Reducing epsilon-DC Checking for Conditional Simple Temporal Networks to DC Checking
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.
Conditional Simple Temporal Networks
Dynamic Consistency
Temporal Constraints
Computing methodologies~Temporal reasoning
Theory of computation~Network optimization
Theory of computation~Dynamic graph algorithms
Mathematics of computing~Graph algorithms
15:1-15:15
Regular Paper
Luke
Hunsberger
Luke Hunsberger
Department of Computer Science, Vassar College, NY, USA
Roberto
Posenato
Roberto Posenato
Department of Computer Science, University of Verona, Verona, Italy
https://orcid.org/0000-0003-0944-0419
10.4230/LIPIcs.TIME.2018.15
Luke Hunsberger and Roberto Posenato
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode