## Linear time and memory-efficient computation (1992)

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Citations: | 4 - 0 self |

### BibTeX

@TECHREPORT{Regan92lineartime,

author = {Kenneth W. Regan},

title = {Linear time and memory-efficient computation},

institution = {},

year = {1992}

}

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### Abstract

Abstract. A realistic model of computation called the Block Move (BM) model is developed. The BM regards computation as a sequence of finite transductions in memory, and operations are timed according to a memory cost parameter µ. Unlike previous memory-cost models, the BM provides a rich theory of linear time, and in contrast to what is known for Turing machines, the BM is proved to be highly robust for linear time. Under a wide range of µ parameters, many forms of the BM model, ranging from a fixed-wordsize RAM down to a single finite automaton iterating itself on a single tape, are shown to simulate each other up to constant factors in running time. The BM is proved to enjoy efficient universal simulation, and to have a tight deterministic time hierarchy. Relationships among BM and TM time complexity classes are studied. Key words. Computational complexity, theory of computation, machine models, Turing machines, random-access machines, simulation, memory hierarchies, finite automata, linear time, caching. AMS/MOS classification: 68Q05,68Q10,68Q15,68Q68.

### Citations

4144 |
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- 1979
(Show Context)
Citation Context ...esults on memory-efficiency are in Section 5. The second main result of this paper, in Section 6, shows that like the RAM but unlike what is known for the standard multitape Turing machine model (see =-=[36, 24]-=-), the BM carries only a constant factor overhead for universal simulation. The universal BM given is efficient under anysd , while separate constructions work forslog . In consequence, for any fixeds... |

840 |
Matrix multiplication via arithmetic progressions
- Coppersmith, Winograd
- 1987
(Show Context)
Citation Context ...olvable in linear time on a RAM at all. The best method known involves computing A 2 + A, and squaring n \Theta n integer matrices takes time approximately N 1:188 , where N = n 2 , by the methods of =-=[19]-=-. (For directed triangles, cubing A is the best way known.) Open Problem 1. Do any of the above languages belong to TLIN? If not, prove nonlinear lower bounds. A BM can be made nondeterministic (NBM) ... |

561 |
The Input/Output complexity of sorting and related problems
- Aggarwal, Vitter
- 1988
(Show Context)
Citation Context ...in reasonable models of computation has progressed up to machines apparently just below the BM (unders1 ) in power, so that attacking the problems given here seems a logical next step. The authors of =-=[3] refer to -=-the "challenging open problem" of extending their results when bit-manipulations for dissecting records are available. The bit operations given to the BM seem to be an appropriate setting fo... |

270 |
Vector Models for Data-Parallel Computing
- BLELLOCH
- 1990
(Show Context)
Citation Context ...uctions can be computed by parallel prefix sum. Indeed, the BM is similar to the Pratt-Stockmeyer vector machine [61], and can also be regarded as a fixed-wordsize analogue of Blelloch's "scan&qu=-=ot; model [11]-=-. Results. The first main theorem is that the BM is a very robust model. Many diverse forms of the machine simulate each other up to constant factors in -time, under a wide range of cost functions . A... |

200 |
On the computational complexity of algorithms
- Hartmanis, Stearns
- 1965
(Show Context)
Citation Context ...t cost functions1 that we consider, many interesting nonregular languages and functions are computable in linear time. Previous models. It has long been realized that the standard unit-cost RAM model =-=[21, 31, 18] is too po-=-werful for many practical purposes. Feldman and Shapiro [22] contend that realistic models M, both sequential and parallel, should have a property they call "polynomial vicinity" which we st... |

155 |
A machine-independent theory of the complexity of recursive functions
- Blum
- 1967
(Show Context)
Citation Context ...t efficient or parsimonious programs make good use of a memory cache. Definition 2.9 does not imply that the given BM M is optimal for the function f it computes. Indeed, from Blum's speed-up theorem =-=[12]-=- and the fact that -time is a complexity measure, there exist computable functions with no -time optimal programs at all. To apply the concepts of memory efficiency and parsimony to languages and func... |

155 |
On Uniform Circuit Complexity
- Ruzzo
- 1981
(Show Context)
Citation Context ...bic vicinity. The RAM model, however, has exponential vicinity even under the log-cost criterion advocated by Cook and Reckhow [18]. So do the random-access Turing machine (RAM-TM) forms described in =-=[30, 26, 7, 14, 64]-=-, and TMs with tree-structured tapes (see [57, 63, 51, 52]). Turing machines with d-dimensional tapes (see [31, 60, 50]) have vicinity O(t d ), regardless of the number of such tapes or number of head... |

