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 ICAPS 2020 L. Hunsberger, R. Posenato Faster Dynamic-Consistency Checking for CSTN
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 �− 7 , ¬ p � Y V W �− 10 , ¬ p � � 10 , pq � � 12 , ¬ p � � ¬ p � 3 , p � � � 5 , p − 7 , � � 0 , ⊡ � �− 10 , p � �− 10 , p ¬ q � P ? Q ? Z U L. Hunsberger, R. Posenato Faster Dynamic-Consistency Checking for CSTN 1 / 10
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 �− 7 , ¬ p � Y V W �− 10 , ¬ p � � 10 , pq � � 12 , ¬ p � � ¬ p � 3 , p � � � 5 , p − 7 , � � 0 , ⊡ � �− 10 , p � �− 10 , p ¬ q � Q ? Z P ? U L. Hunsberger, R. Posenato Faster Dynamic-Consistency Checking for CSTN 2 / 10
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 HP 18 Algorithm (Hunsberger & Posenato, 2018) [3] The HP 19 Algorithm (Hunsberger & Posenato, 2019) [4] L. Hunsberger, R. Posenato Faster Dynamic-Consistency Checking for CSTN 3 / 10
Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions The HP 18 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 HP 18 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
Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions The HP 18 Algorithm Simulation �− 5 , ¬ p � � 1 , q � Q ? P ? Y X � 2 , p � �− 3 , ¬ q � − 13 − 13 Z L. Hunsberger, R. Posenato Faster Dynamic-Consistency Checking for CSTN 5 / 10
Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions The HP 18 Algorithm Simulation �− 5 , ¬ p � � 1 , q � Q ? P ? Y X �− 3 , ¬ q � � 2 , p � − 13 − 13 �− 11 , p � Z L. Hunsberger, R. Posenato Faster Dynamic-Consistency Checking for CSTN 5 / 10
Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions The HP 18 Algorithm Simulation �− 5 , ¬ p � � 1 , q � Q ? P ? Y X � 2 , p � �− 3 , ¬ q � − 13 �− 11 , p � − 11 − 13 Z L. Hunsberger, R. Posenato Faster Dynamic-Consistency Checking for CSTN 5 / 10
Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions The HP 18 Algorithm Simulation �− 5 , ¬ p � � 1 , q � Q ? P ? Y X � 2 , p � �− 3 , ¬ q � �− 16 , ¬ p � − 13 �− 11 , p � − 11 − 13 Z L. Hunsberger, R. Posenato Faster Dynamic-Consistency Checking for CSTN 5 / 10
Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions The HP 18 Algorithm Simulation � 1 , q � �− 5 , ¬ p � Q ? P ? Y X �− 3 , ¬ q � � 2 , p � �− 16 , ¬ p � − 13 �− 11 , p � − 11 �− 12 , q � − 13 Z L. Hunsberger, R. Posenato Faster Dynamic-Consistency Checking for CSTN 5 / 10
Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions The HP 18 Algorithm Simulation �− 5 , ¬ p � � 1 , q � Q ? P ? Y X � 2 , p � �− 3 , ¬ q � �− 12 , q � − 12 �− 16 , ¬ p � �− 11 , p � − 11 − 13 − 13 Z L. Hunsberger, R. Posenato Faster Dynamic-Consistency Checking for CSTN 5 / 10
Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions The HP 18 Algorithm Simulation �− 5 , ¬ p � � 1 , q � Q ? P ? Y X � 2 , p � �− 3 , ¬ q � �− 15 , ¬ q � �− 12 , q � − 12 �− 16 , ¬ p � �− 11 , p � − 11 − 13 − 13 Z L. Hunsberger, R. Posenato Faster Dynamic-Consistency Checking for CSTN 5 / 10
Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions The HP 18 Algorithm Simulation �− 5 , ¬ p � � 1 , q � Q ? P ? Y X � 2 , p � �− 3 , ¬ q � �− 16 , ¬ p � �− 15 , ¬ q � �− 15 , ¬ q � �− 12 , q � − 12 �− 11 , p � − 11 − 13 − 13 Z L. Hunsberger, R. Posenato Faster Dynamic-Consistency Checking for CSTN 5 / 10
Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions The HP 18 Algorithm Simulation �− 5 , ¬ p � � 1 , q � Q ? P ? Y X � 2 , p � �− 3 , ¬ q � �− 16 , ¬ p � �− 15 , ¬ q � − 15 �− 15 , ¬ q � �− 12 , q � − 12 �− 11 , p � − 11 − 13 − 13 Z L. Hunsberger, R. Posenato Faster Dynamic-Consistency Checking for CSTN 5 / 10
Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions The HP 18 Algorithm Simulation �− 5 , ¬ p � � 1 , q � Q ? P ? Y X � 2 , p � �− 3 , ¬ q � �− 16 , ¬ p � �− 15 , ¬ q � − 15 �− 15 , ¬ q � �− 15 , ¬ p � �− 12 , q � − 12 �− 11 , p � − 11 − 13 − 13 Z L. Hunsberger, R. Posenato Faster Dynamic-Consistency Checking for CSTN 5 / 10
Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions The HP 18 Algorithm Simulation �− 5 , ¬ p � � 1 , q � Q ? P ? Y X � 2 , p � �− 3 , ¬ q � �− 15 , ¬ q � �− 15 , ¬ p � − 15 �− 16 , ¬ p � �− 15 , ¬ q � − 15 �− 12 , q � − 12 �− 11 , p � − 11 − 13 − 13 Z L. Hunsberger, R. Posenato Faster Dynamic-Consistency Checking for CSTN 5 / 10
Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions The HP 18 Algorithm Simulation �− 5 , ¬ p � � 1 , q � Q ? P ? Y X � 2 , p � �− 3 , ¬ q � �− 15 , ¬ q � �− 15 , ¬ p � − 15 �− 16 , ¬ p � �− 15 , ¬ q � − 15 �− 12 , q � − 12 �− 11 , p � − 11 − 13 − 13 Z L. Hunsberger, R. Posenato Faster Dynamic-Consistency Checking for CSTN 5 / 10
Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions The HP 19 Algorithm Hunsberger & Posenato (2019) [4] Goal: Recognize negative q-loops. New rule leads to immediate value of −∞ on certain self-loops �− 8 , p ( ¬ q ) r � �−∞ , p (? q )(? r ) � Example: X W Meaning: � 2 , q ( ¬ r ) � 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. �− 3 , ¬ p � �−∞ , p (? q ) � Example: X W �−∞ , (? p )(? q ) � Propagation rules generate edges between any time-points —not just edges aimed at Z . HP 19 not empirically evaluated (was not main focus of paper). L. Hunsberger, R. Posenato Faster Dynamic-Consistency Checking for CSTN 6 / 10
Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions The HP 19 Algorithm Simulation �− 5 , ¬ p � � 1 , q � Q ? P ? �−∞ , ? p � �−∞ , ? q � Y X � 2 , p � �− 3 , ¬ q � − 13 − 13 Z L. Hunsberger, R. Posenato Faster Dynamic-Consistency Checking for CSTN 7 / 10
Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions The HP 19 Algorithm Simulation �− 5 , ¬ p � � 1 , q � Q ? �−∞ , ? p � P ? �−∞ , ? q � Y X �− 3 , ¬ q � � 2 , p � − 13 − 13 Z L. Hunsberger, R. Posenato Faster Dynamic-Consistency Checking for CSTN 7 / 10
Introduction Dynamic Consistency of CSTNs Empirical Evaluation Conclusions The HP 19 Algorithm Simulation �− 5 , ¬ p � � 1 , q � Q ? P ? �−∞ , ? p � �−∞ , ? q � Y X � 2 , p � �− 3 , ¬ q � �−∞ , ? p � − 13 − 13 Z L. Hunsberger, R. Posenato Faster Dynamic-Consistency Checking for CSTN 7 / 10
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