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Complete Volume

**Published in:** LIPIcs, Volume 278, 30th International Symposium on Temporal Representation and Reasoning (TIME 2023)

LIPIcs, Volume 278, TIME 2023, Complete Volume

30th International Symposium on Temporal Representation and Reasoning (TIME 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 278, pp. 1-254, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Proceedings{artikis_et_al:LIPIcs.TIME.2023, title = {{LIPIcs, Volume 278, TIME 2023, Complete Volume}}, booktitle = {30th International Symposium on Temporal Representation and Reasoning (TIME 2023)}, pages = {1--254}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-298-3}, ISSN = {1868-8969}, year = {2023}, volume = {278}, editor = {Artikis, Alexander and Bruse, Florian and Hunsberger, Luke}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2023}, URN = {urn:nbn:de:0030-drops-190890}, doi = {10.4230/LIPIcs.TIME.2023}, annote = {Keywords: LIPIcs, Volume 278, TIME 2023, Complete Volume} }

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Front Matter

**Published in:** LIPIcs, Volume 278, 30th International Symposium on Temporal Representation and Reasoning (TIME 2023)

Front Matter, Table of Contents, Preface, Conference Organization

30th International Symposium on Temporal Representation and Reasoning (TIME 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 278, pp. 0:i-0:xiv, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{artikis_et_al:LIPIcs.TIME.2023.0, author = {Artikis, Alexander and Bruse, Florian and Hunsberger, Luke}, title = {{Front Matter, Table of Contents, Preface, Conference Organization}}, booktitle = {30th International Symposium on Temporal Representation and Reasoning (TIME 2023)}, pages = {0:i--0:xiv}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-298-3}, ISSN = {1868-8969}, year = {2023}, volume = {278}, editor = {Artikis, Alexander and Bruse, Florian and Hunsberger, Luke}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2023.0}, URN = {urn:nbn:de:0030-drops-190907}, doi = {10.4230/LIPIcs.TIME.2023.0}, annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization} }

