput. Sci..

[6]  Sebastian Siebertz,et al.  Dynamic definability , 2012, ICDT '12.

[7]  Marcelo Arenas,et al.  Counting beyond a Yottabyte, or how SPARQL 1.1 property paths will prevent adoption of the standard , 2012, WWW.

[8]  Christoph Koch,et al.  Incremental query evaluation in a ring of databases , 2010, PODS.

[9]  Michael Mortimer,et al.  On languages with two variables , 1975, Math. Log. Q..

[10]  Erich Grädel,et al.  Two-variable logic with counting is decidable , 1997, Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science.

[11]  Thomas Schwentick,et al.  Dynamic Complexity Theory Revisited , 2005, Theory of Computing Systems.

[12]  Limsoon Wong,et al.  Incremental Recomputation of Recursive Queries with Nested Sets and Aggregate Functions , 1997, DBPL.

[13]  Thomas Zeume,et al.  The dynamic descriptive complexity of k-clique , 2014, Inf. Comput..

[14]  Alberto O. Mendelzon,et al.  Finding Regular Simple Paths in Graph Databases , 1989, SIAM J. Comput..

[15]  Kousha Etessami,et al.  Dynamic Tree Isomorphism via First-Order Updates. , 1998, PODS 1998.

[16]  Martin Otto,et al.  Two variable first-order logic over ordered domains , 2001, Journal of Symbolic Logic.

[17]  Limsoon Wong,et al.  Query Languages for Bags and Aggregate Functions , 1997, J. Comput. Syst. Sci..

[18]  Peter T. Wood,et al.  Query languages for graph databases , 2012, SGMD.

[19]  V. S. Subrahmanian,et al.  Maintaining views incrementally , 1993, SIGMOD Conference.

[20]  Raghav Kulkarni,et al.  Dynamic Complexity of Directed Reachability and Other Problems , 2014, ICALP.

[21]  Phokion G. Kolaitis,et al.  On the Decision Problem for Two-Variable First-Order Logic , 1997, Bulletin of Symbolic Logic.

[22]  Eric Allender,et al.  Making nondeterminism unambiguous , 1997, Proceedings 38th Annual Symposium on Foundations of Computer Science.

[23]  Neil Immerman,et al.  Dyn-FO: A Parallel, Dynamic Complexity Class , 1997, J. Comput. Syst. Sci..

[24]  Philippe Schnoebelen,et al.  Multiply-Recursive Upper Bounds with Higman's Lemma , 2011, ICALP.

[25]  Chaoyi Pang,et al.  Maintaining Transitive Closure in First Order After Node-Set and Edge-Set Deletions , 1997, Inf. Process. Lett..

[26]  Thomas W. Reps,et al.  Finite differencing of logical formulas for static analysis , 2010, TOPL.

[27]  Jianwen Su,et al.  Incremental and Decremental Evaluation of Transitive Closure by First-Order Queries , 1995, Inf. Comput..

[28]  Jianwen Su,et al.  Arity Bounds in First-Order Incremental Evaluation and Definition of Polynomial Time Database Queries , 1998, J. Comput. Syst. Sci..

[29]  Diego Figueira.  Satisfiability for two-variable logic with two successor relations on finite linear orders , 2012, ArXiv.

[30]  Jakub Michaliszyn,et al.  Two-Variable First-Order Logic with Equivalence Closure , 2014, SIAM J. Comput..

[31]  Peter Bro Miltersen,et al.  Complexity Models for Incremental Computation , 1994, Theor. Comput. Sci..

[32]  A. Turing.  On Computable Numbers, with an Application to the Entscheidungsproblem. , 1937 .

[33]  Thomas Schwentick,et al.  On the quantifier-free dynamic complexity of Reachability , 2013, Inf. Comput..

[34]  Yoav Shoham,et al.  A propositional modal logic of time intervals , 1991, JACM.

[35]  E. F. CODD,et al.  A relational model of data for large shared data banks , 1970, CACM.

[36]  Marcelo Arenas,et al.  nSPARQL: A navigational language for RDF , 2010, J. Web Semant..

[37]  Jin-Yi Cai.  Lower Bounds for Constant-Depth Circuits in the Presence of Help Bits , 1990, Inf. Process. Lett..

[38]  Thomas Wilke,et al.  Program Complexity of Dynamic LTL Model Checking , 2003, CSL.

[39]  Emanuel Kieronski,et al.  Decidability Issues for Two-Variable Logics with Several Linear Orders , 2011, CSL.

[40]  Giuseppe F. Italiano,et al.  Mantaining Dynamic Matrices for Fully Dynamic Transitive Closure , 2001, Algorithmica.

