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Faster Dynamic-Consistency Checking for Conditional Simple Temporal Networks Luke Hunsberger 1 Roberto Posenato 2 1 Department of Computer Science, Vassar College, Poughkeepsie, NY, USA 2 Department of Computer Science, University of Verona, Italy

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Faster Dynamic-Consistency Checking for Conditional Simple Temporal Networks

Luke Hunsberger1 Roberto Posenato2

1Department of Computer Science, Vassar College, Poughkeepsie, NY, USA 2Department of Computer Science, University of Verona, Italy

ICAPS 2020

  • L. Hunsberger, R. Posenato

Faster Dynamic-Consistency Checking for CSTN

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Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions

Conditional Simple Temporal Networks (CSTNs)

Tsamardinos et al. (2003) [6], Hunsberger et al. (2015) [5]

A CSTN is like a Simple Temporal Network (STN), except that: Some time-points are observation time-points (OTPs), and Constraints can be labeled by conjunctions of propositional literals. Example

Z P? Q? Y U W V

0, ⊡ −10, p¬q 10, pq −10, p 3, p −7, ¬p 12, ¬p −10, ¬p

  • 5

, ¬ p

  • −

7 , p

  • L. Hunsberger, R. Posenato

Faster Dynamic-Consistency Checking for CSTN 1 / 10

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Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions

CSTNs–continued

Each OTP P? has a corresponding propositional letter p. Executing P? generates a truth value for p. As OTPs are executed and truth values incrementally revealed, a complete scenario is eventually determined. A constraint labeled by, say, p(¬q) need only hold in scenarios where p is true, and q is false. Example

Z P? Q? Y U W V

0, ⊡ −10, p¬q 10, pq −10, p 3, p −7, ¬p 12, ¬p −10, ¬p

  • 5

, ¬ p

  • −

7 , p

  • L. Hunsberger, R. Posenato

Faster Dynamic-Consistency Checking for CSTN 2 / 10

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Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions

Dynamic Consistency of CSTNs

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 scenario is eventually revealed.

The π-DC semantics of Cairo et al. (2017) [1] allows execution strategies that can react instantaneously to observations. Existing π-DC-checking algorithms

The HP18 Algorithm (Hunsberger & Posenato, 2018) [3] The HP19 Algorithm (Hunsberger & Posenato, 2019) [4]

  • L. Hunsberger, R. Posenato

Faster Dynamic-Consistency Checking for CSTN 3 / 10

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Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions

The HP18 Algorithm

Hunsberger & Posenato (2018) [3]

Only generates constraints involving Z (the zero time-point) Propagation can generate q-labeled constraints (e.g., (?p)q(¬r)). A constraint labeled by (?p)q(¬r) must hold as long as p is not yet known, q is true or not yet known, and r is false or not yet known. The ⋆ operator generalizes conjunction to q-labeled constraints. Example: (p(¬q)r(?t)) ⋆ ((¬p)q(¬s)) = (?p)(?q)r(¬s)(?t) The HP18 algorithm is sound and complete, but can get bogged down cycling through negative q-loops.

  • L. Hunsberger, R. Posenato

Faster Dynamic-Consistency Checking for CSTN 4 / 10

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Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions

The HP18 Algorithm

Simulation Z P? X Q? Y

−13 −13 −3, ¬q 1, q −5, ¬p 2, p

  • L. Hunsberger, R. Posenato

Faster Dynamic-Consistency Checking for CSTN 5 / 10

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Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions

The HP18 Algorithm

Simulation Z P? X Q? Y

−13 −13 −3, ¬q 1, q −5, ¬p 2, p −11, p

  • L. Hunsberger, R. Posenato

Faster Dynamic-Consistency Checking for CSTN 5 / 10

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Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions

The HP18 Algorithm

Simulation Z P? X Q? Y

−13 −13 −3, ¬q 1, q −5, ¬p 2, p −11, p −11

  • L. Hunsberger, R. Posenato

Faster Dynamic-Consistency Checking for CSTN 5 / 10

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Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions

The HP18 Algorithm

Simulation Z P? X Q? Y

−13 −13 −3, ¬q 1, q −5, ¬p 2, p −11, p −11 −16, ¬p

  • L. Hunsberger, R. Posenato

Faster Dynamic-Consistency Checking for CSTN 5 / 10

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Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions

The HP18 Algorithm

Simulation Z P? X Q? Y

−13 −13 −3, ¬q 1, q −5, ¬p 2, p −11, p −11 −16, ¬p −12, q

  • L. Hunsberger, R. Posenato

Faster Dynamic-Consistency Checking for CSTN 5 / 10

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Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions

The HP18 Algorithm

Simulation Z P? X Q? Y

−13 −13 −3, ¬q 1, q −5, ¬p 2, p −11, p −11 −16, ¬p −12, q −12

  • L. Hunsberger, R. Posenato

Faster Dynamic-Consistency Checking for CSTN 5 / 10

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Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions