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Extended Abstract

**Published in:** LIPIcs, Volume 278, 30th International Symposium on Temporal Representation and Reasoning (TIME 2023)

In many sectors of real-world industry, it is necessary to plan and schedule tasks allocated to agents participating in complex processes. Temporal planning aims to schedule tasks while respecting temporal constraints such as release times, maximum durations, and deadlines, which requires quantitative temporal reasoning. Over the years, several major application developers have highlighted the need for the explicit representation of actions with uncertain durations; efficient algorithms for determining whether plans involving such actions are controllable; and efficient algorithms for converting such plans into forms that enable them to be executed in real time with minimal computation, while preserving maximum flexibility.
A Simple Temporal Network with Uncertainty (STNU) is a data structure for reasoning about time constraints on actions that may have uncertain durations. An STNU is a triple (𝒯, 𝒞, ℒ) where 𝒯 is a set of real-valued variables called timepoints, 𝒞 is a set of constraints of the form Y-X ≤ δ, where X, Y ∈ 𝒯 and δ ∈ 𝐑, and ℒ is a set of contingent links of the form (A,x,y,C), where A,C ∈ 𝒯 and 0 < x < y < ∞. A contingent link (A,x,y,C) represents an uncertain duration where A is the activation timepoint, C is the contingent timepoint, and y-x is the uncertainty in the duration C-A. Typically, an executor controls the execution of A, but only observes the execution of C in real time. Although uncontrollable, the duration is guaranteed to satisfy C-A ∈ [x,y]. We let n = |𝒯|, m = |𝒞| and k = |ℒ|.
An STNU graph is a pair (𝒯, ℰ), where the timepoints in 𝒯 serve as nodes in the graph, and the edges in ℰ correspond to the constraints in 𝒞 and contingent links in ℒ. For each Y-X ≤ δ in 𝒞, ℰ contains an ordinary edge X-δ->Y. For each (A,x,y,C) ∈ ℒ, ℰ contains a lower-case (LC) edge, A-c:y->C, and an upper-case (UC) edge, C-C:-y->A, representing the respective possibilities that C-A might take its minimum or maximum value. The LO-edges are the LC or ordinary edges; the OU-edges are the ordinary or UC edges.
For any STNU, it is important to determine whether it is dynamically controllable (DC) (i.e., whether it is possible, in real time, to schedule its non-contingent timepoints such that all constraints will necessarily be satisfied no matter what durations turn out for the contingent links). Polynomial-time algorithms are available to solve this DC-checking problem. Each uses rules to generate new edges aiming to bypass certain kinds of edges in the STNU graph. Morris' O(n⁴)-time DC-checking algorithm [Paul Morris, 2006] starts from LC edges, propagating forward along OU-edges, looking for opportunities to generate new OU-edges that bypass the LC edges. Morris' O(n³)-time algorithm [Morris, 2014] starts from negative OU-edges, propagating backward along LO-edges, aiming to bypass negative edges with non-negative edges. The O(mn+k²n + knlog n)-time RUL¯ algorithm [Massimo Cairo et al., 2018] starts from UC edges, propagating backward along LO-edges, aiming to bypass UC edges with ordinary edges. After propagating, each algorithm checks for certain kinds of negative cycles to decide DC-vs.-non-DC.
However, being DC only asserts the existence of a dynamic scheduler. It is also crucial to be able to execute a DC STNU efficiently in real time. For maximum flexibility and minimal space and time requirements, a dynamic scheduler for an STNU is typically computed incrementally, in real time, so that it can react to observations of contingent executions as they occur. An efficient dynamic scheduler can be realized by first transforming an STNU into an equivalent dispatchable form [Muscettola et al., 1998; Ioannis Tsamardinos et al., 1998]. Then, to execute the dispatchable STNU, it suffices to maintain time-windows for each timepoint and, as each timepoint X is executed, only updating time-windows for neighbors of X in the graph. Dispatchable STNUs are very important in applications that demand quick responses to observations of contingent events.
Of the existing DC-checking algorithms, only Morris' O(n³)-time algorithm necessarily generates a dispatchable STNU for DC inputs. This abstract describes a faster, O(mn + kn² + n² log n)-time algorithm for converting DC STNUs into dispatchable form. (The full journal article is available elsewhere [Luke Hunsberger and Roberto Posenato, 2023].) This improvement is significant for applications (e.g., modeling business processes) where networks are typically sparse. For example, if m = O(n log n) and k = O(log n), then our algorithm runs in O(n²log n) ≪ O(n³) time.
Our new Fast Dispatch algorithm, FD_STNU, has three phases. The first phase is similar to the RUL¯ DC-checking algorithm, but generates an order-of-magnitude fewer edges overall, while also generating new UC edges that correspond to wait constraints. The second phase is a version of Morris' 2006 algorithm that propagates forward from LC edges, but only along LO-edges, aiming to generate ordinary bypass edges. The third phase focuses on the subgraph of ordinary edges, which comprise a Simple Temporal Network (STN). It uses an existing dispatchability algorithm for STNs [Ioannis Tsamardinos et al., 1998] to convert that ordinary subgraph into a dispatchable STN. After completing the three phases, the STNU is guaranteed to be dispatchable.
We provide the source code of a Java implementation of the considered algorithms (Morris, RUL¯, and FD_STNU) [Posenato, 2022] and the benchmarks used to compare their performances.

Luke Hunsberger and Roberto Posenato. Converting Simple Temporal Networks with Uncertainty into Dispatchable Form - Faster (Extended Abstract). In 30th International Symposium on Temporal Representation and Reasoning (TIME 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 278, pp. 20:1-20:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{hunsberger_et_al:LIPIcs.TIME.2023.20, author = {Hunsberger, Luke and Posenato, Roberto}, title = {{Converting Simple Temporal Networks with Uncertainty into Dispatchable Form - Faster}}, booktitle = {30th International Symposium on Temporal Representation and Reasoning (TIME 2023)}, pages = {20:1--20:3}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-298-3}, ISSN = {1868-8969}, year = {2023}, volume = {278}, editor = {Artikis, Alexander and Bruse, Florian and Hunsberger, Luke}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2023.20}, URN = {urn:nbn:de:0030-drops-191104}, doi = {10.4230/LIPIcs.TIME.2023.20}, annote = {Keywords: Temporal constraint networks, contingent durations, dispatchable network} }

