# Dynamic controllability via Timed Game Automata

- 316 Downloads
- 3 Citations

## Abstract

Temporal networks are data structures for representing and reasoning about temporal constraints on activities. Many kinds of temporal networks have been defined in the literature, differing in their expressiveness. The simplest kinds of networks have polynomial algorithms for determining their temporal consistency or different levels of controllability, but corresponding algorithms for more expressive networks (e.g., those that include observation nodes or disjunctive constraints) have so far been unavailable. This paper introduces a new approach to determine the dynamic controllability of a very expressive class of temporal networks that accommodates observation nodes and disjunctive constraints. The approach is based on encoding the dynamic controllability problem into a reachability game for Timed Game Automata (TGAs). This is the first sound and complete approach for determining the dynamic controllability of such networks. The encoding also highlights the theoretical relationships between various kinds of temporal networks and TGAs. The new algorithms have immediate applications in the design and analysis of workflow models being developed to automate business processes, including workflows in the health-care domain.

## Keywords

Dynamic controllability Temporal networks Timed Game Automata## References

- 1.Abdeddaim, Y., Asarin, E., Sighireanu, M.: Simple algorithm for simple timed games. In: TIME, pp. 99–106 (2009)Google Scholar
- 2.Allen, J.F.: Maintaining knowledge about temporal intervals. Commun. ACM
**26**(11), 832–843 (1983)CrossRefzbMATHGoogle Scholar - 3.Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci.
**126**(2), 183–235 (1994)MathSciNetCrossRefzbMATHGoogle Scholar - 4.Augusto, J.C.: Temporal reasoning for decision support in medicine. Artif. Intell. Med.
**33**(1), 1–24 (2005)MathSciNetCrossRefGoogle Scholar - 5.Behrmann, G., Cougnard, A., David, A., Fleury, E., Larsen, K., Lime, D.: Uppaal-Tiga: time for playing games!. In: Damm, W., Hermanns, H. (eds.) Proceedings of the 19th Conference on Computer Aided Verification (CAV-2007). Lecture Notes in Computer Science, vol. 4590, pp. 121–125. Springer, Berlin (2007)CrossRefGoogle Scholar
- 6.Cassez, F., David, A., Fleury, E., Larsen, K.G., Lime, D.: Efficient on-the-fly algorithms for the analysis of timed games. In: CONCUR, pp. 66–80 (2005)Google Scholar
- 7.Cesta, A., Fratini, S., Orlandini, A., Finzi, A.: Flexible plan verification: feasibility results. Fundam. Inform.
**107**(2–3), 111–137 (2011)MathSciNetzbMATHGoogle Scholar - 8.Cheikhrouhou, S., Kallel, S., Guermouche, N., Jmaiel, M.: Toward a time-centric modeling of business processes in BPMN 2.0. In: International Conference on Information Integration and Web-based Applications and Services, pp. 154–163. ACM (2013)Google Scholar
- 9.Cimatti, A., Hunsberger, L., Micheli, A., Posenato, R., Roveri, M.: Sound and complete algorithms for checking the dynamic controllability of temporal networks with uncertainty, disjunction and observation. In: Cesta, A., Combi, C., Laroussinie, F. (eds.) 21st International Symposium on Temporal Representation and Reasoning, TIME 2014, Verona, Italy, September 8–10, 2014, pp. 27–36. IEEE Computer Society (2014). doi: 10.1109/TIME.2014.21
- 10.Cimatti, A., Hunsberger, L., Micheli, A., Roveri, M.: Using timed game automata to synthesize execution strategies for simple temporal networks with uncertainty. In: Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence, July 27–31, 2014, Québec City, Québec, Canada, pp. 2242–2249 (2014)Google Scholar
- 11.Cimatti, A., Micheli, A., Roveri, M.: Solving temporal problems using SMT: weak controllability. In: AAAI, pp. 448–454 (2012)Google Scholar
- 12.Cimatti, A., Micheli, A., Roveri, M.: Solving strong controllability of temporal problems with uncertainty using SMT. Constraints
