The Complexity of the Membership Problem for Two Subclasses of Polynomial Ideals

1986 ◽  
Vol 15 (2) ◽  
pp. 581-594 ◽  
Author(s):  
Dung T. Huynh
Keyword(s):  
Membership Problem ◽  
Polynomial Ideals

scholarly journals The membership problem for unmixed polynomial ideals is solvable in single exponential time

1991 ◽  
Vol 33 (1-3) ◽  
pp. 73-94 ◽  
Author(s):  
Alicia Dickenstein ◽  
Noaï Fitchas ◽  
Marc Giusti ◽  
Carmen Sessa
Keyword(s):  
Membership Problem ◽  
Exponential Time ◽  
Polynomial Ideals ◽  
Single Exponential

WHEN CHURCH-ROSSER BECOMES CONTEXT FREE

2007 ◽  
Vol 18 (06) ◽  
pp. 1293-1302 ◽  
Author(s):  
MARTIN KUTRIB ◽  
ANDREAS MALCHER
Keyword(s):  
Linear Time ◽  
Membership Problem ◽  
Closure Properties ◽  
Context Free Language ◽  
Arithmetic Hierarchy ◽  
Context Free ◽  
Free Language

We investigate the intersection of Church-Rosser languages and (strongly) context-free languages. The intersection is still a proper superset of the deterministic context-free languages as well as of their reversals, while its membership problem is solvable in linear time. For the problem whether a given Church-Rosser or context-free language belongs to the intersection we show completeness for the second level of the arithmetic hierarchy. The equivalence of Church-Rosser and context-free languages is Π1-complete. It is proved that all considered intersections are pairwise incomparable. Finally, closure properties under several operations are investigated.

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