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.

TWO TOPICS CONCERNING TWO-DIMENSIONAL AUTOMATA OPERATING IN PARALLEL

1992 ◽  
Vol 06 (02n03) ◽  
pp. 211-225 ◽  
Author(s):  
KATSUSHI INOUE ◽  
ITSUO SAKURAMOTO ◽  
MAKOTO SAKAMOTO ◽  
ITSUO TAKANAMI
Keyword(s):  
Turing Machine ◽  
Finite Automata ◽  
Space Complexity ◽  
Two Dimensional ◽  
Turing Machines ◽  
Small Space ◽  
Bottom Up ◽  
Constructible Function ◽  
Deterministic Turing Machine ◽  
Alternating Turing Machines

This paper deals with two topics concerning two-dimensional automata operating in parallel. We first investigate a relationship between the accepting powers of two-dimensional alternating finite automata (2-AFAs) and nondeterministic bottom-up pyramid cellular acceptors (NUPCAs), and show that Ω ( diameter × log diameter ) time is necessary for NUPCAs to simulate 2-AFAs. We then investigate space complexity of two-dimensional alternating Turing machines (2-ATMs) operating in small space, and show that if L (n) is a two-dimensionally space-constructible function such that lim n → ∞ L (n)/ loglog n > 1 and L (n) ≤ log n, and L′ (n) is a function satisfying L′ (n) =o (L(n)), then there exists a set accepted by some strongly L (n) space-bounded two-dimensional deterministic Turing machine, but not accepted by any weakly L′ (n) space-bounded 2-ATM, and thus there exists a rich space hierarchy for weakly S (n) space-bounded 2-ATMs with loglog n ≤ S (n) ≤ log n.

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 $9$.

CLOSURE PROPERTY OF SPACE-BOUNDED TWO-DIMENSIONAL ALTERNATING TURING MACHINES, PUSHDOWN AUTOMATA, AND COUNTER AUTOMATA

2001 ◽  
Vol 15 (07) ◽  
pp. 1143-1165 ◽  
Author(s):  
TOKIO OKAZAKI ◽  
KATSUSHI INOUE ◽  
AKIRA ITO ◽  
YUE WANG
Keyword(s):  
Turing Machine ◽  
Nondecreasing Function ◽  
Closure Property ◽  
Two Dimensional ◽  
Turing Machines ◽  
Pushdown Automaton ◽  
Alternating Turing Machines ◽  
Positive Integers ◽  
Pushdown Automata

This paper investigates closure property of the classes of sets accepted by space-bounded two-dimensional alternating Turing machines (2-atm's) and space-bounded two-dimensional alternating pushdown automata (2-apda's), and space-bounded two-dimensional alternating counter automata (2-aca's). Let L(m, n): N2 → N (N denotes the set of all positive integers) be a function with two variables m (= the number of rows of input tapes) and n (= the number of columns of input tapes). We show that (i) for any function f(m) = o( log m) (resp. f(m) = o( log m/ log log m)) and any monotonic nondecreasing function g(n) space-constructible by a two-dimensional Turing machine (2-Tm) (resp. two-dimensional pushdown automaton (2-pda)), the class of sets accepted by L(m,n) space-bounded 2-atm's (2-apda's) is not closed under row catenation, row + or projection, and (ii) for any function f(m) = o(m/ log ) (resp. for any function f(m) such that log f(m) = o( log m)) and any monotonic nondecreasing function g(n) space-constructible by a two-dimensional counter automaton (2-ca), the class of sets accepted by L(m, n) space-bounded 2-aca's is not closed under row catenation, row + or projection, where L(m, n) = f(m) + g(n) (resp. L(m, n) = f(m) × g(n)).

scholarly journals The computing power of Turing machine based on quantum logic

10.29007/k8cb ◽  
2018 ◽  
Author(s):  
Yun Shang ◽  
Xian Lu ◽  
Ruqian Lu
Keyword(s):  
Quantum Logic ◽  
Turing Machine ◽  
Turing Machines ◽  
Computational Power ◽  
Orthomodular Lattices ◽  
Locally Finite ◽  
Computing Power ◽  
Truth Value ◽  
Quantum Language

Turing machines based on quantum logic can solve undecidableproblems. In this paper we will give recursion-theoreticalcharacterization of the computational power of this kind of quantumTuring machines. In detail, for the unsharp case, it is proved that&#931<sup>0</sup><sub>1</sub>&#8746&#928<sup>0</sup><sub>1</sub>&#8838L<sup>T</sup><sub>d</sub>(&#949,&#931)(L<sup>T</sup><sub>w</sub>(&#949,&#931))&#8838&#928<sup>0</sup><sub>2</sub>when the truth value lattice is locally finite and the operation &#8743is computable, whereL<sup>T</sup><sub>d</sub>(&#949,&#931)(L<sup>T</sup><sub>w</sub>(&#949,&#931))denotes theclass of quantum language accepted by these Turing machine indepth-first model (respectively, width-first model);for the sharp case, we can obtain similar results for usual orthomodular lattices.

Concurrent Program Schemes

1987 ◽  
Vol 10 (4) ◽  
pp. 337-361
Author(s):  
A.J. Kfoury ◽  
P. Urzyczyn
Keyword(s):  
Concurrent Programs ◽  
Turing Machines ◽  
Computational Power ◽  
Sequential Programs ◽  
Concurrent Program ◽  
Nondeterministic Choice ◽  
Flow Diagrams ◽  
Alternating Turing Machines

We study the programming formalism FD of “flow-diagrams” to which we gradually add various features of concurrency. The weakest form of concurrency is introduced by the construct “and”, which is dual to the nondeterministic choice “or” and plays a role similar to universal states in alternating Turing machines. Stronger (and more realistic) forms of concurrency are obtained when processes are allowed to communicate. We consider communication by channels and communication by messages. We calibrate the computational power of classes of concurrent programs FD+α against that of sequential programs, where α is the addition of one of the following features: {and}, {and, or}, {and, or, channels}, or {and, or, messages}.

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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