The HP18 Algorithm

Simulation Z P? X Q? Y

−13 −13 −3, ¬q 1, q −5, ¬p 2, p −11, p −11 −16, ¬p −12, q −12 −15, ¬q

  • L. Hunsberger, R. Posenato

Faster Dynamic-Consistency Checking for CSTN 5 / 10

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Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions

The HP18 Algorithm

Simulation Z P? X Q? Y

−13 −13 −3, ¬q 1, q −5, ¬p 2, p −11, p −11 −16, ¬p −15, ¬q −12, q −12 −15, ¬q

  • L. Hunsberger, R. Posenato

Faster Dynamic-Consistency Checking for CSTN 5 / 10

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Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions

The HP18 Algorithm

Simulation Z P? X Q? Y

−13 −13 −3, ¬q 1, q −5, ¬p 2, p −11, p −11 −16, ¬p −15, ¬q −15 −12, q −12 −15, ¬q

  • L. Hunsberger, R. Posenato

Faster Dynamic-Consistency Checking for CSTN 5 / 10

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Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions

The HP18 Algorithm

Simulation Z P? X Q? Y

−13 −13 −3, ¬q 1, q −5, ¬p 2, p −11, p −11 −16, ¬p −15, ¬q −15 −12, q −12 −15, ¬q −15, ¬p

  • L. Hunsberger, R. Posenato

Faster Dynamic-Consistency Checking for CSTN 5 / 10

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Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions

The HP18 Algorithm

Simulation Z P? X Q? Y

−13 −13 −3, ¬q 1, q −5, ¬p 2, p −11, p −11 −16, ¬p −15, ¬q −15 −12, q −12 −15, ¬q −15, ¬p −15

  • L. Hunsberger, R. Posenato

Faster Dynamic-Consistency Checking for CSTN 5 / 10

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Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions

The HP18 Algorithm

Simulation Z P? X Q? Y

−13 −13 −3, ¬q 1, q −5, ¬p 2, p −11, p −11 −16, ¬p −15, ¬q −15 −12, q −12 −15, ¬q −15, ¬p −15

  • L. Hunsberger, R. Posenato

Faster Dynamic-Consistency Checking for CSTN 5 / 10

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Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions

The HP19 Algorithm

Hunsberger & Posenato (2019) [4]

Goal: Recognize negative q-loops. New rule leads to immediate value of −∞ on certain self-loops Example: X

−∞, p(?q)(?r)

W

−8, p(¬q)r 2, q(¬r)

Meaning: X must not be executed as long as p might be true, and q and r are both unknown.

Propagation rules extended to allow propagating −∞ values. Example: X

−∞, p(?q)

W

−3, ¬p −∞, (?p)(?q)

Propagation rules generate edges between any time-points —not just edges aimed at Z. HP19 not empirically evaluated (was not main focus of paper).

  • L. Hunsberger, R. Posenato

Faster Dynamic-Consistency Checking for CSTN 6 / 10

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Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions

The HP19 Algorithm

Simulation Z P? X Q? Y

−13 −13 −3, ¬q 1, q −5, ¬p 2, p −∞, ?p −∞, ?q

  • L. Hunsberger, R. Posenato

Faster Dynamic-Consistency Checking for CSTN 7 / 10

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Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions

The HP19 Algorithm

Simulation Z P? X Q? Y

−13 −13 −3, ¬q 1, q −5, ¬p 2, p −∞, ?p −∞, ?q

  • L. Hunsberger, R. Posenato

Faster Dynamic-Consistency Checking for CSTN 7 / 10

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Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions

The HP19 Algorithm

Simulation Z P? X Q? Y

−13 −13 −3, ¬q 1, q −5, ¬p 2, p −∞, ?p −∞, ?q −∞, ?p

  • L. Hunsberger, R. Posenato

Faster Dynamic-Consistency Checking for CSTN 7 / 10

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Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions

The HP19 Algorithm

Simulation Z P? X Q? Y

−13 −13 −3, ¬q 1, q −5, ¬p 2, p −∞, ?p −∞, ?q −∞, ?p

  • L. Hunsberger, R. Posenato

Faster Dynamic-Consistency Checking for CSTN 7 / 10

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Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions

The HP19 Algorithm

Simulation Z P? X Q? Y

−13 −13 −3, ¬q 1, q −5, ¬p 2, p −∞, ?p −∞, ?q −∞, ?p −∞, ?q

  • L. Hunsberger, R. Posenato

Faster Dynamic-Consistency Checking for CSTN 7 / 10

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Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions

The HP19 Algorithm

Simulation Z P? X Q? Y

−13 −13 −3, ¬q 1, q −5, ¬p 2, p −∞, ?p −∞, ?q −∞, ?p −∞, ?q −∞, ?q

  • L. Hunsberger, R. Posenato

Faster Dynamic-Consistency Checking for CSTN 7 / 10

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Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions

The HP19 Algorithm

Simulation Z P? X Q? Y

−13 −13 −3, ¬q 1, q −5, ¬p 2, p −∞, ?p −∞, ?q −∞, ?p −∞, ?q −∞, ?p −∞, ?q

  • L. Hunsberger, R. Posenato

Faster Dynamic-Consistency Checking for CSTN 7 / 10

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Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions

