A machine independent description of complexity classes, definable by nondeterministic as well as deterministic turing machines with primitiv recursive tape or time bounds

1976 ◽  
pp. 345-351
Author(s):  
H. Huwig
Keyword(s):  
Complexity Classes ◽  
Turing Machines ◽  
Time Bounds

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).

scholarly journals Space and time complexity for infinite time Turing machines

2020 ◽  
Vol 30 (6) ◽  
pp. 1239-1255
Author(s):  
Merlin Carl
Keyword(s):  
Time Complexity ◽  
Space Complexity ◽  
Complexity Classes ◽  
Turing Machines ◽  
Infinite Time ◽  
Space And Time ◽  
Open Questions ◽  
Separation Results ◽  
Ordinal Computability

Abstract We consider notions of space by Winter [21, 22]. We answer several open questions about these notions, among them whether low space complexity implies low time complexity (it does not) and whether one of the equalities P=PSPACE, P$_{+}=$PSPACE$_{+}$ and P$_{++}=$PSPACE$_{++}$ holds for ITTMs (all three are false). We also show various separation results between space complexity classes for ITTMs. This considerably expands our earlier observations on the topic in Section 7.2.2 of Carl (2019, Ordinal Computability: An Introduction to Infinitary Machines), which appear here as Lemma $6$ up to Corollary $9$.

ON THE POWER OF ONE-WAY GLOBALLY DETERMINISTIC SYNCHRONIZED ALTERNATING TURING MACHINES AND MULTIHEAD AUTOMATA

1995 ◽  
Vol 06 (04) ◽  
pp. 431-446 ◽  
Author(s):  
ANNA SLOBODOVÁ
Keyword(s):  
Turing Machine ◽  
Simple Form ◽  
Space Complexity ◽  
Complexity Classes ◽  
Turing Machines ◽  
Computational Power ◽  
Parallel Processes ◽  
Open Questions ◽  
The One ◽  
Alternating Turing Machines

The alternating model augmented by a special simple form of communication among parallel processes—the so-called synchronized alternating (SA) model, provides (besides others) nice characterizations of the space complexity classes defined by nondeterministic Turing machines. The model investigated in this paper — globally deterministic synchronized alternating (GDSA) model—is obtained by a feasible restriction of nondeterminism in SA. It is known that it characterizes the deterministic counterparts of the nondeterministic space classes characterized by the SA model. In the paper we resume in the investigation of GDSA solving the open questions about the computational power of the one-way GDSA models. It is known that in the case of space-bounded Turing machine and multihead automata, the one-way SA models are equivalent to their two-way counterparts. We show that the same holds for GDSA models. The results contribute to the knowledge about the model and imply new characterizations of the deterministic space complexity classes.

scholarly journals Limits to measurement in experiments governed by algorithms

2010 ◽  
Vol 20 (6) ◽  
pp. 1019-1050 ◽  
Author(s):  
EDWIN J. BEGGS ◽  
JOSÉ FÉLIX COSTA ◽  
JOHN V. TUCKER
Keyword(s):  
Physical Experiment ◽  
Complexity Classes ◽  
List Type ◽  
Turing Machines ◽  
Experimental Procedure ◽  
Physical Systems ◽  
Physical Measurements ◽  
Physical Experiments ◽  
Physical Quantities

We pose the following question: If a physical experiment were to be completely controlled by an algorithm, what effect would the algorithm have on the physical measurements made possible by the experiment?In a programme to study the nature of computation possible by physical systems, and by algorithms coupled with physical systems, we have begun to analyse: (i)the algorithmic nature of experimental procedures; and(ii)the idea of using a physical experiment as an oracle to Turing Machines. To answer the question, we will extend our theory of experimental oracles so that we can use Turing machines to model the experimental procedures that govern the conduct of physical experiments. First, we specify an experiment that measures mass via collisions in Newtonian dynamics and examine its properties in preparation for its use as an oracle. We begin the classification of the computational power of polynomial time Turing machines with this experimental oracle using non-uniform complexity classes. Second, we show that modelling an experimenter and experimental procedure algorithmically imposes a limit on what can be measured using equipment. Indeed, the theorems suggest a new form of uncertainty principle for our knowledge of physical quantities measured in simple physical experiments. We argue that the results established here are representative of a huge class of experiments.

Relations among simultaneous complexity classes of nondeterministic and alternating Turing machines

1993 ◽  
Vol 30 (3) ◽  
pp. 267-278
Author(s):  
Shigeki Iwata ◽  
Takumi Kasai ◽  
Etsuro Moriya
Keyword(s):  
Complexity Classes ◽  
Turing Machines ◽  
Alternating Turing Machines

scholarly journals THREE FORMS OF PHYSICAL MEASUREMENT AND THEIR COMPUTABILITY

2014 ◽  
Vol 7 (4) ◽  
pp. 618-646 ◽  
Author(s):  
EDWIN BEGGS ◽  
JOSÉ FÉLIX COSTA ◽  
JOHN V TUCKER
Keyword(s):  
Lower Bounds ◽  
Theory Of Measurement ◽  
Complexity Classes ◽  
Turing Machines ◽  
Computational Power ◽  
Physical Measurement ◽  
Experimental Procedure ◽  
Measurement Algorithm ◽  
Abstract Interface ◽  
The Church

AbstractWe have begun a theory of measurement in which an experimenter and his or her experimental procedure are modeled by algorithms that interact with physical equipment through a simple abstract interface. The theory is based upon using models of physical equipment as oracles to Turing machines. This allows us to investigate the computability and computational complexity of measurement processes. We examine eight different experiments that make measurements and, by introducing the idea of an observable indicator, we identify three distinct forms of measurement process and three types of measurement algorithm. We give axiomatic specifications of three forms of interfaces that enable the three types of experiment to be used as oracles to Turing machines, and lemmas that help certify an experiment satisfies the axiomatic specifications. For experiments that satisfy our axiomatic specifications, we give lower bounds on the computational power of Turing machines in polynomial time using nonuniform complexity classes. These lower bounds break the barrier defined by the Church-Turing Thesis.

Computational complexity with experiments as oracles. II. Upper bounds

2009 ◽  
Vol 465 (2105) ◽  
pp. 1453-1465 ◽  
Author(s):  
Edwin Beggs ◽  
José Félix Costa ◽  
Bruno Loff ◽  
J.V. Tucker
Keyword(s):  
Upper Bounds ◽  
Physical Parameters ◽  
Complexity Classes ◽  
Turing Machines ◽  
Computational Power ◽  
Experimental Procedure ◽  
Physical Experiments ◽  
New Form

Earlier, to explore the idea of combining physical experiments with algorithms, we introduced a new form of analogue–digital (AD) Turing machine. We examined in detail a case study where an experimental procedure, based on Newtonian kinematics, is used as an oracle with classes of Turing machines. The physical cost of oracle calls was counted and three forms of AD queries were studied, in which physical parameters can be set exactly and approximately. Here, in this sequel, we complete the classification of the computational power of these AD Turing machines and determine precisely what they can compute, using non-uniform complexity classes and probabilities.

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