**20**(1), 1–29 (2015)MathSciNetCrossRefzbMATHGoogle Scholar - 13.Combi, C., Gambini, M., Migliorini, S., Posenato, R.: Representing business processes through a temporal data-centric workflow modeling language: an application to the management of clinical pathways. IEEE Trans. Syst. Man Cybern. Syst.
**44**(9), 1182–1203 (2014). doi: 10.1109/TSMC.2014.2300055 CrossRefGoogle Scholar - 14.Combi, C., Gozzi, M., Posenato, R., Pozzi, G.: Conceptual modeling of flexible temporal workflows. ACM Trans. Autono. Adapt. Syst. (TAAS)
**7**(2), 19 (2012). doi: 10.1145/2240166.2240169 Google Scholar - 15.Combi, C., Hunsberger, L., Posenato, R.: An algorithm for checking the dynamic controllability of a conditional simple temporal network with uncertainty. In: Filipe, J., Fred, A.L.N. (eds.) ICAART 2013—Proceedings of the 5th International Conference on Agents and Artificial Intelligence, vol. 2, Barcelona, Spain, 15–18 February, 2013, pp. 144–156. SciTePress (2013)Google Scholar
- 16.Combi, C., Posenato, R.: Controllability in temporal conceptual workflow schemata. In: Dayal, U., Eder, J., Koehler, J., Reijers, H.A. (eds.) Business Process Management, 7th International Conference, BPM 2009, Ulm, Germany, September 8–10, 2009. Proceedings, Lecture Notes in Computer Science, vol. 5701, pp. 64–79. Springer (2009). doi: 10.1007/978-3-642-03848-8_6
- 17.Combi, C., Pozzi, G.: Architectures for a temporal workflow management system. In: Proceedings of the 2004 ACM Symposium on Applied Computing (SAC-2004), pp. 659–666. ACM, New York (2004)Google Scholar
- 18.Comin, C., Posenato, R., Rizzi, R.: A tractable generalization of simple temporal networks and its relation to mean payoff games. In: Cesta, A., Combi, C., Laroussinie, F. (eds.) 21st International Symposium on Temporal Representation and Reasoning, TIME 2014, Verona, Italy, September 8–10, 2014, pp. 7–16. IEEE Computer Society (2014). doi: 10.1109/TIME.2014.19
- 19.Dechter, R., Meiri, I., Pearl, J.: Temporal constraint networks. Artif. Intell.
**49**, 61–95 (1991)MathSciNetCrossRefzbMATHGoogle Scholar - 20.Eder, J., Panagos, E., Rabinovich, M.: Time constraints in workflow systems. In: Jarke, M., Oberweis, A. (eds.) Advanced Information Systems Engineering, LNCS, vol. 1626, pp. 286–300. Springer, Berlin (1999)CrossRefGoogle Scholar
- 21.Hollingsworth, D.: The workflow reference model. http://www.wfmc.org/standards/model.htm (1995)
- 22.Hunsberger, L.: Fixing the semantics for dynamic controllability and providing a more practical characterization of dynamic execution strategies. In: Lutz, C., Raskin, J. (eds.) TIME 2009, 16th International Symposium on Temporal Representation and Reasoning, Bressanone-Brixen, Italy, 23–25 July 2009, Proceedings, pp. 155–162. IEEE Computer Society (2009). doi: 10.1109/TIME.2009.25
- 23.Hunsberger, L.: A fast incremental algorithm for managing the execution of dynamically controllable temporal networks. In: Markey, N., Wijsen, J. (eds.) TIME 2010–17th International Symposium on Temporal Representation and Reasoning, Paris, France, 6–8 September 2010, pp. 121–128. IEEE Computer Society (2010). doi: 10.1109/TIME.2010.16
- 24.Hunsberger, L.: A faster execution algorithm for dynamically controllable stnus. In: Sánchez, C., Venable, K.B., Zimányi, E. (eds.) 2013 20th International Symposium on Temporal Representation and Reasoning, Pensacola, FL, USA, September 26–28, 2013, pp. 26–33. IEEE Computer Society (2013). doi: 10.1109/TIME.2013.13
- 25.Hunsberger, L.: A faster algorithm for checking the dynamic controllability of simple temporal networks with uncertainty. In: Duval, B., van den Herik, H.J., Loiseau, S., Filipe, J. (eds.) ICAART 2014 - Proceedings of the 6th International Conference on Agents and Artificial Intelligence, vol. 1, ESEO, Angers, Loire Valley, France, 6–8 March, 2014, pp. 63–73. SciTePress (2014). doi: 10.5220/0004758100630073
- 26.Hunsberger, L., Posenato, R., Combi, C.: The dynamic controllability of conditional STNs with uncertainty. In: Proceedings of the Workshop on Planning and Plan Execution for Real-World Systems: Principles and Practices (PlanEx) at ICAPS-2012, pp. 1–8 (2012). arXiv:1212.2005
- 27.Kleene, S.: Mathematical Logic. Wiley, Hoboken (1967)zbMATHGoogle Scholar
- 28.Lanz, A., Posenato, R., Combi, C., Reichert, M.: Controllability of time-aware processes at run time. In: Meersman, R., Panetto, H., Dillon, T.S., Eder, J., Bellahsene, Z., Ritter, N., Leenheer, P.D., Dou, D. (eds.) On the Move to Meaningful Internet Systems: OTM 2013 Conferences—Confederated International Conferences: CoopIS, DOA-Trusted Cloud, and ODBASE 2013, Graz, Austria, September 9–13, 2013. Proceedings, Lecture Notes in Computer Science, vol. 8185, pp. 39–56. Springer (2013). doi: 10.1007/978-3-642-41030-7_4
- 29.Lanz, A., Posenato, R., Combi, C., Reichert, M.: Simple temporal networks with partially shrinkable uncertainty. In: Loiseau, S., Filipe, J., Duval, B., van den Herik, H.J. (eds.) ICAART 2015—Proceedings of the International Conference on Agents and Artificial Intelligence, vol. 2, Lisbon, Portugal, 10–12 January, 2015, pp. 370–381. SciTePress (2015)Google Scholar
- 30.Lanz, A., Weber, B., Reichert, M.: Workflow time patterns for process-aware information systems. In: Mylopoulos, J., Sadeh, N.M., Shaw, M.J., Szyperski, C., Bider, I., Halpin, T., Krogstie, J., Nurcan, S., Proper, E., Schmidt, R., Ukor, R. (eds.) Enterprise, Business-Process and Information Systems Modeling 11th International Workshop, BPMDS 2010, and 15th International Conference, EMMSAD 2010, pp. 94–107. Springer, Berlin (2010)Google Scholar
- 31.Lewis, H.R., Papadimitriou, C.H.: Elements of the Theory of Computation, 2nd edn. Prentice-Hall Inc, Upper Saddle River (1998)Google Scholar
- 32.Maler, O., Pnueli, A., Sifakis, J.: On the synthesis of discrete controllers for timed systems. In: STACS, pp. 229–242 (1995)Google Scholar
- 33.Morris, P.: A structural characterization of temporal dynamic controllability. In: Principles and Practice of Constraint Programming (CP-2006), Lecture Notes in Computer Science, vol. 4204, pp. 375–389. Springer (2006)Google Scholar
- 34.Morris, P.: Dynamic controllability and dispatchability relationships. In: Simonis, H. (ed.) Integration of AI and OR Techniques in Constraint Programming—11th International Conference (CPAIOR-2014), Lecture Notes in Computer Science, vol. 8451, pp. 464–479. Springer (2014)Google Scholar
- 35.Morris, P., Muscettola, N., Vidal, T.: Dynamic control of plans with temporal uncertainty. In: Nebel, B. (ed.) Proceedings of the 17th International Joint Conference on Artificial Intelligence (IJCAI-2001), pp. 494–499. Morgan Kaufmann (2001)Google Scholar
- 36.Morris, P.H., Muscettola, N.: Temporal dynamic controllability revisited. In: AAAI, pp. 1193–1198 (2005)Google Scholar
- 37.Orlandini, A., Finzi, A., Cesta, A., Fratini, S.: TGA-based controllers for flexible plan execution. In: KI, no. 7006 in LNAI, pp. 233–245. Springer (2011)Google Scholar
- 38.Peintner, B., Venable, K.B., Yorke-Smith, N.: Strong controllability of disjunctive temporal problems with uncertainty. In: Principles and Practice of Constraint Programming (CP-2007), pp. 856–863 (2007)Google Scholar
- 39.Rossi, F., Venable, K.B., Yorke-Smith, N.: Uncertainty in soft temporal constraint problems: a general framework and controllability algorithms for the fuzzy case. J. Artif. Intell. Res.
**27**, 617–674 (2006)zbMATHGoogle Scholar - 40.Tsamardinos, I., Pollack, M.E.: Efficient solution techniques for disjunctive temporal reasoning problems. Artif. Intell.
**151**, 43–89 (2003)MathSciNetCrossRefzbMATHGoogle Scholar - 41.Tsamardinos, I., Vidal, T., Pollack, M.: CTP: a new constraint-based formalism for conditional, temporal planning. Constraints
**8**(4), 365–388 (2003)MathSciNetCrossRefzbMATHGoogle Scholar - 42.Venable, K.B., Volpato, M., Peintner, B., Yorke-Smith, N.: Weak and dynamic controllability of temporal problems with disjunctions and uncertainty. In: Proceedings of the Workshop on Constraint Satisfaction Techniques for Planning and Scheduling Problems (COPLAS-2010) in ICAPS-2010, pp. 50–59 (2010)Google Scholar
- 43.Venable, K.B., Yorke-Smith, N.: Disjunctive temporal planning with uncertainty. In: Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI-2005), pp. 1721–1722 (2005)Google Scholar
- 44.Vidal, T.: Controllability characterization and checking in contingent temporal constraint networks. In: KR, pp. 559–570 (2000)Google Scholar
- 45.Vidal, T., Fargier, H.: Contingent durations in temporal CSPS: from consistency to controllabilities. In: Proceedings of the 4th International Symposium on Temporal Representation and Reasoning (TIME-1997) (1997)Google Scholar
- 46.Vidal, T., Fargier, H.: Handling contingency in temporal constraint networks: from consistency to controllabilities. J. Exp. Theor. Artif. Intell.
**11**(1), 23–45 (1999)CrossRefzbMATHGoogle Scholar - 47.Vidal, T., Ghallab, M.: Temporal constraints in planning: free or not free? In: Proceedings of the International Workshop on Constraint-Based Reasoning (CONSTRAINT-1995) in FLAIRS-1995 (1995)Google Scholar
- 48.Vidal, T., Ghallab, M.: Dealing with uncertain durations in temporal constraint networks dedicated to planning. In: Wahlster, W. (ed.) Proceedings of the 12th European Conference on Artificial Intelligence (ECAI-1996), pp. 48–54. Wiley, Chichester (1996)Google Scholar