[41]  Michael Sipser,et al.  Parity, circuits, and the polynomial-time hierarchy , 1981, 22nd Annual Symposium on Foundations of Computer Science (sfcs 1981).

[42]  Jianwen Su,et al.  Maintaining Transitive Closure of Graphs in SQL , 1999 .

[43]  Thomas Schwentick,et al.  The dynamic complexity of formal languages , 2008, TOCL.

[44]  Yuri Gurevich,et al.  The Classical Decision Problem , 1997, Perspectives in Mathematical Logic.

[45]  Carsten Lutz,et al.  Non-Uniform Data Complexity of Query Answering in Description Logics , 2012, Description Logics.

[46]  Kousha Etessami,et al.  Two Variables and Unary Temporal Logic , 1997 .

[47]  Beatrix Potter.  The Tale of Squirrel Nutkin , 1903 .

[48]  U. Hustadt,et al.  A Survey of Decidable First-Order Fragments and Description Logics , 2004 .

[49]  Thomas Schwentick,et al.  A Short Note on Two-Variable Logic with a Linear Order Successor and a Preorder Successor , 2013, ArXiv.

[50]  Thomas Schwentick,et al.  Two-Variable Logic with Two Order Relations - (Extended Abstract) , 2010, CSL.

[51]  Andrzej Szepietowski.  Turing Machines with Sublogarithmic Space , 1994, Lecture Notes in Computer Science.

[52]  Lidia Tendera,et al.  On Finite Satisfiability of Two-Variable First-Order Logic with Equivalence Relations , 2009, 2009 24th Annual IEEE Symposium on Logic In Computer Science.

[53]  Patricia Bouyer,et al.  A logical characterization of data languages , 2002, Inf. Process. Lett..

[54]  Neil Immerman,et al.  Complete problems for dynamic complexity classes , 2002, Proceedings 17th Annual IEEE Symposium on Logic in Computer Science.

[55]  Neil Immerman,et al.  On Uniformity within NC¹ , 1990, J. Comput. Syst. Sci..

[56]  Ashok K. Chandra,et al.  Optimal implementation of conjunctive queries in relational data bases , 1977, STOC '77.

[57]  Leonid Libkin,et al.  Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series) , 2004 .

[58]  Yde Venema,et al.  Expressiveness and Completeness of an Interval Tense Logic , 1990, Notre Dame J. Formal Log..

[59]  Alon Itai,et al.  Maintenance of views , 1984, SIGMOD '84.

[60]  Thomas Schwentick,et al.  Dynamic conjunctive queries , 2017, Journal of computer and system sciences (Print).

[61]  Guozhu Dong,et al.  Incremental Evaluation of Datalog Queries , 1992, ICDT.

[62]  Serge Abiteboul,et al.  Regular path queries with constraints , 1997, J. Comput. Syst. Sci..

[63]  Amaldev Manuel.  Two Variables and Two Successors , 2010, MFCS.

[64]  Alonzo Church,et al.  A note on the Entscheidungsproblem , 1936, Journal of Symbolic Logic.

[65]  Anthony Widjaja Lin,et al.  Expressive Languages for Path Queries over Graph-Structured Data , 2012, TODS.

[66]  Heribert Vollmer,et al.  Introduction to Circuit Complexity: A Uniform Approach , 2010 .

[67]  Milos Nikolic,et al.  DBToaster: Higher-order Delta Processing for Dynamic, Frequently Fresh Views , 2012, Proc. VLDB Endow..

[68]  A. Hajnal,et al.  Partition relations for cardinal numbers , 1965 .

[69]  Uri Zwick,et al.  Improved Dynamic Reachability Algorithms for Directed Graphs , 2008, SIAM J. Comput..

[70]  Pablo Barceló,et al.  Querying graph databases , 2013, PODS '13.

[71]  Martin Otto,et al.  Small substructures and decidability issues for first-order logic with two variables , 2005, 20th Annual IEEE Symposium on Logic in Computer Science (LICS' 05).

[72]  Wieslaw Szwast,et al.  FO^2 with one transitive relation is decidable , 2013, STACS.

[73]  Neil Immerman,et al.  Dynamic computational complexity , 2003 .

[74]  Jianwen Su,et al.  Deterministic FOIES are strictly weaker , 2004, Annals of Mathematics and Artificial Intelligence.

[75]  Limsoon Wong,et al.  Incremental recomputation in local languages , 2003, Inf. Comput..

[76]  Thomas Zeume,et al.  Two-Variable Logic on 2-Dimensional Structures , 2013, CSL.

[77]  Vojtech Rödl,et al.  Shift graphs and lower bounds on Ramsey numbers rk(l; r) , 1995, Discret. Math..