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Invited Talk

**Published in:** LIPIcs, Volume 206, 28th International Symposium on Temporal Representation and Reasoning (TIME 2021)

Since Simple Temporal Networks (STNs) were first introduced in 1991, there have been numerous theoretic and algorithmic advances that have made them practical for a wide variety of applications. However, the presentation of most of the important advances have been scattered across numerous conference papers and journal articles. As a result, it is too easy for even experienced researchers to be unaware of results that could positively impact their work. In this talk we review the most important results about STNs for researchers in Artificial Intelligence who are interested in incorporating the management of time and temporal constraints into their projects.

Luke Hunsberger and Roberto Posenato. Simple Temporal Networks: A Practical Foundation for Temporal Representation and Reasoning (Invited Talk). In 28th International Symposium on Temporal Representation and Reasoning (TIME 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 206, pp. 1:1-1:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{hunsberger_et_al:LIPIcs.TIME.2021.1, author = {Hunsberger, Luke and Posenato, Roberto}, title = {{Simple Temporal Networks: A Practical Foundation for Temporal Representation and Reasoning}}, booktitle = {28th International Symposium on Temporal Representation and Reasoning (TIME 2021)}, pages = {1:1--1:5}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-206-8}, ISSN = {1868-8969}, year = {2021}, volume = {206}, editor = {Combi, Carlo and Eder, Johann and Reynolds, Mark}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2021.1}, URN = {urn:nbn:de:0030-drops-147770}, doi = {10.4230/LIPIcs.TIME.2021.1}, annote = {Keywords: Simple Temporal Networks, Consistency Checking, Restoring Consistency, Dispatchability, Temporal Decoupling Problem} }

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**Published in:** LIPIcs, Volume 120, 25th International Symposium on Temporal Representation and Reasoning (TIME 2018)

Simple Temporal Networks (STNs) are a well-studied model for representing and reasoning about time. An STN comprises a set of real-valued variables called time-points, together with a set of binary constraints, each of the form Y <= X+w. The problem of finding a feasible schedule (i.e., an assignment of real numbers to time-points such that all of the constraints are satisfied) is equivalent to the Single Source Shortest Path problem (SSSP) in the STN graph.
Simple Temporal Networks with Uncertainty (STNUs) augment STNs to include contingent links that can be used, for example, to represent actions with uncertain durations. The duration of a contingent link is not controlled by the planner, but is instead controlled by a (possibly adversarial) environment. Each contingent link has the form, <A,l,u,C>, where 0 < l <= u < infty. Once the planner executes the activation time-point A, the environment must execute the contingent time-point C at some time A+Delta, where Delta in [l,u]. Crucially, the planner does not know the value of Delta in advance, but only discovers it when C executes. An STNU is dynamically controllable (DC) if there is a strategy that the planner can use to execute all of the non-contingent time-points, such that all of the constraints are guaranteed to be satisfied no matter which durations the environment chooses for the contingent links. The strategy can be dynamic in that it can react in real time to the contingent durations it observes. Recently, an upper bound of O(N^3) was given for the DC-checking problem for STNUs, where N is the number of time-points.
This paper introduces a new algorithm, called the RUL^- algorithm, for solving the DC-checking problem for STNUs that improves on the O(N^3) bound. The worst-case complexity of the RUL^- algorithm is O(MN+K^2N+KN log N), where N is the number of time-points, M is the number of constraints, and K is the number of contingent time-points. If M is O(N^2), then the complexity reduces to O(N^3); however, in sparse graphs the complexity can be much less. For example, if M is O(N log N), and K is O(sqrt{N}), then the complexity of the RUL^- algorithm reduces to O(N^2 log N).
The RUL^- algorithm begins by using the Bellman-Ford algorithm to compute a potential function. It then performs at most 2K rounds of computations, interleaving novel applications of Dijkstra's algorithm to (1) generate new edges and (2) update the potential function in response to those new edges. The constraint-propagation/edge-generation rules used by the RUL^- algorithm are distinguished from related work in two ways. First, they only generate unlabeled edges. Second, their applicability conditions are more restrictive. As a result, the RUL^- algorithm requires only O(K) rounds of Dijkstra's algorithm, instead of the O(N) rounds required by other approaches. The paper proves that the RUL^- algorithm is sound and complete for the DC-checking problem for STNUs.

