Convergence of Datalog over (Pre-) Semirings-Reference-Cited by-同舟云学术

Convergence of Datalog over (Pre-) Semirings

Published:2023-06-07 Issue:1 Volume:52 Page:75-82
ISSN:0163-5808
Container-title:ACM SIGMOD Record
language:en
Short-container-title:SIGMOD Rec.

Author:

Abo Khamis Mahmoud¹,Ngo Hung Q.¹,Pichler Reinhard²,Suciu Dan³,Remy Wang Yisu³

Affiliation:

1. relationalAI

2. TU Wien

3. University of Washington

Abstract

Recursive queries have been traditionally studied in the framework of datalog, a language that restricts recursion to monotone queries over sets, which is guaranteed to converge in polynomial time in the size of the input. But modern big data systems require recursive computations beyond the Boolean space. In this paper we study the convergence of datalog when it is interpreted over an arbitrary semiring. We consider an ordered semiring, define the semantics of a datalog program as a least fixpoint in this semiring, and study the number of steps required to reach that fixpoint, if ever. We identify algebraic properties of the semiring that correspond to certain convergence properties of datalog programs. Finally, we describe a class of ordered semirings on which one can generalize the semi-na¨ve evaluation algorithm to compute their minimal fixpoints.

Publisher

Association for Computing Machinery (ACM)

Subject

Information Systems,Software

Link

https://dl.acm.org/doi/pdf/10.1145/3604437.3604454

Reference34 articles.

1. Abadi , M. , Barham , P. , Chen , J. , Chen , Z. , Davis , A. , Dean , J. , Devin , M. , Ghemawat , S. , Irving , G. , Isard , M. , Kudlur , M. , Levenberg , J. , Monga , R. , Moore , S. , Murray , D. G. , Steiner , B. , Tucker , P. A. , Vasudevan , V. , Warden , P. , Wicke , M. , Yu , Y. , and Zheng , X . Tensorflow: A system for large-scale machine learning . In 12th USENIX Symposium on Operating Systems Design and Implementation, OSDI 2016 , Savannah, GA, USA, November 2--4 , 2016 (2016), K. Keeton and T. Roscoe, Eds., USENIX Association, pp. 265 -- 283 . Abadi, M., Barham, P., Chen, J., Chen, Z., Davis, A., Dean, J., Devin, M., Ghemawat, S., Irving, G., Isard, M., Kudlur, M., Levenberg, J., Monga, R., Moore, S., Murray, D. G., Steiner, B., Tucker, P. A., Vasudevan, V., Warden, P., Wicke, M., Yu, Y., and Zheng, X. Tensorflow: A system for large-scale machine learning. In 12th USENIX Symposium on Operating Systems Design and Implementation, OSDI 2016, Savannah, GA, USA, November 2--4, 2016 (2016), K. Keeton and T. Roscoe, Eds., USENIX Association, pp. 265--283.

2. The generalized distributive law

3. Carr´e , B. Graphs and networks . The Clarendon Press, Oxford University Press , New York , 1979 . Oxford Applied Mathematics and Computing Science Series. Carr´e, B. Graphs and networks. The Clarendon Press, Oxford University Press, New York, 1979. Oxford Applied Mathematics and Computing Science Series.

4. Cormen , T. H. , Leiserson , C. E. , Rivest , R. L. , and Stein , C . Introduction to algorithms , third ed. MIT Press , Cambridge, MA , 2009 . Cormen, T. H., Leiserson, C. E., Rivest, R. L., and Stein, C. Introduction to algorithms, third ed. MIT Press, Cambridge, MA, 2009.