Parallel and nondeterministic time complexity classes

1978 ◽  
pp. 411-424 ◽  
Author(s):  
Walter J. Savitch
Keyword(s):  
Time Complexity ◽  
Complexity Classes

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 Gap-languages and log-time complexity classes

1997 ◽  
Vol 188 (1-2) ◽  
pp. 101-116 ◽  
Author(s):  
Kenneth W. Regan ◽  
Heribert Vollmer
Keyword(s):  
Time Complexity ◽  
Complexity Classes

Fine Separation of Average-Time Complexity Classes

1999 ◽  
Vol 28 (4) ◽  
pp. 1310-1325 ◽  
Author(s):  
Jin-Yi Cai ◽  
Alan L. Selman
Keyword(s):  
Time Complexity ◽  
Complexity Classes

scholarly journals A note on almost-everywhere-complex sets and separating deterministic-time-complexity classes

1991 ◽  
Vol 92 (1) ◽  
pp. 97-104 ◽  
Author(s):  
John G. Geske ◽  
Dung T. Huynh ◽  
Joel I. Seiferas
Keyword(s):  
Time Complexity ◽  
Complexity Classes ◽  
Almost Everywhere

scholarly journals Low complexity algorithms in knot theory

2019 ◽  
Vol 29 (02) ◽  
pp. 245-262
Author(s):  
Olga Kharlampovich ◽  
Alina Vdovina
Keyword(s):  
Computational Complexity ◽  
Time Complexity ◽  
Linear Time ◽  
Circuit Complexity ◽  
Equivalence Problem ◽  
Low Complexity ◽  
Combinatorial Structure ◽  
Complexity Classes ◽  
Np Complete ◽  
Almost All

Agol, Haas and Thurston showed that the problem of determining a bound on the genus of a knot in a 3-manifold, is NP-complete. This shows that (unless P[Formula: see text]NP) the genus problem has high computational complexity even for knots in a 3-manifold. We initiate the study of classes of knots where the genus problem and even the equivalence problem have very low computational complexity. We show that the genus problem for alternating knots with n crossings has linear time complexity and is in Logspace[Formula: see text]. Alternating knots with some additional combinatorial structure will be referred to as standard. As expected, almost all alternating knots of a given genus are standard. We show that the genus problem for these knots belongs to [Formula: see text] circuit complexity class. We also show, that the equivalence problem for such knots with [Formula: see text] crossings has time complexity [Formula: see text] and is in Logspace[Formula: see text] and [Formula: see text] complexity classes.

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.

A predicative approach to the classification problem

2001 ◽  
Vol 11 (1) ◽  
pp. 95-116 ◽  
Author(s):  
SALVATORE CAPORASO ◽  
EMANUELE COVINO ◽  
GIOVANNI PANI
Keyword(s):  
Time Complexity ◽  
Classification Problem ◽  
Elementary Level ◽  
Complexity Classes ◽  
Elementary Functions ◽  
Recursion Scheme ◽  
Slow Growing

We harmonize many time-complexity classes DTIMEF(f(n)) (f(n) [ges ] n) with the PR functions (at and above the elementary level) in a transfinite hierarchy of classes of functions [Tscr ]α. Class [Tscr ]α is obtained by means of unlimited operators, namely: a variant Π of the predicative or safe recursion scheme, introduced by Leivant, and by Bellantoni and Cook, if α is a successor; and constructive diagonalization if α is a limit. Substitution (SBST) is discarded because the time complexity classes are not closed under this scheme. [Tscr ]α is a structure for the PR functions finer than [Escr ]α, to the point that we have [Tscr ]ε0 = [Escr ]3 (elementary functions). Although no explicit use is made of hierarchy functions, it is proved that f(n) ∈ [Tscr ]α implies f(n) [les ] nGα(n), where Gα belongs to the slow growing hierarchy (of functions) studied, in particular, by Girard and Wainer.

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