scholarly journals Satisfiability Allows No Nontrivial Sparsification unless the Polynomial-Time Hierarchy Collapses

2014 ◽  
Vol 61 (4) ◽  
pp. 1-27 ◽  
Author(s):  
Holger Dell ◽  
Dieter Van Melkebeek
Keyword(s):  
Polynomial Time ◽  
Polynomial Time Hierarchy

The polynomial-time hierarchy and sparse oracles

1986 ◽  
Vol 33 (3) ◽  
pp. 603-617 ◽  
Author(s):  
Jose L. Balcázar ◽  
Ronald V. Book ◽  
Uwe Schöning
Keyword(s):  
Polynomial Time ◽  
Polynomial Time Hierarchy

ON HIGHER ARTHUR-MERLIN CLASSES

2004 ◽  
Vol 15 (01) ◽  
pp. 3-19
Author(s):  
JIN-YI CAI ◽  
DENIS CHARLES ◽  
A. PAVAN ◽  
SAMIK SENGUPTA
Keyword(s):  
Polynomial Time ◽  
Upper Bounds ◽  
Complexity Classes ◽  
Polynomial Time Hierarchy

We study higher Arthur-Merlin classes defined via several natural probabilistic operators BP, R and coR. We investigate the complexity classes they define, and a number of interactions between these operators and the standard polynomial time hierarchy. We prove a hierarchy theorem for these higher Arthur-Merlin classes involving interleaving operators, and a theorem giving non-trivial upper bounds to the intersection of the complementary classes in the hierarchy.

Parity, circuits, and the polynomial-time hierarchy

1984 ◽  
Vol 17 (1) ◽  
pp. 13-27 ◽  
Author(s):  
Merrick Furst ◽  
James B. Saxe ◽  
Michael Sipser
Keyword(s):  
Polynomial Time ◽  
Polynomial Time Hierarchy
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