Weaker Forms of Monotonicity for Declarative Networking

The CALM-conjecture, first stated by Hellerstein [2010] and proved in its revised form by Ameloot et al. [2013] within the framework of relational transducer networks, asserts that a query has a coordination-free execution strategy if and only if the query is monotone. Zinn et al. [2012] extended the framework of relational transducer networks to allow for specific data distribution strategies and showed that the nonmonotone win-move query is coordination-free for domain-guided data distributions. In this article, we extend the story by equating increasingly larger classes of coordination-free computations with increasingly weaker forms of monotonicity and present explicit Datalog variants that capture each of these classes. One such fragment is based on stratified Datalog where rules are required to be connected with the exception of the last stratum. In addition, we characterize coordination-freeness as those computations that do not require knowledge about all other nodes in the network, and therefore, can not globally coordinate. The results in this article can be interpreted as a more fine-grained answer to the CALM-conjecture.

[1]  William W. Tait,et al.  A counterexample to a conjecture of Scott and Suppes , 1959, Journal of Symbolic Logic.

[2]  Kevin J. Compton,et al.  Some useful preservation theorems , 1983, Journal of Symbolic Logic.

[3]  Phokion G. Kolaitis,et al.  On the expressive power of datalog: tools and a case study , 1990, J. Comput. Syst. Sci..

[4]  Masatoshi Yoshikawa,et al.  ILOG: Declarative Creation and Manipulation of Object Identifiers , 1990, VLDB.

[5]  Oded Shmueli,et al.  Equivalence of DATALOG Queries is Undecidable , 1993, J. Log. Program..

[6]  Jianwen Su,et al.  Algebraic and Calculus Query Languages for Recursively Typed Complex Objects , 1993, J. Comput. Syst. Sci..

[7]  Serge Abiteboul,et al.  Foundations of Databases , 1994 .

[8]  Mihalis Yannakakis,et al.  On Datalog vs. Polynomial Time , 1995, J. Comput. Syst. Sci..

[9]  Eric Rosen.  Finite model theory and finite variable logics , 1996 .

[10]  Serge Abiteboul,et al.  Relational transducers for electronic commerce , 1998, J. Comput. Syst. Sci..

[11]  Luca Cabibbo,et al.  The Expressive Power of Stratified Logic Programs with Value Invention , 1998, Inf. Comput..

[12]  Dan Suciu,et al.  Dynamically distributed query evaluation , 2001, PODS.

[13]  Tomás Feder,et al.  Homomorphism closed vs. existential positive , 2003, 18th Annual IEEE Symposium of Logic in Computer Science, 2003. Proceedings..

[14]  Serge Abiteboul,et al.  Diagnosis of asynchronous discrete event systems: datalog to the rescue! , 2005, PODS.

[15]  Gerhard Weikum,et al.  ACM Transactions on Database Systems , 2005 .

[16]  Anuj Dawar,et al.  Preservation Under Extensions on Well-Behaved Finite Structures , 2005, ICALP.

[17]  Alin Deutsch,et al.  Verification of communicating data-driven web services , 2006, PODS '06.

[18]  Ion Stoica,et al.  Declarative networking: language, execution and optimization , 2006, SIGMOD Conference.

[19]  Alin Deutsch,et al.  Specification and verification of data-driven Web applications , 2007, J. Comput. Syst. Sci..

[20]  Serge Abiteboul,et al.  The Active XML project: an overview , 2008, The VLDB Journal.

[21]  Stephan Kreutzer,et al.  On Datalog vs. LFP , 2008, ICALP.

[22]  Jeffrey D. Ullman,et al.  Optimizing joins in a map-reduce environment , 2010, EDBT '10.

[23]  Fang Wang,et al.  Netlog, a Rule-Based Language for Distributed Programming , 2010, PADL.

[24]  David Maier,et al.  Dedalus: Datalog in Time and Space , 2010, Datalog.

[25]  Joseph M. Hellerstein,et al.  The declarative imperative: experiences and conjectures in distributed logic , 2010, SGMD.

[26]  Dan Suciu,et al.  Parallel evaluation of conjunctive queries , 2011, PODS.

[27]  Jeffrey D. Ullman,et al.  Map-reduce extensions and recursive queries , 2011, EDBT/ICDT '11.

[28]  Joseph M. Hellerstein,et al.  Consistency Analysis in Bloom: a CALM and Collected Approach , 2011, CIDR.

[29]  Serge Abiteboul,et al.  A rule-based language for web data management , 2011, PODS.

[30]  Jeffrey D. Ullman,et al.  Transitive closure and recursive Datalog implemented on clusters , 2012, EDBT '12.

[31]  Jan Van den Bussche,et al.  On the CRON Conjecture , 2012, Datalog.

[32]  David Maier,et al.  Logic and lattices for distributed programming , 2012, SoCC '12.

[33]  Bertram Ludäscher,et al.  Win-move is coordination-free (sometimes) , 2012, ICDT '12.

[34]  Daniel Zinn.  Weak Forms of Monotonicity and Coordination-Freeness , 2012, ArXiv.

[35]  Jan Van den Bussche,et al.  Deciding eventual consistency for a simple class of relational transducer networks , 2012, ICDT '12.

[36]  Paraschos Koutris,et al.  Communication steps for parallel query processing , 2013, PODS '13.

[37]  Frank Neven,et al.  Relational transducers for declarative networking , 2010, JACM.

[38]  Tom J. Ameloot.  Deciding Correctness with Fairness for Simple Transducer Networks , 2014, ICDT.

[39]  David Maier,et al.  Blazes: Coordination analysis for distributed programs , 2013, 2014 IEEE 30th International Conference on Data Engineering.

[40]  Dan Suciu,et al.  Parallel Skyline Queries , 2012, ICDT '12.

[41]  Frank Neven,et al.  Optimal Broadcasting Strategies for Conjunctive Queries over Distributed Data , 2016, Theory of Computing Systems.

[42]  Frank Neven,et al.  Weaker Forms of Monotonicity for Declarative Networking: A More Fine-Grained Answer to the CALM-Conjecture , 2016 .

[43]  Frank Neven,et al.  Datalog Queries Distributing over Components , 2017, ACM Trans. Comput. Log..