On the Complexity of the Differential-Algebraic Description of Analytic Complexity Classes

2019 ◽  
Vol 105 (3-4) ◽  
pp. 309-315
Author(s):  
V. K. Beloshapka
Keyword(s):  
Complexity Classes ◽  
Analytic Complexity ◽  
Algebraic Description

Logical Decision Problems and Complexity of Logic Programs

1987 ◽  
Vol 10 (1) ◽  
pp. 1-33
Author(s):  
Egon Börger ◽  
Ulrich Löwen
Keyword(s):  
Fixed Point ◽  
Computational Complexity ◽  
Decision Problem ◽  
Decision Problems ◽  
Complexity Classes ◽  
Logic Programs ◽  
Finite Structures ◽  
Syntactic Restrictions

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.

Algebraic description of bounded real matrixes

1966 ◽  
Vol 2 (12) ◽  
pp. 464 ◽  
Author(s):  
B.D.O. Anderson
Keyword(s):  
Algebraic Description

scholarly journals Homological epimorphisms, homotopy epimorphisms and acyclic maps

2020 ◽  
Vol 32 (6) ◽  
pp. 1395-1406
Author(s):  
Joseph Chuang ◽  
Andrey Lazarev
Keyword(s):  
Wide Class ◽  
Topological Spaces ◽  
Loop Spaces ◽  
Graded Algebras ◽  
Differential Graded Algebras ◽  
Algebraic Description ◽  
Acyclic Map ◽  
Induced Maps

AbstractWe show that the notions of homotopy epimorphism and homological epimorphism in the category of differential graded algebras are equivalent. As an application we obtain a characterization of acyclic maps of topological spaces in terms of induced maps of their chain algebras of based loop spaces. In the case of a universal acyclic map we obtain, for a wide class of spaces, an explicit algebraic description for these induced maps in terms of derived localization.

Completeness for nondeterministic complexity classes

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

scholarly journals Languages that Capture Complexity Classes

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

scholarly journals Computing over the Reals with Addition and Order: Higher Complexity Classes

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

Logical Characterizations of Bounded Query Classes I: Logspace Oracle Machines

1993 ◽  
Vol 18 (1) ◽  
pp. 65-92
Author(s):  
Iain A. Stewart
Keyword(s):  
Truth Table ◽  
Complexity Class ◽  
Polynomial Hierarchy ◽  
Complexity Classes ◽  
Turing Machines ◽  
Complete Problems

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