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 Algorithmic Manifold and Space Complexity

2017 ◽  
Author(s):  
Takuya Yabu
Keyword(s):  
Time Complexity ◽  
Space Complexity ◽  
Turing Machines ◽  
Topological Properties ◽  
The Relationship

In the previous paper, algorithmic manifolds were applied to the time complexity and discussed.　In this paper, I define algorithmic manifolds expressing space complexity and discuss topological properties. I also discuss the relationship between non-deterministic space complexity problems and deterministic Turing machines.

scholarly journals Introducing a Space Complexity Measure for P Systems

2009 ◽  
Vol 4 (3) ◽  
pp. 301 ◽  
Author(s):  
Antonio E. Porreca ◽  
Alberto Leporati ◽  
Giancarlo Mauri ◽  
Claudio Zandron
Keyword(s):  
Time Complexity ◽  
Membrane Computing ◽  
Complexity Measure ◽  
Space Complexity ◽  
P Systems ◽  
Complexity Classes ◽  
Mutual Relations ◽  
Initial Results

We define space complexity classes in the framework of membrane computing, giving some initial results about their mutual relations and their connection with time complexity classes, and identifying some potentially interesting problems which require further research.

BRUTE FORCE DETERMINIZATION OF NFAs BY MEANS OF STATE COVERS

2005 ◽  
Vol 16 (03) ◽  
pp. 441-451 ◽  
Author(s):  
J.-M. CHAMPARNAUD ◽  
F. COULON ◽  
T. PARANTHOËN
Keyword(s):  
Time Complexity ◽  
Regular Expression ◽  
Blow Up ◽  
Finite Automata ◽  
A Priori ◽  
Search Algorithms ◽  
Space Complexity ◽  
Brute Force ◽  
Practical Applications ◽  
Space And Time

Finite automata determinization is a critical operation for numerous practical applications such as regular expression search. Algorithms have to deal with the possible blow up of determinization. There exist solutions to control the space and time complexity like the so called "on the fly" determinization. Another solution consists in performing brute force determinization, which is robust and technically fast, although a priori its space complexity constitutes a weakness. However, one can reduce this complexity by perfoming a partial brute force determinization. This paper provides optimizations that consist in detecting classes of unreachable states and transitions of the subset automaton, which leads in average to an exponential reduction of the complexity of brute force and partial brute force determinization.

scholarly journals Synchronous Context-Free Grammars and Optimal Parsing Strategies

2016 ◽  
Vol 42 (2) ◽  
pp. 207-243
Author(s):  
Daniel Gildea ◽  
Giorgio Satta
Keyword(s):  
Approximation Algorithms ◽  
Time Complexity ◽  
Space Complexity ◽  
Sentence Length ◽  
Np Hard ◽  
Space And Time ◽  
Context Free ◽  
General Graphs ◽  
Context Free Grammars

The complexity of parsing with synchronous context-free grammars is polynomial in the sentence length for a fixed grammar, but the degree of the polynomial depends on the grammar. Specifically, the degree depends on the length of rules, the permutations represented by the rules, and the parsing strategy adopted to decompose the recognition of a rule into smaller steps. We address the problem of finding the best parsing strategy for a rule, in terms of space and time complexity. We show that it is NP-hard to find the binary strategy with the lowest space complexity. We also show that any algorithm for finding the strategy with the lowest time complexity would imply improved approximation algorithms for finding the treewidth of general graphs.

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).

Sign in / Sign up

Export Citation Format

Share Document