The HP19 Algorithm

Simulation Z P? X Q? Y

−13 −13 −3, ¬q 1, q −5, ¬p 2, p −∞, ?p −∞, ?q −∞, ?p −∞, ?q −∞ −∞, ?p −∞, ?q

  • L. Hunsberger, R. Posenato

Faster Dynamic-Consistency Checking for CSTN 7 / 10

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Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions

The HP19 Algorithm

Simulation Z P? X Q? Y

−13 −13 −3, ¬q 1, q −5, ¬p 2, p −∞, ?p −∞, ?q −∞, ?p −∞, ?q −∞ −∞ −∞, ?p −∞, ?q

  • L. Hunsberger, R. Posenato

Faster Dynamic-Consistency Checking for CSTN 7 / 10

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Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions

The HP19 Algorithm

Simulation Z P? X Q? Y

−13 −13 −3, ¬q 1, q −5, ¬p 2, p −∞, ?p −∞, ?q −∞, ?p −∞, ?q −∞ −∞ −∞, ?p −∞, ?q

  • L. Hunsberger, R. Posenato

Faster Dynamic-Consistency Checking for CSTN 7 / 10

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Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions

The HP20 Algorithm

Observation: Semantics of edge labeled by −∞, α depends only

  • n source node, not on target node.

Thus, much propagation of −∞, α by HP19 is redundant. Solution:

Associate −∞, α with node, not edge. NQLFinder: pre-process that discovers some negative q-loops, generating −∞, α values for some nodes. All remaining propagation generates edges aimed only at Z. Such edges can be viewed as providing potentials for nodes. Main algorithm focuses exclusively on labeled values for nodes —not labeled values on edges.

  • L. Hunsberger, R. Posenato

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Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions

Empirical Evaluation — Sample Results

43 59 75 91 107 123 139 155 0.3s 3s 30s 1m 5m

Benchmark 1 N=10, |P|=3 Benchmark 2 N=20, |P|=5 Benchmark 3 N=30, |P|=7 Benchmark 4 N=40, |P|=9

n

Execution time

HP18 HP19 HP20

All algorithms implemented in Java, freely available. Each plotted point represents the average execution time over 250 DC-instances generated from random workflows [2].

  • L. Hunsberger, R. Posenato

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Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions

Conclusions: DC-checking for CSTNs

The HP18 algorithm can get bogged down, cycling through negative q-loops. The HP19 algorithm can avoid cycling through certain negative q-loops, but does lots of redundant propagation of −∞, α values. The new HP20 algorithm is significantly faster than HP18 and HP19 across existing benchmarks and a new set of benchmarks.

HP20 more efficiently identifies negative q-loops and more efficiently manages the propagation of labeled values of the form −∞, α. HP20, unlike previous algorithms, only updates labeled values—whether finite or infinite—on nodes, not edges.

  • L. Hunsberger, R. Posenato

Faster Dynamic-Consistency Checking for CSTN 10 / 10

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References

References I

[1] Massimo Cairo, Luke Hunsberger, Roberto Posenato, and Romeo Rizzi. A Streamlined Model of Conditional Simple Temporal Networks - Semantics and Equivalence Results. In 24th Int. Symp. on Temporal Representation and Reasoning (TIME-2017), volume 90 of LIPIcs, pages 10:1–10:19, 2017. [2] Luke Hunsberger and Roberto Posenato. Checking the dynamic consistency of conditional temporal networks with bounded reaction times. In Amanda Jane Coles, Andrew Coles, Stefan Edelkamp, Daniele Magazzeni, and Scott Sanner, editors, 26th Int. Conf. on Automated Planning and Scheduling, ICAPS 2016, pages 175–183, 2016. [3] Luke Hunsberger and Roberto Posenato. Simpler and Faster Algorithm for Checking the Dynamic Consistency of Conditional Simple Temporal Networks. In 26th Int. Joint Conf. on Artificial Intelligence, (IJCAI-2018), pages 1324–1330, 2018. [4] Luke Hunsberger and Roberto Posenato. Propagating Piecewise-Linear Weights in Temporal Networks. In 29th International Conference on Automated Planning and Scheduling, ICAPS 2019, volume 29, pages 223–231. AAAI Press, 2019.

  • L. Hunsberger, R. Posenato

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References

References II

[5] Luke Hunsberger, Roberto Posenato, and Carlo Combi. A Sound-and-Complete Propagation-based Algorithm for Checking the Dynamic Consistency of Conditional Simple Temporal Networks. In Fabio Grandi, Martin Lange, and Alessio Lomuscio, editors, 22nd Int. Symp. on Temporal Representation and Reasoning (TIME-2015), pages 4–18, 2015. [6] Ioannis Tsamardinos, Thierry Vidal, and Martha E. Pollack. CTP: A new constraint-based formalism for conditional, temporal planning. Constraints, 8:365–388, 2003.

  • L. Hunsberger, R. Posenato

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