scholarly journals Uniform normal form for general time-bounded complexity classes

1986 ◽  
Vol 32 (3) ◽  
pp. 363-369
Author(s):  
Bernard R. Hodgson ◽  
Clement F. Kent
Keyword(s):  
Normal Form ◽  
Complexity Classes ◽  
Bounded Complexity ◽  
General Time

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.

Complete problems for fixed-point logics

1995 ◽  
Vol 60 (2) ◽  
pp. 517-527 ◽  
Author(s):  
Martin Grohe
Keyword(s):  
Fixed Point ◽  
Computational Complexity ◽  
Normal Form ◽  
Query Language ◽  
Main Step ◽  
Complexity Classes ◽  
Complete Problem ◽  
Complete Problems ◽  
Database Query Language ◽  
Natural Description

The notion of logical reducibilities is derived from the idea of interpretations between theories. It was used by Lovász and Gács [LG77] and Immerman [Imm87] to give complete problems for certain complexity classes and hence establish new connections between logical definability and computational complexity.However, the notion is also interesting in a purely logical context. For example, it is helpful to establish nonexpressibility results.We say that a class of τ-structures is a >complete problem for a logic under L-reductions if it is definable in [τ] and if every class definable in can be ”translated” into by L-formulae (cf. §4).We prove the following theorem:1.1. Theorem. There are complete problemsfor partial fixed-point logic andfor inductive fixed-point logic under quantifier-free reductions.The main step of the proof is to establish a new normal form for fixed-point formulae (which might be of some interest itself). To obtain this normal form we use theorems of Abiteboul and Vianu [AV91a] that show the equivalence between the fixed-point logics we consider and certain extensions of the database query language Datalog.In [Dah87] Dahlhaus gave a complete problem for least fixed-point logic. Since least fixed-point logic equals inductive fixed-point logic by a well-known result of Gurevich and Shelah [GS86], this already proves one part of our theorem.However, our class gives a natural description of the fixed-point process of an inductive fixed-point formula and hence sheds some light on completely different aspects of the logic than Dahlhaus's construction, which is strongly based on the features of least fixed-point formulae.

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 Classes of bent functions identified by specific normal forms and generated using Boolean differential equations

2011 ◽  
Vol 24 (3) ◽  
pp. 357-383 ◽  
Author(s):  
Bernd Steinbach ◽  
Christian Posthoff
Keyword(s):  
Normal Form ◽  
Differential Equations ◽  
Boolean Functions ◽  
Differential Calculus ◽  
Normal Forms ◽  
Direct Calculation ◽  
Bent Functions ◽  
Second Step ◽  
Complexity Classes ◽  
The Relationship

This paper aims at the identification of classes of bent functions in order to allow their construction without searching or sieving. In order to reach this aim, we studied first the relationship between bent functions and complexity classes defined by the Specific Normal Forms of all Boolean functions. As result of this exploration we found classes of bent functions which are embedded in different complexity classes defined by the Specific Normal Form. In the second step to reach our global aim, we utilized the found classes of bent functions in order to express bent functions in terms of derivative operations of the Boolean Differential Calculus. In detail, we studied bent functions of two and four variables. This exploration leads finally to Boolean differential equations that will allow the direct calculation of all bent functions of two and four variables. A given generalization allows to calculate subsets of bent functions for each even number of Boolean variables.

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
Sign in / Sign up

Export Citation Format

Share Document