E. Grandjean. Invariance properties of RAMs and linear time. Computational Complexity, 4:62-106, 1994. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
A Logical Characterisation of Linear Time on.. - Lautemann.. (1999) (Correct)
....to capture the notion of linear time as used in algorithm design, Turing machines seem far too restrictive: apparantly, simple operations, such as traversing a tree, cannot be done. Therefore, a number of alternative models have been proposed to capture this notion. Notably, in a series of papers ([9, 8, 10]) Grandjean introduced and investigated linear time classes DLIN and NLIN, based on determistic and nondeterministic random access machines. NLIN contains NTIME(n) as a subclass but it is not known whether this inclusion is strict. Grandjean proved that Lynch s logic even captures (at least) all ....
E. Grandjean. Invariance properties of RAMs and linear time. Computational Complexity, 4:62--106, 1994.
Descriptive Complexity, Lower Bounds and Linear Time - Schwentick (1998) (Correct)
....of linear time. Some authors tried to circumvent this problem by considering so called quasi linear time, i.e. time O(npolylog(n) Sch78, GS89, Gra90] But there is even no general agreement whether linear time on Turing machines is too weak or too powerful [Reg93] In a series of articles [Gra94b, Gra94a, Gra96] Grandjean invented a very reasonable formalization of (deterministic as well as non deterministic) linear time. Before we get into the details of Grandjean s definitions let us first have a closer look at why linear time on Turing machines (DTIME(n) has little to do with linear time algorithms ....
E. Grandjean. Invariance properties of RAMs and linear time. Computational Complexity, 4:62--106, 1994.
Algebraic and Logical Characterizations of Deterministic Linear .. - Schwentick (1996) (Correct)
....and the representation of the input. In this paper we give an algebraic characterization, a logical characterization and a complete problem for some of the classes, that have been proposed to capture deterministic linear time, namely the classes DLIN and DLINEAR, that were introduced by Grandjean [Gra94b, Gra94a, Gra96]. For other attempts to capture deterministic linear time see, e.g. Reg93, Sch78, GS89, Gra90a] We first describe the computational model that is used to define DLIN. As mentioned before, the notion of deterministic linear time depends on the representation of the input. For graphs, as an ....
....considered as linear time require the input graph to be represented by adjacency lists, which in turn can be easily represented by finite structures: the universe consists of the vertices and edges of G and the adjacency lists of G are encoded by two unary functions, in a natural way. Grandjean [Gra94b, Gra94a, Gra96] has pointed out that this is also possible for binary strings as inputs. He views a string x of length n as a sequence x 0 ; xm of words of size (log n) Of course, every single word can be interpreted as a number and hence we can represent x, via f(i) x i , as a unary function on ....
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E. Grandjean. Invariance properties of RAMs and linear time. Computational Complexity, 4:62--106, 1994.
Easy Instances for Model Checking - Frick (2001) (Correct)
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E. Grandjean. Invariance properties of RAMs and linear time. Computational Complexity, 4:62-106, 1994.
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