Introduction

Constraint-based temporal reasoning has been widely used in many different applications across many different domains. Over the years, different formalisms have been presented to address specific requirements that frequently arise in real-world applications. The most commonly used formalism is probably the Simple Temporal Network (STN), in which a set of real-valued variables, called time-points, are subject to binary difference constraints [1]. Time-points represent the occurrence of events (when a time-point is set to a value t, it means that the event occurred at the instant t and/or that the time-point is executed at the time t) while the binary difference constraints represent the temporal constraint between a pair of time-points (X-Y ≤ 10 means that X can occur 10-time units after Y at most).

The two main and interesting problems regarding STN are the consistency problem and the dispatchability one.

The consistency problem asks to determine if an STN admits one or more time-point assignments that satisfy all temporal constraints. In a consistent STN, for each time-point, it is possible to determine a range of possible execution instants for it (time-window).

The dispatchability problem asks to determine a dynamic schedule of the time-points, i.e., a schedule that, once a time-point is executed in an allowed instant, updates the time-windows of other unexecuted time-points guaranteeing that all time-points can be executed in order as time flows.

Recently, a significant amount of research has focused on temporal reasoning in the presence of uncertainty.
Temporal uncertainty arises, for example, when the duration of some activities (i.e., the duration of some temporal intervals) are not controlled by the executor of the network, but instead are only observed in real-time as the activities complete. In such settings, the executor seeks a dynamic strategy for executing the controllable time-points such that all relevant constraints will necessarily be satisfied no matter how the uncertain durations turn out. To accommodate this kind of uncertainty, STNs have been augmented to include contingent links, where each contingent link represents an interval whose duration is bounded but uncontrollable; the resulting network is called a Simple Temporal Network with Uncertainty (STNU) [2].
The most important property of an STNU is whether it is dynamically controllable (DC)—that is, whether there exists a strategy for executing the controllable time-points such that all relevant constraints are guaranteed to be satisfied no matter how the durations of the contingent links turn out.

Although STNUs have been successful in some domains, many domains require a richer set of constraints.
For example, in the healthcare domain, where workflow management systems are being developed to automate medical-treatment processes, medical tests for any given patient frequently generate information in real-time that can affect which pathway that patient will follow [3].
The system must guarantee that any possible execution of the workflow strictly satisfies all specified temporal constraints no matter which test outcomes are observed. A set of test outcomes is called scenario. The Conditional Simple Temporal Network (CSTN) model allows the representation of temporal constraints in conjunction with scenarios. In this way, it is possible to specify, for each possible scenario, a proper set of constraints that must be satisfied if the scenario occurs in an execution of the network. For CSTNs, different researches determined many results and algorithms for managing CSTNs properly [8], [9], [11], [12], [13], [15] [16].

The Conditional Simple Temporal Network with Uncertainty (CSTNU) model extends the CSTN one allowing the representation of contingent links. Different works determined properties and possible applications of CSTNUs [5], [6], [7], [10], [14].

The Conditional Simple Temporal Network with Partially Shrinkable Uncertainty (CSTNPSU) model extends the CSTNU one allowing each contingent link to have a wider range that can be shrunk a little at design/execution time for obtaining a successful execution.

The goal of this open-source project is to offer:

• a JAVA library for representing and checking temporal constraint networks of any above type: (C)STN(PS)(U);
• a graphical JAVA editor for designing and checking (C)STN(PS)(U) from scratch.

If you use this tool in your research, you are invited to cite this project giving this address and citing the paper [17] where I present this project in SoftwareX journal.

Benchmarks

Some algorithm implementations present in the tool have been tested using some benchmarks. In general, each benchmark is made of some temporal networks that were generated in a random way using some criteria. For each benchmark, we describe the building criteria, the characteristics of each random instance, the DC/NOT-DC property.

An analysis of the benchmarks and algorithm performances obtained in such benchmarks is available at Benchmarks.

The directory containing benchmarks is https://profs.scienze.univr.it/~posenato/software/benchmarks/

The articles in which such benchmarks are presented and use used are [9] [10] [11] [12] [13] [14] [15] [16].

Bibliography

[1] R. Dechter, I. Meiri, and J. Pearl, “Temporal constraint networks,” Artificial Intelligence, vol. 49, pp. 61–95, 1991.

[2] P. Morris, N. Muscettola, and T. Vidal, “Dynamic control of plans with temporal uncertainty,” in 17th International Joint Conference on Artificial Intelligence (IJCAI-01), Morgan Kaufmann, 2001, pp. 494–499.

