scholarly journals Space-bounded complexity classes and iterated deterministic substitution

1980 ◽  
Vol 44 (3) ◽  
pp. 282-299 ◽  
Author(s):  
Peter R.J. Asveld
Keyword(s):  
Complexity Classes ◽  
Bounded Complexity

Tighter and Broader Complexity Results for Reconfigurable Models

1998 ◽  
Vol 08 (03) ◽  
pp. 271-282 ◽  
Author(s):  
Jerry L. Trahan ◽  
Anu G. Bourgeois ◽  
Ramachandran Vaidyanathan
Keyword(s):  
Fast Algorithms ◽  
Constant Time ◽  
Complexity Classes ◽  
Complexity Results ◽  
Reconfigurable Mesh ◽  
Bounded Complexity

A number of models allow processors to reconfigure their local connections to create and alter various bus configurations. This reconfiguration enables development of fast algorithms for fundamental problems, many in constant time. We investigate the ability of such models by relating time and processor bounded complexity classes defined for these models to each other and to those of more traditional models. In this work, (1) we tighten the relations for some of the models, placing them more precisely in relation to each other than was previously known (particularly, the Linear Reconfigurable Network and Directed Reconfigurable Network relative to circuit-defined classes), and (2) we include models (Fusing-Restricted Reconfigurable Mesh and Pipelined Reconfigurable Mesh) not previously considered.

Delineating classes of computational complexity via second order theories with weak set existence principles. I

1995 ◽  
Vol 60 (1) ◽  
pp. 103-121 ◽  
Author(s):  
Aleksandar Ignjatović
Keyword(s):  
Computational Complexity ◽  
Polynomial Time ◽  
Second Order ◽  
Complexity Classes ◽  
Bounded Arithmetic ◽  
Recursive Functions ◽  
Speed Up ◽  
Bounded Complexity ◽  
Polynomial Time Hierarchy ◽  
Comprehension Axiom

AbstractIn this paper we characterize the well-known computational complexity classes of the polynomial time hierarchy as classes of provably recursive functions (with graphs of suitable bounded complexity) of some second order theories with weak comprehension axiom schemas but without any induction schemas (Theorem 6). We also find a natural relationship between our theories and the theories of bounded arithmetic (Lemmas 4 and 5). Our proofs use a technique which enables us to “speed up” induction without increasing the bounded complexity of the induction formulas. This technique is also used to obtain an interpretability result for the theories of bounded arithmetic (Theorem 4).

ANALYSIS OF PRAM INSTRUCTION SETS FROM A LOG COST PERSPECTIVE

1994 ◽  
Vol 05 (03n04) ◽  
pp. 231-246
Author(s):  
JERRY L. TRAHAN ◽  
SUNDARARAJAN VEDANTHAM
Keyword(s):  
Parallel Machines ◽  
Unit Cost ◽  
Random Access ◽  
Complexity Classes ◽  
Turing Machines ◽  
Instruction Set ◽  
Instruction Sets ◽  
Parallel Random Access Machine ◽  
Bounded Complexity ◽  
Crcw Pram

The log cost measure has been viewed as a more reasonable method of measuring the time complexity of an algorithm than the unit cost measure. The more widely used unit cost measure becomes unrealistic if the algorithm handles extremely large integers. Parallel machines have not been examined under the log cost measure. In this paper, we investigate the Parallel Random Access Machine under the log cost measure. Let the instruction set of a basic PRAM include addition, subtraction, and Boolean operations. We relate resource-bounded complexity classes of log cost PRAMs to complexity classes of Turing machines and circuits. We also relate log cost PRAMs with different instruction sets by simulations that are much more efficient than possible in the unit cost case. Let LCRCWk(CRCWk) denote the class of languages accepted by a log cost (unit cost) basic CRCW PRAM in O( log k n) time with the polynomial in n number of processors. We position the log cost PRAM in the hierarchy of parallel complexity classes as: ACk=CRCWk⊆(NCk+1, LCRCWk+1)⊆ACk+1=CRCWk+1.

scholarly journals Some hierarchies of relativized time-bounded complexity classes

1985 ◽  
Vol 21 (3) ◽  
pp. 439-453
Author(s):  
Hisao Tanaka ◽  
Masa-aki Izumi ◽  
Nobuyuki Takahashi
Keyword(s):  
Complexity Classes ◽  
Bounded Complexity
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