Conditional Uncertainty in Constraint Networks

  • Matteo Zavatteri
  • Luca Viganò
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11352)


Constraint Networks (CNs) are a framework to model the Constraint Satisfaction Problem (CSP), which is the problem of finding an assignment of values to a set of variables satisfying a set of given constraints. Therefore, CSP is a satisfiability problem. When the CSP turns conditional, consistency analysis extends to finding also an assignment to these conditions such that the relevant part of the initial CN is consistent. However, CNs fail to model CSPs expressing an uncontrollable conditional part (i.e., a conditional part that cannot be decided but merely observed as it occurs). To bridge this gap, in this paper we propose Constraint Networks Under Conditional Uncertainty (CNCUs), and we define weak, strong and dynamic controllability of a CNCU. We provide algorithms to check each of these types of controllability and discuss how to synthesize (dynamic) execution strategies that drive the execution of a CNCU saying which value to assign to which variable depending on how the uncontrollable part behaves. We discuss Zeta, a tool that we developed for CNCUs to carry out an experimental evaluation. What we propose is fully automated from analysis to simulation.


Constraint Networks Under Conditional Uncertainty CNCU Directional consistency Resource controllability Zeta AI-based security 


  1. 1.
    Dechter, R., Meiri, I., Pearl, J.: Temporal constraint networks. Artif. Intell. 49, 61–95 (1991)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Morris, P.H., Muscettola, N., Vidal, T.: Dynamic control of plans with temporal uncertainty. In: IJCAI 2001 (2001)Google Scholar
  3. 3.
    Hunsberger, L., Posenato, R., Combi, C.: A sound-and-complete propagation-based algorithm for checking the dynamic consistency of conditional simple temporal networks. In: TIME 2015 (2015)Google Scholar
  4. 4.
    Tsamardinos, I., Vidal, T., Pollack, M.E.: CTP: a new constraint-based formalism for conditional, temporal planning. Constraints 8, 365–388 (2003)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Hunsberger, L., Posenato, R., Combi, C.: The dynamic controllability of conditional STNs with uncertainty. In: PlanEx 2012 (2012)Google Scholar
  6. 6.
    Zavatteri, M.: Conditional simple temporal networks with uncertainty and decisions. In: TIME 2017. LIPIcs (2017)Google Scholar
  7. 7.
    Cimatti, A., Hunsberger, L., Micheli, A., Posenato, R., Roveri, M.: Dynamic controllability via timed game automata. Acta Inf. 53, 681–722 (2016)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Cimatti, A., Micheli, A., Roveri, M.: An SMT-based approach to weak controllability for disjunctive temporal problems with uncertainty. Artif. Intell. 224, 1–27 (2015)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Cimatti, A., Micheli, A., Roveri, M.: Solving strong controllability of temporal problems with uncertainty using SMT. Constraints 20, 1–29 (2015)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Dechter, R.: Constraint Processing. Elsevier, Amsterdam (2003)zbMATHGoogle Scholar
  11. 11.
    Fargier, H., Lang, J., Schiex, T.: Mixed constraint satisfaction: a framework for decision problems under incomplete knowledge. In: IAAI 1996 (1996)Google Scholar
  12. 12.
    Mittal, S., Falkenhainer, B.: Dynamic constraint satisfaction problems. In: AAAI 1990 (1990)Google Scholar
  13. 13.
    Fargier, H., Lang, J.: Uncertainty in constraint satisfaction problems: a probabilistic approach. In: Clarke, M., Kruse, R., Moral, S. (eds.) ECSQARU 1993. LNCS, vol. 747, pp. 97–104. Springer, Heidelberg (1993). Scholar
  14. 14.
    Zavatteri, M., Combi, C., Posenato, R., Viganò, L.: Weak, strong and dynamic controllability of access-controlled workflows under conditional uncertainty. In: Carmona, J., Engels, G., Kumar, A. (eds.) BPM 2017. LNCS, vol. 10445, pp. 235–251. Springer, Cham (2017). Scholar
  15. 15.
    Zavatteri, M., Viganò, L.: Constraint networks under conditional uncertainty. In: 10th International Conference on Agents and Artificial Intelligence (ICAART 2018), vol. 2, pp. 41–52. INSTICC, SciTePress (2018)Google Scholar
  16. 16.
    Montanari, U.: Networks of constraints: fundamental properties and applications to picture processing. Inf. Sci. 7, 95–132 (1974)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Gottlob, G.: On minimal constraint networks. Artif. Intell. 191–192, 42–60 (2012)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Mackworth, A.K.: Consistency in networks of relations. Artif. Intell. 8, 99–118 (1977)CrossRefGoogle Scholar
  19. 19.
    Freuder, E.C.: A sufficient condition for backtrack-free search. J. ACM 29, 24–32 (1982)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Dechter, R., Pearl, J.: Network-based heuristics for constraint-satisfaction problems. Artif. Int. 34, 1–38 (1987)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Knuth, D.E.: The Art of Computer Programming, Volume I: Fundamental Algorithms. Addison-Wesley, Boston (1968)zbMATHGoogle Scholar
  22. 22.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 3rd edn. The MIT Press, Cambridge (2009)zbMATHGoogle Scholar
  23. 23.
    Luo, X., Lee, J.H.M., Leung, H.F., Jennings, N.R.: Prioritised fuzzy constraint satisfaction problems: axioms, instantiation and validation. Fuzzy Sets Syst. 136, 155–188 (2003)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Combi, C., Viganò, L., Zavatteri, M.: Security constraints in temporal role-based access-controlled workflows. In: Proceedings of the Sixth ACM Conference on Data and Application Security and Privacy, CODASPY 2016. ACM (2016)Google Scholar
  25. 25.
    Combi, C., Posenato, R., Viganò, L., Zavatteri, M.: Access controlled temporal networks. In: ICAART 2017. INSTICC, ScitePress (2017)Google Scholar
  26. 26.
    Wang, Q., Li, N.: Satisfiability and resiliency in workflow authorization systems. ACM Trans. Inf. Syst. Secur. 13, 40:1–40:35 (2010). Scholar
  27. 27.
    Cabanillas, C., Resinas, M., del-Río-Ortega, A., Cortés, A.R.: Specification and automated design-time analysis of the business process human resource perspective. Inf. Syst. 52, 55–82 (2015)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Dipartimento di InformaticaUniversità di VeronaVeronaItaly
  2. 2.Department of InformaticsKing’s College LondonLondonUK

Personalised recommendations