Constraints

, Volume 21, Issue 1, pp 22–40 | Cite as

Using finite transducers for describing and synthesising structural time-series constraints

  • Nicolas Beldiceanu
  • Mats Carlsson
  • Rémi Douence
  • Helmut Simonis
Article

Abstract

We describe a large family of constraints for structural time series by means of function composition. These constraints are on aggregations of features of patterns that occur in a time series, such as the number of its peaks, or the range of its steepest ascent. The patterns and features are usually linked to physical properties of the time series generator, which are important to capture in a constraint model of the system, i.e. a conjunction of constraints that produces similar time series. We formalise the patterns using finite transducers, whose output alphabet corresponds to semantic values that precisely describe the steps for identifying the occurrences of a pattern. Based on that description, we automatically synthesise automata with accumulators, as well as constraint checkers. The description scheme not only unifies the structure of the existing 30 time-series constraints in the Global Constraint Catalogue, but also leads to over 600 new constraints, with more than 100,000 lines of synthesised code.

Keywords

Global constraint Time series Global constraint catalogue Constraint synthesis Finite transducer 

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References

  1. 1.
    Abney, S. (1996). Partial parsing via finite-state cascades. Natural Language Engineering, 2(4), 337–344.CrossRefGoogle Scholar
  2. 2.
    Beldiceanu, N., Carlsson, M., Debruyne, R., & Petit, T. (2005). Reformulation of global constraints based on constraints checkers. Constraints, 10(4), 339–362.MATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    Beldiceanu, N., Carlsson, M., Demassey, S., & Petit, T. (2007). Global constraint catalogue: Past, present and future. Constraints, 12(1), 21–62.MATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Beldiceanu, N., Carlsson, M., Flener, P., & Pearson, J. (2013). On the reification of global constraints. Constraints, 18(1), 1–6.MathSciNetCrossRefGoogle Scholar
  5. 5.
    Beldiceanu, N., Carlsson, M., Flener, P., Rodríguez, M.A.F., & Pearson, J. (2014). Linking prefixes and suffixes for constraints encoded using automata with accumulators. In B. O’Sullivan (Ed.), Principles and practice of constraint programming (CP 2014), LNCS, (Vol. 8656 pp. 142–157): Springer.Google Scholar
  6. 6.
    Beldiceanu, N., Carlsson, M., & Rampon, J.X. Global constraint catalog, 2nd edition (revision a). Tech. Rep. T2012-03, Swedish Institute of Computer Science (2012), current version available at, http://sofdem.github.io/gccat/.
  7. 7.
    Beldiceanu, N., Flener, P., Monette, J.N., Pearson, J., & Simonis, H. (2014). Toward sustainable development in constraint programming. Constraints, 19 (2), 139–149.CrossRefGoogle Scholar
  8. 8.
    Beldiceanu, N., Ifrim, G., Lenoir, A., & Simonis, H. (2013). Describing and generating solutions for the EDF unit commitment problem with the ModelSeeker. In C. Schulte (Ed.), Principles and practice of constraint programming (CP 2013), LNCS, (Vol. 8124 pp. 733–748): Springer.Google Scholar
  9. 9.
    Beldiceanu, N., & Simonis, H. (2011). A constraint seeker: Finding and ranking global constraints from examples. In J. Lee (Ed.), Principles and Practice of Constraint Programming (CP 2011), LNCS, (Vol. 6876 pp. 12–26): Springer.Google Scholar
  10. 10.
    Beldiceanu, N., & Simonis, H. (2012). A model seeker: Extracting global constraint models from positive examples. In M. Milano (Ed.), Principles and Practice of Constraint Programming - 18th International Conference, CP 2012, Quebec City, QC, Canada, October 8-12, 2012. Proceedings. Lecture Notes in Computer Science, (Vol. 7514 pp. 141–157): Springer. doi:10.1007/978-3-642-33558-7_13.
