scholarly journals The computability path ordering

2015 ◽  
Vol 11 (4) ◽  
Author(s):  
Frédéric Blanqui ◽  
Jean-Pierre Jouannaud ◽  
Albert Rubio
Keyword(s):  
Path Ordering

A fuzzy-based path ordering algorithm for QoS routing in non-deterministic communication networks

2005 ◽  
Vol 150 (3) ◽  
pp. 401-417 ◽  
Author(s):  
A. Cohen ◽  
E. Korach ◽  
M. Last ◽  
R. Ohayon
Keyword(s):  
Communication Networks ◽  
Qos Routing ◽  
Path Ordering

TERMINATION OF ABSTRACT REDUCTION SYSTEMS

2009 ◽  
Vol 20 (01) ◽  
pp. 57-82
Author(s):  
JEREMY E. DAWSON ◽  
RAJEEV GORÉ
Keyword(s):  
General Theorem ◽  
Combinatory Logic ◽  
Rewrite Systems ◽  
Path Ordering

We present a general theorem capturing conditions required for the termination of abstract reduction systems. We show that our theorem generalises another similar general theorem about termination of such systems. We apply our theorem to give interesting proofs of termination for typed combinatory logic. Thus, our method can handle most path-orderings in the literature as well as the reducibility method typically used for typed combinators. Finally we show how our theorem can be used to prove termination for incrementally defined rewrite systems, including an incremental general path ordering. All proofs have been formally machine-checked in Isabelle/HOL.

A family of bounds for the transient behavior of a Jackson network

1986 ◽  
Vol 23 (2) ◽  
pp. 543-549 ◽  
Author(s):  
William A. Massey
Keyword(s):  
Length Distribution ◽  
Sample Path ◽  
Transient Behavior ◽  
Original Network ◽  
Index Set ◽  
Partially Order ◽  
Jackson Network ◽  
Jackson Networks ◽  
Queue Length Distribution ◽  
Path Ordering

Using operator methods, we derive a family of stochastic bounds for the Jackson network. For its transient joint queue-length distribution, we can stochastically bound it above by various networks that decouple into smaller independent Jackson networks. Each bound is determined by a distinct partitioning of the index set for the nodes. Except for the trivial cases, none of these bounds can be extended to a sample path ordering between it and the original network. Finally, we can partially order the bounds themselves whenever one partition of the index set is the refinement of another. These results suggest new types of partial orders for stochastic processes that are not equivalent to sample-path orderings.

scholarly journals Discussion of ‘Detecting possibly frequent change-points: Wild Binary Segmentation 2 and steepest-drop model selection’

2020 ◽  
Vol 49 (4) ◽  
pp. 1076-1080
Author(s):  
Haeran Cho ◽  
Claudia Kirch
Keyword(s):  
Model Selection ◽  
Change Point ◽  
Frequent Change ◽  
New Model ◽  
Interesting Paper ◽  
Selection Step ◽  
Binary Segmentation ◽  
Novel Method ◽  
Low Levels ◽  
Path Ordering

AbstractWe congratulate the author for this interesting paper which introduces a novel method for the data segmentation problem that works well in a classical change point setting as well as in a frequent jump situation. Most notably, the paper introduces a new model selection step based on finding the ‘steepest drop to low levels’ (SDLL). Since the new model selection requires a complete (or at least relatively deep) solution path ordering the change point candidates according to some measure of importance, a new recursive variant of the Wild Binary Segmentation (Fryzlewicz in Ann Stat 42:2243–2281, 2014, WBS) named WBS2, has been proposed for candidate generation.

A family of bounds for the transient behavior of a Jackson network

1986 ◽  
Vol 23 (02) ◽  
pp. 543-549 ◽  
Author(s):  
William A. Massey
Keyword(s):  
Length Distribution ◽  
Sample Path ◽  
Transient Behavior ◽  
Original Network ◽  
Index Set ◽  
Partially Order ◽  
Jackson Network ◽  
Jackson Networks ◽  
Queue Length Distribution ◽  
Path Ordering

Using operator methods, we derive a family of stochastic bounds for the Jackson network. For its transient joint queue-length distribution, we can stochastically bound it above by various networks that decouple into smaller independent Jackson networks. Each bound is determined by a distinct partitioning of the index set for the nodes. Except for the trivial cases, none of these bounds can be extended to a sample path ordering between it and the original network. Finally, we can partially order the bounds themselves whenever one partition of the index set is the refinement of another. These results suggest new types of partial orders for stochastic processes that are not equivalent to sample-path orderings.

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