scholarly journals Lower complexity bounds of first-order methods for convex-concave bilinear saddle-point problems

2019 ◽  
Author(s):  
Yuyuan Ouyang ◽  
Yangyang Xu
Keyword(s):  
Saddle Point ◽  
Saddle Point Problems ◽  
Complexity Bounds ◽  
First Order ◽  
Lower Complexity ◽  
Lower Complexity Bounds ◽  
First Order Methods

scholarly journals Lower complexity bounds for lifted inference

2014 ◽  
Vol 15 (2) ◽  
pp. 246-263 ◽  
Author(s):  
MANFRED JAEGER
Keyword(s):  
Knowledge Bases ◽  
Modeling Languages ◽  
Complexity Bounds ◽  
Lifted Inference ◽  
Probabilistic Relational Models ◽  
Lower Complexity ◽  
Logical Modeling ◽  
Inference Techniques ◽  
And Function ◽  
Lower Complexity Bounds

AbstractOne of the big challenges in the development of probabilistic relational (or probabilistic logical) modeling and learning frameworks is the design of inference techniques that operate on the level of the abstract model representation language, rather than on the level of ground, propositional instances of the model. Numerous approaches for such “lifted inference” techniques have been proposed. While it has been demonstrated that these techniques will lead to significantly more efficient inference on some specific models, there are only very recent and still quite restricted results that show the feasibility of lifted inference on certain syntactically defined classes of models. Lower complexity bounds that imply some limitations for the feasibility of lifted inference on more expressive model classes were established earlier in Jaeger (2000; Jaeger, M. 2000. On the complexity of inference about probabilistic relational models. Artificial Intelligence 117, 297–308). However, it is not immediate that these results also apply to the type of modeling languages that currently receive the most attention, i.e., weighted, quantifier-free formulas. In this paper we extend these earlier results, and show that under the assumption that NETIME≠ETIME, there is no polynomial lifted inference algorithm for knowledge bases of weighted, quantifier-, and function-free formulas. Further strengthening earlier results, this is also shown to hold for approximate inference and for knowledge bases not containing the equality predicate.

scholarly journals Lower complexity bounds for interpolation algorithms

2011 ◽  
Vol 27 (2) ◽  
pp. 151-187 ◽  
Author(s):  
Nardo Giménez ◽  
Joos Heintz ◽  
Guillermo Matera ◽  
Pablo Solernó
Keyword(s):  
Complexity Bounds ◽  
Interpolation Algorithms ◽  
Lower Complexity ◽  
Lower Complexity Bounds

scholarly journals Data Complexity and Rewritability of Ontology-Mediated Queries in Metric Temporal Logic under the Event-Based Semantics

2019 ◽  
Author(s):  
Vladislav Ryzhikov ◽  
Przemyslaw Andrzej Walega ◽  
Michael Zakharyaschev
Keyword(s):  
Temporal Logic ◽  
Transitive Closure ◽  
Order Logic ◽  
Data Complexity ◽  
Complexity Bounds ◽  
Metric Temporal Logic ◽  
First Order ◽  
Primitive Recursion ◽  
Lower Complexity ◽  
Event Based

We investigate the data complexity of answering queries mediated by metric temporal logic ontologies under the event-based semantics assuming that data instances are finite timed words timestamped with binary fractions. We identify classes of ontology-mediated queries answering which can be done in AC0, NC1, L, NL, P, and coNP for data complexity, provide their rewritings to first-order logic and its extensions with primitive recursion, transitive closure or datalog, and establish lower complexity bounds.

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