Massimo Cairo, Luke Hunsberger, and Romeo Rizzi. Faster Dynamic Controllability Checking for Simple Temporal Networks with Uncertainty. In 25th International Symposium on Temporal Representation and Reasoning (TIME 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 120, pp. 8:1-8:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{cairo_et_al:LIPIcs.TIME.2018.8, author = {Cairo, Massimo and Hunsberger, Luke and Rizzi, Romeo}, title = {{Faster Dynamic Controllability Checking for Simple Temporal Networks with Uncertainty}}, booktitle = {25th International Symposium on Temporal Representation and Reasoning (TIME 2018)}, pages = {8:1--8:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-089-7}, ISSN = {1868-8969}, year = {2018}, volume = {120}, editor = {Alechina, Natasha and N{\o}rv\r{a}g, Kjetil and Penczek, Wojciech}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2018.8}, URN = {urn:nbn:de:0030-drops-97734}, doi = {10.4230/LIPIcs.TIME.2018.8}, annote = {Keywords: Simple Temporal Networks with Uncertainty, Dynamic Controllability, Temporal Planning under Uncertainty} }

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**Published in:** LIPIcs, Volume 120, 25th International Symposium on Temporal Representation and Reasoning (TIME 2018)

A Conditional Simple Temporal Network with Uncertainty (CSTNU) is a data structure for representing and reasoning about time. CSTNUs incorporate observation time-points from Conditional Simple Temporal Networks (CSTNs) and contingent links from Simple Temporal Networks with Uncertainty (STNUs). A CSTNU is dynamically controllable (DC) if there exists a strategy for executing its time-points that guarantees the satisfaction of all relevant constraints no matter how the uncertainty associated with its observation time-points and contingent links is resolved in real time. This paper presents the first sound-and-complete DC-checking algorithms for CSTNUs that are based on the propagation of labeled constraints and demonstrates their practicality.

Luke Hunsberger and Roberto 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). Leibniz International Proceedings in Informatics (LIPIcs), Volume 120, pp. 14:1-14:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{hunsberger_et_al:LIPIcs.TIME.2018.14, author = {Hunsberger, Luke and Posenato, Roberto}, title = {{Sound-and-Complete Algorithms for Checking the Dynamic Controllability of Conditional Simple Temporal Networks with Uncertainty}}, booktitle = {25th International Symposium on Temporal Representation and Reasoning (TIME 2018)}, pages = {14:1--14:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-089-7}, ISSN = {1868-8969}, year = {2018}, volume = {120}, editor = {Alechina, Natasha and N{\o}rv\r{a}g, Kjetil and Penczek, Wojciech}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2018.14}, URN = {urn:nbn:de:0030-drops-97795}, doi = {10.4230/LIPIcs.TIME.2018.14}, annote = {Keywords: Temporal Networks, Conditional Simple Temporal Problem with Uncertainty, Dynamic Controllability, Checking Algorithm} }

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**Published in:** LIPIcs, Volume 120, 25th International Symposium on Temporal Representation and Reasoning (TIME 2018)

Recent work on Conditional Simple Temporal Networks (CSTNs) has introduced the problem of checking the dynamic consistency (DC) property for the case where the reaction time of an execution strategy to observations is bounded below by some fixed epsilon > 0, the so-called epsilon-DC-checking problem. This paper proves that the epsilon-DC-checking problem for CSTNs can be reduced to the standard DC-checking problem for CSTNs - without incurring any computational cost. Given any CSTN S with k observation time-points, the paper defines a new CSTN S_0 that is the same as S, except that for each observation time-point P? in S: (i) P? is demoted to a non-observation time-point in S_0; and (ii) a new observation time-point P_0?, constrained to occur exactly epsilon units after P?, is inserted into S_0. The paper proves that S is epsilon-DC if and only if S_0 is (standard) DC, and that the application of the epsilon-DC-checking constraint-propagation rules to S is equivalent to the application of the corresponding (standard) DC-checking constraint-propagation rules to S_0. Two versions of these results are presented that differ only in whether a dynamic strategy for S_0 can react instantaneously to observations, or only after some arbitrarily small, positive delay. Finally, the paper demonstrates empirically that building S_0 and DC-checking it incurs no computational cost as the sizes of the instances increase.

Luke Hunsberger and Roberto Posenato. Reducing epsilon-DC Checking for Conditional Simple Temporal Networks to DC Checking. In 25th International Symposium on Temporal Representation and Reasoning (TIME 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 120, pp. 15:1-15:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{hunsberger_et_al:LIPIcs.TIME.2018.15, author = {Hunsberger, Luke and Posenato, Roberto}, title = {{Reducing epsilon-DC Checking for Conditional Simple Temporal Networks to DC Checking}}, booktitle = {25th International Symposium on Temporal Representation and Reasoning (TIME 2018)}, pages = {15:1--15:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-089-7}, ISSN = {1868-8969}, year = {2018}, volume = {120}, editor = {Alechina, Natasha and N{\o}rv\r{a}g, Kjetil and Penczek, Wojciech}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2018.15}, URN = {urn:nbn:de:0030-drops-97808}, doi = {10.4230/LIPIcs.TIME.2018.15}, annote = {Keywords: Conditional Simple Temporal Networks, Dynamic Consistency, Temporal Constraints} }

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**Published in:** LIPIcs, Volume 90, 24th International Symposium on Temporal Representation and Reasoning (TIME 2017)

A Conditional Simple Temporal Network (CSTN) augments a Simple Temporal Network (STN) to include special time-points, called observation time-points. In a CSTN, the agent executing the network controls the execution of every time-point. However, each observation time-point has a unique propositional letter associated with it and, when the agent executes that time-point, the environment assigns a truth value to the corresponding letter. Thus, the agent observes but, does not control the assignment of truth values. A CSTN is dynamically consistent (DC) if there exists a strategy for executing its time-points such that all relevant constraints will be satisfied no matter which truth values the environment assigns to the propositional letters.
Alternatively, in a Labeled Simple Temporal Network (Labeled STN) - also called a Temporal Plan with Choice - the agent executing the network controls the assignment of values to the so-called choice variables. Furthermore, the agent can make those assignments at any time. For this reason, a Labeled STN is equivalent to a Disjunctive Temporal Network.
This paper incorporates both of the above extensions by augmenting a CSTN to include not only observation time-points but also decision time-points. A decision time-point is like an observation time-point in that it has an associated propositional letter whose value is determined when the decision time-point is executed. It differs in that the agent - not the environment - selects that value. The resulting network is called a CSTN with Decisions (CSTND). This paper shows that a CSTND generalizes both CSTNs and Labeled STNs, and proves that the problem of determining whether any given CSTND is dynamically consistent is PSPACE-complete. It also presents algorithms that address two sub-classes of CSTNDs:
(1) those that contain only decision time-points; and (2) those in which all decisions are made before execution begins.

Massimo Cairo, Carlo Combi, Carlo Comin, Luke Hunsberger, Roberto Posenato, Romeo Rizzi, and Matteo Zavatteri. Incorporating Decision Nodes into Conditional Simple Temporal Networks. In 24th International Symposium on Temporal Representation and Reasoning (TIME 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 90, pp. 9:1-9:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{cairo_et_al:LIPIcs.TIME.2017.9, author = {Cairo, Massimo and Combi, Carlo and Comin, Carlo and Hunsberger, Luke and Posenato, Roberto and Rizzi, Romeo and Zavatteri, Matteo}, title = {{Incorporating Decision Nodes into Conditional Simple Temporal Networks}}, booktitle = {24th International Symposium on Temporal Representation and Reasoning (TIME 2017)}, pages = {9:1--9:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-052-1}, ISSN = {1868-8969}, year = {2017}, volume = {90}, editor = {Schewe, Sven and Schneider, Thomas and Wijsen, Jef}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2017.9}, URN = {urn:nbn:de:0030-drops-79155}, doi = {10.4230/LIPIcs.TIME.2017.9}, annote = {Keywords: Conditional Simple Temporal Networks with Decisions, Dynamic Consistency, SAT Solver, Hyper Temporal Networks, PSPACE} }

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**Published in:** LIPIcs, Volume 90, 24th International Symposium on Temporal Representation and Reasoning (TIME 2017)

A Conditional Simple Temporal Network (CSTN) augments a Simple Temporal Network to include a new kind of time-points, called observation time-points. The execution of an observation time-point generates information in real time, specifically, the truth value of a propositional letter. In addition, time-points and temporal constraints may be labeled by conjunctions of (positive or negative) propositional letters. A CSTN is called dynamically consistent (DC) if there exists a dynamic strategy for executing its time-points such that no matter how the observations turn out during execution, the time-points whose labels are consistent with those observations have all been executed, and the constraints whose labels are consistent with those observations have all been satisfied. The strategy is dynamic in that its execution decisions may react to observations.
The original formulation of CSTNs included propositional labels only on time-points, but the DC-checking algorithm was impractical because it was based on a conversion of the semantic constraints into an exponentially-sized Disjunctive Temporal Network. Later work added propositional labels to temporal constraints, and yielded a sound-and-complete propagation-based DC-checking algorithm, empirically demonstrated to be practical across a variety of CSTNs.
This paper introduces a streamlined version of a CSTN in which propositional labels may appear on constraints, but not on time-points. This change simplifies the definition of the DC property, as well as the propagation rules for the DC-checking algorithm. It also simplifies the proofs of the soundness and completeness of those rules.
This paper provides two translations from traditional CSTNs to streamlined CSTNs. Each translation preserves the DC property and, for any DC network, ensures that any dynamic execution strategy for that network can be extended to a strategy for its streamlined counterpart.
Finally, this paper presents an empirical comparison of two versions of the DC-checking algorithm: the original version and a simplified version for streamlined CSTNs. The comparison is based on CSTN benchmarks from earlier work. For small-sized CSTNs, the original version shows the best performance, but the performance difference between the two versions decreases as the number of time-points in the CSTN increases. We conclude that the simplified algorithm is a practical alternative for checking the dynamic consistency of CSTNs.

Massimo Cairo, Luke Hunsberger, Roberto Posenato, and Romeo Rizzi. A Streamlined Model of Conditional Simple Temporal Networks - Semantics and Equivalence Results. In 24th International Symposium on Temporal Representation and Reasoning (TIME 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 90, pp. 10:1-10:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{cairo_et_al:LIPIcs.TIME.2017.10, author = {Cairo, Massimo and Hunsberger, Luke and Posenato, Roberto and Rizzi, Romeo}, title = {{A Streamlined Model of Conditional Simple Temporal Networks - Semantics and Equivalence Results}}, booktitle = {24th International Symposium on Temporal Representation and Reasoning (TIME 2017)}, pages = {10:1--10:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-052-1}, ISSN = {1868-8969}, year = {2017}, volume = {90}, editor = {Schewe, Sven and Schneider, Thomas and Wijsen, Jef}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2017.10}, URN = {urn:nbn:de:0030-drops-79145}, doi = {10.4230/LIPIcs.TIME.2017.10}, annote = {Keywords: Conditional Simple Temporal Networks, Dynamic Consistency, Temporal Constraints} }

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