  11. 11.
    Berstel, J. (1979). Transductions and context-free languages: Teubner.Google Scholar
  12. 12.
    Carlsson, M., & et al. SICStus Prolog User’s Manual. Swedish Institute of Computer Science, 4.3.1 edn. (November 2014), current version available at, https://sicstus.sics.se/sicstus/docs/latest4/pdf/sicstus.pdf.
  13. 13.
    Fu, T. (2011). A review on time series data mining. Engineering Applications of Artificial Intelligence, 24(1), 164–181. http://www.sciencedirect.com/science/article/pii/S0952197610001727.CrossRefGoogle Scholar
  14. 14.
    Fung, D.S.C. (2006). Methods for the estimation of missing values in time series. Master’s thesis. Perth: Edith Cowan University.Google Scholar
  15. 15.
    Gent, I.P., Jefferson, C., Linton, S., Miguel, I., & Nightingale, P. (2014). Generating custom propagators for arbitrary constraints. Artificial Intelligence, 211, 1–33.MATHMathSciNetCrossRefGoogle Scholar
  16. 16.
    Goldin, D.Q., & Kanellakis, P.C. (1995). On similarity queries for time-series data: Constraint specification and implementation. In U. Montanari, & F. Rossi (Eds.), Principles and Practice of Constraint Programming (CP 1995), LNCS, (Vol. 976 pp. 137–153): Springer.Google Scholar
  17. 17.
    Guns, T., Nijssen, S., & De Raedt, L. (2011). Itemset mining: A constraint programming perspective. Artificial Intelligence, 175(12–13), 1951–1983.MATHMathSciNetCrossRefGoogle Scholar
  18. 18.
    Harvey, A. (1991). Forecasting, structural time series models and the Kalman filter: Cambridge University Press.Google Scholar
  19. 19.
    Laurière, J.L. Constraint propagation or automatic programming. Tech. Rep. 19, IBP-Laforia (1996), in French, available at, https://www.lri.fr/sebag/Slides/Lauriere/Rabbit.pdf.
  20. 20.
    Liao, T.W. (2005). Clustering of time series data - a survey. Pattern Recognition, 38(11), 1857–1874. doi:10.1016/j.patcog.2005.01.025.MATHCrossRefGoogle Scholar
  21. 21.
    Nhon, D.T., & Wilkinson, L. (2013). TimeExplorer: Similarity search time series by their signatures. In G. Bebis, R. Boyle, B. Parvin, D. Koracin, B. Li, F. Porikli, V.B. Zordan, J.T. Klosowski, S. Coquillart, X. Luo, M. Chen, & D. Gotz (Eds.), 9th International Symposium on Advances in Visual Computing (ISVC 2013), LNCS, (Vol. 8033 pp. 280–289): Springer.Google Scholar
  22. 22.
    Perng, C.S., Wang, H., Zhang, S.R., & Parker, D.S. (2000). Landmarks: A new model for similarity-based pattern querying in time series databases. In 16th International Conference on Data Engineering (ICDE 2000) (pp. 33–42): IEEE.Google Scholar
  23. 23.
    Ratanamahatana, C., Lin, J., Gunopulos, D., Keogh, E., Vlachos, M., & Das, G. (2010). Mining time series data. In O. Maimon, & L. Rokach (Eds.), Data mining and knowledge discovery handbook (pp. 1049–1077). US: Springer. doi:10.1007/978-0-387-09823-4_56.Google Scholar
  24. 24.
    Sakarovitch, J. (2009). Elements of language theory: Cambridge University Press.Google Scholar
  25. 25.
    Smith, D.R., & Westfold, S.J. Toward the synthesis of constraint solvers. Tech. Rep. TR-1311, Kestrel Institute (2013), available at, http://www.kestrel.edu/home/people/smith/pub/CW-report.pdf.
  26. 26.
    Veanes, M., Hooimeijer, P., Livshits, B., Molnar, D., & Bjørner, N. (2012). Symbolic finite state transducers: algorithms and applications. In J. Field, & M. Hicks (Eds.), Proceedings of the 39th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 2012, Philadelphia, Pennsylvania, USA (pp. 137–150): ACM.Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Nicolas Beldiceanu
    • 1
  • Mats Carlsson
    • 2
  • Rémi Douence
    • 3
  • Helmut Simonis
    • 4
  1. 1.TASC (CNRS/INRIA)Mines NantesNantesFrance
  2. 2.SICSKistaSweden
  3. 3.ASCOLA (CNRS/INRIA)Mines NantesNantesFrance
  4. 4.Insight Centre for Data AnalyticsUniversity College CorkCorkIreland

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