scholarly journals An efficient implementation of the algorithm computing the Borel-fixed points of a Hilbert scheme

2012 ◽  
Author(s):  
Paolo Lella
Keyword(s):  
Fixed Points ◽  
Hilbert Scheme ◽  
Efficient Implementation

scholarly journals Tabling with Sound Answer Subsumption

2016 ◽  
Vol 16 (5-6) ◽  
pp. 933-949 ◽  
Author(s):  
ALEXANDER VANDENBROUCKE ◽  
MACIEJ PIRÓG ◽  
BENOIT DESOUTER ◽  
TOM SCHRIJVERS
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Efficient Implementation ◽  
Logic Programs ◽  
Formal Framework ◽  
Fixed Point Semantics ◽  
Do So

AbstractTabling is a powerful resolution mechanism for logic programs that captures their least fixed point semantics more faithfully than plain Prolog. In many tabling applications, we are not interested in the set of all answers to a goal, but only require an aggregation of those answers. Several works have studied efficient techniques, such as lattice-based answer subsumption and mode-directed tabling, to do so for various forms of aggregation.While much attention has been paid to expressivity and efficient implementation of the different approaches, soundness has not been considered. This paper shows that the different implementations indeed fail to produce least fixed points for some programs. As a remedy, we provide a formal framework that generalises the existing approaches and we establish a soundness criterion that explains for which programs the approach is sound.

On $\alpha$-nonexpansive mapping and fixed-points in Banach spaces

2018 ◽  
Vol 2018 (-) ◽  
Author(s):  
Prondanai Kaskasem ◽  
Chakkrid Klin-eam ◽  
Suthep Suantai
Keyword(s):  
Nonexpansive Mapping ◽  
Fixed Points ◽  
Banach Spaces

Fixed Points of Sequences of Mappings

2018 ◽  
Vol 2018 (-) ◽  
Author(s):  
C. Ganesa Moorthy ◽  
S. Iruthaya Raj
Keyword(s):  
Fixed Points
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