Space complexity of alternating Turing machines

2006 ◽  
pp. 1-7 ◽  
Author(s):  
Māris Alberts
Keyword(s):  
Space Complexity ◽  
Turing Machines ◽  
Alternating Turing Machines

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.

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.

Preface

1997 ◽  
Vol 11 (07) ◽  
pp. 1023-1024
Author(s):  
Serge Miguet ◽  
Annick Montanvert ◽  
P. S. P. Wang
Keyword(s):  
Finite State Machine ◽  
Finite Automata ◽  
Upper Bounds ◽  
Two Dimensional ◽  
Turing Machines ◽  
Closure Properties ◽  
Working Space ◽  
Finite State ◽  
The Individual ◽  
Alternating Turing Machines

Several nonclosure properties of each class of sets accepted by two-dimensional alternating one-marker automata, alternating one-marker automata with only universal states, nondeterministic one-marker automata, deterministic one-marker automata, alternating finite automata, and alternating finite automata with only universal states are shown. To do this, we first establish the upper bounds of the working space used by "three-way" alternating Turing machines with only universal states to simulate those "four-way" non-storage machines. These bounds provide us a simplified and unified proof method for the whole variants of one-marker and/or alternating finite state machine, without directly analyzing the complex behavior of the individual four-way machine on two-dimensional rectangular input tapes. We also summarize the known closure properties including Boolean closures for all the variants of two-dimensional alternating one-marker automata.

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 $9$.

scholarly journals On reversal bounded alternating Turing machines

1987 ◽  
Vol 54 (2-3) ◽  
pp. 331-339 ◽  
Author(s):  
Maciej Liśkiewicz ◽  
Krzysztof Loryś ◽  
Marek Piotrów
Keyword(s):  
Turing Machines ◽  
Alternating Turing Machines

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)).

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