133 |
A model for hierarchical memory
- Aggarwal, Alpern, et al.
- 1987
(Show Context)
Citation Context ...t time per item. This is a reasonable reflection of how pipelining can hide memory latency, and accords with the behavior of physical memory devices (see [3], p1117, or [34], p 214). An earlier paper =-=[1]-=- studied a model called HMM which lacked the blocktransfer construct. The main memory cost functions treated in these papers areslog (a) := dlog 2 (a + 1)e, which reflects the time required to write d... |

127 | On Uniformity within NC
- Barrington, Immerman, et al.
- 1990
(Show Context)
Citation Context ...bic vicinity. The RAM model, however, has exponential vicinity even under the log-cost criterion advocated by Cook and Reckhow [18]. So do the random-access Turing machine (RAM-TM) forms described in =-=[30, 26, 7, 14, 64]-=-, and TMs with tree-structured tapes (see [57, 63, 51, 52]). Turing machines with d-dimensional tapes (see [31, 60, 50]) have vicinity O(t d ), regardless of the number of such tapes or number of head... |

124 | On uniformity within NC1
- Barrington, Immerman, et al.
- 1990
(Show Context)
Citation Context ...bic vicinity. The RAM model, however, has exponential vicinity even under the log-cost criterion advocated by Cook and Reckhow [18]. So do the random-access Turing machine (RAM-TM) forms described in =-=[30, 26, 7, 14, 64]-=-, and TMs with tree-structured tapes (see [57, 63, 51, 52]). Turing machines with d-dimensional tapes (see [31, 60, 50]) have vicinity O(t d ), regardless of the number of such tapes or number of head... |

112 |
Hierarchical Memory with Block Transfer
- Aggarwal, Chandra, et al.
(Show Context)
Citation Context ...n. This paper develops a new theory of linear-time computation. The Block Move (BM) model introduced here extends ideas and formalism from the Block Transfer (BT) model of Aggarwal, Chandra, and Snir =-=[2]-=-. The BT is a random access machine (RAM) with a special block transfer operation, together with a parameters: N ! N called a memory access cost function. The RAM's registers are indexed 0,1,2,: : : ,... |

102 |
Relations among complexity measures
- Fischer, Pippenger
- 1979
(Show Context)
Citation Context ... [18]. So do the random-access Turing machine (RAM-TM) forms described in [30, 26, 7, 14, 64], and TMs with tree-structured tapes (see [57, 63, 51, 52]). Turing machines with d-dimensional tapes (see =-=[31, 60, 50]) hav-=-e vicinity O(t d ), regardless of the number of such tapes or number of heads on each tape, even with head-to-head jumps allowed. The standard TM model, with d = 1, has linear vicinity. The "RAM ... |

82 |
Reckhow, Time bounded random access machines
- Cook, A
- 1973
(Show Context)
Citation Context ...t cost functions1 that we consider, many interesting nonregular languages and functions are computable in linear time. Previous models. It has long been realized that the standard unit-cost RAM model =-=[21, 31, 18] is too po-=-werful for many practical purposes. Feldman and Shapiro [22] contend that realistic models M, both sequential and parallel, should have a property they call "polynomial vicinity" which we st... |

81 |
Emde Boas, Machine models and simulations
- van
- 1990
(Show Context)
Citation Context ...nd others [45, 66, 67, 49, 10], we move straight to a model that uses "random-access addressing," a mechanism usually considered stronger than pointers (for in-depth comparisons, see [9, 10]=-= and also [68]). The following BM -=-form is based on a random-access Turing machine (RAM-TM; cf. "RTM" in [30] and "indexing TM" in [14, 64, 8]), and is closest to the BT. Definition 3.5. A RAM-BM has one main tape, ... |

73 |
On simultaneous resource bounds
- Pippenger
- 1979
(Show Context)
Citation Context ...e, but we do not pursue space complexity further in this paper. The pass count appears to be sandwiched between two measures of reversals for multitape Turing machines, namely the now-standard one of =-=[59, 35, 16]-=-, and the stricter notion of [43] which essentially counts keeping a TM head stationary as a reversal. Definition 2.8. For any memory cost functionsand recursive function t : N! N, DTIME[t] stands for... |

67 |
Storage Modification Machines
- Schönhage
- 1980
(Show Context)
Citation Context ... “fingers” and “pointers” is that there is no fixed limit on the number of pointers a program can create. Rather than define a form of the BM analogous to the pointer machines of Schönhage and others =-=[45, 66, 67, 49, 10]-=-, we move straight to a model that uses “random-access addressing,” a mechanism usually considered stronger than pointers (for in-depth comparisons, see [9, 10] and also [68]). The following BM form i... |

