Derandomizing Complexity Classes

Author(s):  
Peter Bro Miltersen
Keyword(s):  
1987 ◽  
Vol 10 (1) ◽  
pp. 1-33
Author(s):  
Egon Börger ◽  
Ulrich Löwen

We survey and give new results on logical characterizations of complexity classes in terms of the computational complexity of decision problems of various classes of logical formulas. There are two main approaches to obtain such results: The first approach yields logical descriptions of complexity classes by semantic restrictions (to e.g. finite structures) together with syntactic enrichment of logic by new expressive means (like e.g. fixed point operators). The second approach characterizes complexity classes by (the decision problem of) classes of formulas determined by purely syntactic restrictions on the formation of formulas.


1991 ◽  
Vol 24 (1) ◽  
pp. 179-200 ◽  
Author(s):  
Harry Buhrman ◽  
Steven Homer ◽  
Leen Torenvliet
Keyword(s):  

1987 ◽  
Vol 16 (4) ◽  
pp. 760-778 ◽  
Author(s):  
Neil Immerman
Keyword(s):  

1995 ◽  
Vol 11 (3) ◽  
pp. 358-376 ◽  
Author(s):  
F. Cucker ◽  
P. Koiran
Keyword(s):  

1993 ◽  
Vol 18 (1) ◽  
pp. 65-92
Author(s):  
Iain A. Stewart

We consider three sub-logics of the logic (±HP)*[FOs] and show that these sub-logics capture the complexity classes obtained by considering logspace deterministic oracle Turing machines with oracles in NP where the number of oracle calls is unrestricted and constant, respectively; that is, the classes LNP and LNP[O(1)]. We conclude that if certain logics are of the same expressibility then the Polynomial Hierarchy collapses. We also exhibit some new complete problems for the complexity class LNP via projection translations (the first to be discovered: projection translations are extremely weak logical reductions between problems) and characterize the complexity class LNP[O(1)] as the closure of NP under a new, extremely strict truth-table reduction (which we introduce in this paper).


Sign in / Sign up

Export Citation Format

Share Document