Ω=branching programs and theirs computational power

2005 ◽  
pp. 50-126
Keyword(s):  
Computational Power ◽  
Branching Programs

CONSTANT-DEPTH PERIODIC CIRCUITS

1991 ◽  
Vol 01 (01) ◽  
pp. 49-87 ◽  
Author(s):  
HOWARD STRAUBING
Keyword(s):  
Solvable Groups ◽  
Computational Power ◽  
Constant Depth ◽  
Branching Programs ◽  
Dihedral Groups ◽  
Circuit Element ◽  
Independent Evidence ◽  
Polynomial Size ◽  
And Function ◽  
Fixed Period

This paper is devoted to the languages accepted by constant-depth, polynomial-size families of circuits in which every circuit element computes the sum of its input bits modulo a fixed period q. It has been conjectured that such a circuit family cannot compute the AND function of n inputs. Here it is shown that such circuit families are equivalent in power to polynomial-length programs over finite solvable groups; in particular, the conjecture implies that Barrington's result on the computational power of branching programs over nonsolvable groups cannot be extended to solvable groups. It is also shown that polynomial-length programs over dihedral groups cannot compute the AND function. Furthermore, it is shown that the conjecture is equivalent to a characterization, in terms of finite semigroups and formal logic, of the regular languages accepted by such circuit families. There is, moreover, considerable independent evidence for this characterization. This last result is established using new theorems, of independent interest, concerning the algebraic structure of finite categories.

scholarly journals On Computational Power of Quantum Read-Once Branching Programs

2011 ◽  
Vol 52 ◽  
pp. 1-12 ◽  
Author(s):  
Farid Ablayev ◽  
Alexander Vasiliev
Keyword(s):  
Computational Power ◽  
Branching Programs

ON SERIALIZABLE LANGUAGES

1994 ◽  
Vol 05 (03n04) ◽  
pp. 303-318 ◽  
Author(s):  
MITSUNORI OGIHARA
Keyword(s):  
Lower Bounds ◽  
Upper Bounds ◽  
Turing Machines ◽  
Computational Power ◽  
Branching Programs ◽  
Polynomial Size

Cai and Furst introduced the notion of bottleneck Turing machines. Based on Barrington’s innovating technique, which is used to showed that polynomial-size branching programs have exactly the same power as NC1, Cai and Furst showed that the languages recognized by width-5 bottleneck Turing machines are exactly the same as those in PSPACE. In this paper, computational power of bottleneck Turing machines with widths fewer than 5 is investigated. It is shown that width-2 bottleneck Turing machines capture ⊕P// OptP , the class of sets recognized by ⊕P-machines with pre-computation in OptP. For languages recognized by bottleneck Turing machines with width-3 and width-4, some lower-bounds and upper-bounds are shown.

scholarly journals On Computational Power of Quantum Branching Programs

2001 ◽  
pp. 59-70 ◽  
Author(s):  
Farid Ablayev ◽  
Aida Gainutdinova ◽  
Marek Karpinski
Keyword(s):  
Computational Power ◽  
Branching Programs

scholarly journals Circuits on Cylinders

2002 ◽  
Vol 9 (50) ◽  
Author(s):  
Kristoffer Arnsfelt Hansen ◽  
Peter Bro Miltersen ◽  
V. Vinay
Keyword(s):  
Constant Width ◽  
Computational Power ◽  
Branching Programs ◽  
Polynomial Size

We consider the computational power of constant width polynomial size cylindrical circuits and nondeterministic branching programs. We show that every function computed by a Pi_2 o MOD o AC^0 circuit can also be computed by a constant width polynomial size cylindrical nondeterministic branching program (or cylindrical circuit) and that every function computed by a constant width polynomial size cylindrical circuit belongs to ACC^0.

scholarly journals Polynomial size Ω-branching programs and their computational power

1990 ◽  
Vol 85 (2) ◽  
pp. 163-182 ◽  
Author(s):  
Christoph Meinel
Keyword(s):  
Computational Power ◽  
Branching Programs ◽  
Polynomial Size

On computational power of classical and quantum branching programs

2006 ◽  
Author(s):  
Farid Ablayev
Keyword(s):  
Computational Power ◽  
Branching Programs
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