Cover Combinatorial Filters and their Minimization Problem

@inproceedings{Zhang2021CoverCF,
  title={Cover Combinatorial Filters and their Minimization Problem},
  author={Yulin Zhang and Dylan A. Shell},
  booktitle={WAFR},
  year={2021}
}
A recent research theme has been the development of automatic methods to minimize robots' resource footprints. In particular, the class of combinatorial filters (discrete variants of widely-used probabilistic estimators) has been studied and methods developed for automatically reducing their space requirements. This paper extends existing combinatorial filters by introducing a natural generalization that we dub cover combinatorial filters. In addressing the new---but still NP-complete---problem… Expand
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References

SHOWING 1-10 OF 21 REFERENCES
Integer linear programming formulations of the filter partitioning minimization problem
TLDR
The results show that the proposed ILP technique performs better in computing exact solutions as the filter sizes grow, and that the ILP approach obtains higher-quality feasible solutions, in contexts where time limitations prohibit the computation of exact solutions. Expand
Combinatorial filter reduction: Special cases, approximation, and fixed-parameter tractability
TLDR
It is shown that this combinatorial filter minimization problem is not fixed-parameter tractable for any of the obvious parameters, but it is fixed- Parameter tractability for a certain combination of new parameters. Expand
On the Relationship Between Bisimulation and Combinatorial Filter Reduction
TLDR
It is shown that every filter minimization problem can be solved by computing a quotient of the input filter with some relation, but that for some filters, the bisimilarity relation is not the correct relation for this purpose. Expand
Concise Planning and Filtering: Hardness and Algorithms
TLDR
Hardness results are presented showing that both filtering and planning are NP-hard to perform in an optimally concise way, and that the related decision problems areNP-complete. Expand
Set-labelled filters and sensor transformations
TLDR
The paper substantially expands the expressiveness of combinatorial filters so that, where they were previously limited to quite simple sensors, the richer filters are able to reasonably model a much broader variety of real devices. Expand
Toward a language-theoretic foundation for planning and filtering
TLDR
A new formal structure is introduced that generalizes and consolidates a variety of well-known structures including many forms of plans, planning problems, and filters, into a single data structure called a procrustean graph, and gives these graph structures semantics in terms of ideas based in formal language theory. Expand
A Class of Co-Design Problems With Cyclic Constraints and Their Solution
  • A. Censi
  • Computer Science
  • IEEE Robotics and Automation Letters
  • 2017
TLDR
This letter shows that a large class of codesign problems have a common structure, as they are described by two posets, representing functionality, and resources, as the codesign constraints can be expressed as two maps in opposite directions between the two poset. Expand
The hardness of minimizing design cost subject to planning problems
TLDR
This paper considers various cost functions which model the cost needed to equip a robot with some capabilities, and shows that the general form of this problem is NP-hard, confirming what many perhaps have suspected about this sort of design-time optimization. Expand
Sensing and Filtering: A Fresh Perspective Based on Preimages and Information Spaces
  • S. LaValle
  • Computer Science
  • Found. Trends Robotics
  • 2012
TLDR
The notion of a virtual sensor is explained, which provides a mathematical way to model numerous sensors while abstracting away their particular physical implementation and introduces a novel family of filters that aggregate information from multiple sensor readings. Expand
PySAT: A Python Toolkit for Prototyping with SAT Oracles
TLDR
The PySAT toolkit is proposed, which enables fast Python-based prototyping using SAT oracles and SAT-related technology and also integrates a number of cardinality constraint encodings, all aiming at simplifying the prototyping process. Expand
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