[3] C. Combi, M. Gambini, S. Migliorini, and R. Posenato, “Representing business processes through a temporal data-centric workflow modeling language: An application to the management of clinical pathways,” Systems, Man, and Cybernetics: Systems, IEEE Transactions on,  2014. Available online: https://ieeexplore.ieee.org/xpl/abstractReferences.jsp?arnumber=6733362

[4] L. Hunsberger, R. Posenato, and C. Combi, “The Dynamic Controllability of Conditional STNs with Uncertainty,” in Workshop on Planning and Plan Execution for Real-World Systems: Principles and Practices (PlanEx) @ ICAPS-2012, Atibaia, Jun. 2012, pp. 1–8. Available online: https://arxiv.org/abs/1212.2005

[5] C. Combi, L. Hunsberger, and R. Posenato, “An algorithm for checking the dynamic controllability of a conditional simple temporal network with uncertainty,” in Proc. of the 5th Int. Conf. on Agents and Art. Int. (ICAART-2013), vol. 2, pp. 144–156, SCITEPRESS, Feb. 2013

[6] C. Combi, L. Hunsberger, and R. Posenato, “An algorithm for checking the dynamic controllability of a conditional simple temporal network with uncertainty-revisited,” in Agents and Artificial Intelligence, vol. 449 of Communications in Computer and Information Science, pp. 314–331, Springer-Verlag, 2014. Available online: https://doi.org/10.1007/978-3-662-44440-5_19

[7] A. Cimatti, L. Hunsberger, A. Micheli, R. Posenato, and M. Roveri, “Sound and complete algorithms for checking the dynamic controllability of temporal networks with uncertainty, disjunction and observation,” in 21st International Symposium on Temporal Representation and Reasoning (TIME 2014), pp. 27–36, IEEE Computer Society, Sept. 2014. Available online: https://doi.org/10.1109/TIME.2014.21

[8] L. Hunsberger, R. Posenato, and C. Combi, “A Sound-and-Complete Propagation-based Algorithm for Checking the Dynamic Consistency of Conditional Simple Temporal Networks,” in 22nd International Symposium on Temporal Representation and Reasoning (TIME 2015), pp. 4–18, IEEE Computer Society, Sept. 2015. Available online: https://doi.org/10.1109/TIME.2015.26

[9] L. Hunsberger and R. Posenato, “Checking the Dynamic Consistency of Conditional Simple Temporal Networks with Bounded Reaction Times”, in ICAPS 2016: International Conference on Automated Planning and Scheduling (ICAPS 2016), pp. 175–183, 2016. Available online: https://www.aaai.org/ocs/index.php/ICAPS/ICAPS16/paper/view/13108

[10] A. Cimatti, L. Hunsberger, A. Micheli, R. Posenato, and M. Roveri, ‘Dynamic controllability via Timed Game Automata’, Acta Inform., vol. 53, no. 6–8, pp. 681–722, Oct. 2016. Available online: https://dx.doi.org/10.1007/s00236-016-0257-2

[11] M. Cairo, L. Hunsberger, R. Posenato, and R. Rizzi, ‘A Streamlined Model of Conditional Simple Temporal Networks – Semantics and Equivalence Results’, in 24th International Symposium on Temporal Representation and Reasoning (TIME 2017), 2017, vol. 90, no. 10, pp. 1–10. Available online: https://dx.doi.org/10.4230/LIPIcs.TIME.2017.10

[12] M. Cairo, C. Combi, C. Comin, L. Hunsberger, R. Posenato, R. Rizzi, M. Zavatteri, ‘Incorporating Decision Nodes into Conditional Simple Temporal Networks’, in 24th International Symposium on Temporal Representation and Reasoning (TIME 2017), 2017, vol. 90, p. 9:1–9:18.
Available online: https://dx.doi.org/10.4230/LIPIcs.TIME.2017.9

[13] L. Hunsberger and R. Posenato, ‘Simpler and Faster Algorithm for Checking the Dynamic Consistency of Conditional Simple Temporal Networks’, in Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence, 2018, pp. 1324–1330. Available online: https://dx.doi.org/10.24963/ijcai.2018/184

[14] L. Hunsberger, R. Posenato, ‘Sound-and-Complete Algorithms for Checking the Dynamic Controllability of Conditional Simple Temporal Networks with Uncertainty, in 25th International Symposium on Temporal Representation and Reasoning (TIME 2018), 2018, vol. 120, no. 14, p. 1–17.
Available online: https://dx.doi.org/10.4230/LIPIcs.TIME.2018.14

[15] L. Hunsberger, R. Posenato, ‘Reducing ε-DC Checking for Conditional Simple Temporal Networks to DC Checking’, in 25th International Symposium on Temporal Representation and Reasoning (TIME 2018), 2018, vol. 120, no. 15, pp. 1–15. Available online: https://dx.doi.org/10.4230/LIPIcs.TIME.2018.15

[16] L. Hunsberger and R. Posenato, ‘Faster Dynamic-Consistency Checking for Conditional Simple Temporal Networks‘, in ICAPS 2020: International Conference on Automated Planning and Scheduling (ICAPS 2020), 2020.

[17] R. Posenato, ‘CSTNU Tool: A Java library for checking temporal networks‘, SoftwareX 17, 100905. 2022. https://doi.org/10.1016/j.softx.2021.100905