60 | The Computational Complexity of Universal Hashing
- Mansour, Nisan, et al.
- 1990
(Show Context)
Citation Context ...s [4] prove substantial time-space tradeoffs for the related "sequence equality" problem SE[n]: given x; y 2 f 0; 1; 2 g n , does Er 2 (x) = Er 2 (y)? We inquire whether their techniques, or=-= those of [54]-=-, can be adapted to the BM. The BM in Theorem 7.1 runs in output delay 1=2, 1, or 2 for all passes, so the two kinds of BM can be separated by no more than a log factor. A related question is whether ... |

57 | Two-tape simulation of multitape Turing machines
- Hennie, Stearns
- 1966
(Show Context)
Citation Context ... for the perhaps-largerslog -time classes for the BM variants that do use addressing. 7. Complexity Theory and the BM Model. Our first result shows that the construction in the Hennie-Stearns theorem =-=[33]-=-, which states that any multitape TM that runs in time t(n) can be simulated by a 2-tape TM in time t(n) log t(n), is memory-efficient on the BM unders1 . It has been observed in general that this con... |

57 |
On time versus space
- Hopcroft, Paul, et al.
- 1977
(Show Context)
Citation Context ...y even under the log-cost criterion advocated by Cook and Reckhow [18]. So do the random-access Turing machine (RAM-TM) forms described in [30, 26, 7, 14, 64], and TMs with tree-structured tapes (see =-=[57, 63, 51, 52]-=-). Turing machines with d-dimensional tapes (see [31, 60, 50]) have vicinity O(t d ), regardless of the number of such tapes or number of heads on each tape, even with head-to-head jumps allowed. The ... |

53 |
To the Definition of an Algorithm
- Kolmogorov, Uspensky
- 1958
(Show Context)
Citation Context ... "fingers" and "pointers" is that there is no fixed limit on the number of pointers a program can create. Rather than define a form of the BM analogous to the pointer machines of S=-=chonhage and others [45, 66, 67, 49, 10], we move -=-straight to a model that uses "random-access addressing," a mechanism usually considered stronger than pointers (for in-depth comparisons, see [9, 10] and also [68]). The following BM form i... |

41 |
Uniform memory hierarchies
- Alpern, Carter, et al.
- 1990
(Show Context)
Citation Context ...o-level I/O complexity model of Aggarwal and Vitter [3] has fixed block-size and a fixed cost for accessing the outer level, while the Uniform Memory Hierarchy (UMH) model of Alpern, Carter, and Feig =-=[5]-=- scales block-size and memory access cost upward in steps at higher levels. The BM makes the following changes to the BT. First, the BM fixes the wordsize of the underlying machine, so that registers ... |

41 |
On determinism versus nondeterminism and related problems
- Paul, Pippenger, et al.
- 1983
(Show Context)
Citation Context ...mber of registers that is exponential in t. The BM has polynomial vicinity undersd (though not underslog ), because any access outside the first t d cells costs more than t time units. The theorem of =-=[56]-=- that deterministic linear time on the standard TM (DLIN) is properly contained in nondeterministic TM linear time (NLIN) is not known to carry over to any model of super-linear vicinity. 2 Practical ... |

40 |
Algebraic theory of machines. I. Prime decomposition theorem for finite semigroups and machines
- Krohn, Rhodes
- 1965
(Show Context)
Citation Context ...an argument z is computed. We also remark that M S need not contain the identity mapping on Q, though it does no harm for us to adjoin it. By using known decomposition theorems for finite transducers =-=[47, 32, 48], we could rest-=-rict attention to the cases where each g c either is the identity on Q or identifies two states (a "reset machine") or each g c is a permutation of Q and M S is a group (a "permutation ... |

36 | Satisfiability is quasilinear complete in NQL
- Schnorr
- 1978
(Show Context)
Citation Context ...e simulation of a TM (or RAM-TM) by a log-cost RAM.) For quasilinear time, i.e. time qlin = n(log n) O(1) , the extra log n factors in Theorem 7.1 and Proposition 7.6 do not matter. Following Schnorr =-=[65]-=-, we write DQL and NQL for the TM time classes DTIME[qlin] and NTIME[qlin]. Gurevich and Shelah proved that RAM-TIME log [qlin] is the same as deterministic nearly linear time on the RAM-TM and severa... |

35 |
A practical hierarchical model of parallel computation: I. The model
- Heywood, Ranka
- 1992
(Show Context)
Citation Context ...s can be read or written at unit time per item. This is a reasonable reflection of how pipelining can hide memory latency, and accords with the behavior of physical memory devices (see [3], p1117, or =-=[34]-=-, p 214). An earlier paper [1] studied a model called HMM which lacked the blocktransfer construct. The main memory cost functions treated in these papers areslog (a) := dlog 2 (a + 1)e, which reflect... |

32 |
A density control algorithm for doing insertions and deletions in a sequentially ordered in good worst-case time
- Willard
- 1992
(Show Context)
Citation Context ...w insertions and deletions of the familiar "cut-andpaste " kind; instead, the output flows over the destination block and overwrites or lets stand according to the use of B in Definition 2.3=-=. Willard [69]-=- describes a model of a file system that lacks insertion and deletion, and gives fairly efficient algorithms for simulating them. Many text processors allow the user to define and move markers for poi... |

30 | A charaterization of the power of vector machines
- Pratt, Rabin, et al.
(Show Context)
Citation Context ...s a resource. The latter also serves as a measure of parallel time, since finite transductions can be computed by parallel prefix sum. Indeed, the BM is similar to the Pratt-Stockmeyer vector machine =-=[61], and can -=-also be regarded as a fixed-wordsize analogue of Blelloch's "scan" model [11]. Results. The first main theorem is that the BM is a very robust model. Many diverse forms of the machine simula... |

28 |
Meanders and their applications in lower bounds arguments
- ALON, MAASS
- 1988
(Show Context)
Citation Context ...parate track to remove the padding. That of (b) is proved along the lines of Proposition 4.3. The reverse implications are immediate, and all this needs only the tracking property of . Alon and Maass =-=[4] prove sub-=-stantial time-space tradeoffs for the related "sequence equality" problem SE[n]: given x; y 2 f 0; 1; 2 g n , does Er 2 (x) = Er 2 (y)? We inquire whether their techniques, or those of [54],... |

28 |
Spatial machines: A more realistic approach to parallel computation
- Feldman, Shapiro
- 1992
(Show Context)
Citation Context ...functions are computable in linear time. Previous models. It has long been realized that the standard unit-cost RAM model [21, 31, 18] is too powerful for many practical purposes. Feldman and Shapiro =-=[22] contend t-=-hat realistic models M, both sequential and parallel, should have a property they call "polynomial vicinity" which we state as follows: Let C be a data configuration, and let HC stand for th... |

27 |
Quasi-realtime languages
- BOOK, GREIBACH
- 1970
(Show Context)
Citation Context ...corresponding definition for Turing machines in [36], the additive O(n) term is n+1 and is used to read the input. For the DTM, time O(n) properly contains time n+1, while for the NTM these are equal =-=[13]-=-. For the BM under cost function , the O(n) term is n + (n). Theorem 5.1. With respect to any unbounded memory cost functionsthat has the tape compression property, all of the BM variants described in... |

27 |
Descriptive characterizations of computational complexity
- Leivant
- 1989
(Show Context)
Citation Context ... "fingers" and "pointers" is that there is no fixed limit on the number of pointers a program can create. Rather than define a form of the BM analogous to the pointer machines of S=-=chonhage and others [45, 66, 67, 49, 10], we move -=-straight to a model that uses "random-access addressing," a mechanism usually considered stronger than pointers (for in-depth comparisons, see [9, 10] and also [68]). The following BM form i... |

20 |
Time-space optimal string matching
- Galil, Seiferas
- 1983
(Show Context)
Citation Context ...nt = f x 1 # : : : #xm , y 1 # : : : #ym : (9i; j) x i = y j g: (d) Triangle: L \Delta = fA : A is the adjacency matrix of an undirected graph that contains a triangleg. 31 L pat belongs to DLIN (see =-=[25, 23]-=-), and was recently shown not to be solvable by a one-way non-sensing multihead DFA [42]. L dup and L int can be solved in linear time by a RAM or RAM-TM that treats list elements as cell addresses. L... |

19 |
On one-way cellular arrays
- Ibarra, Jiang
- 1987
(Show Context)
Citation Context ...s on its own output, a form generally known as a "cascading finite automaton" (CFA). Up to small technical differences, CFAs are comparable to the one-way "sweeping automata" studi=-=ed by Ibarra et.al. [39, 41, 40, 37, 38, 15]-=-. These papers characterize both one-way and two-way arrays of identical finite-state machines in terms of these and other automata and language classes. The following shows that the BM can be regarde... |

18 |
Bounds to complexities of networks for sorting and of switching
- Muller, Preparata
- 1975
(Show Context)
Citation Context ... in a larger machine, computing a \Sigma 2 K instead of a \Sigma 1 to follow head moves by T . The counting 19 idea of the next lemma resembles the linear-size circuits constructed for 0-1 sorting in =-=[55]-=-. Lemma 4.12. The function #a(x), which gives the number of occurrences of `a' in a string x 2 f a; bg , is computable in linears1 -time by a BM that observes the strict boundary condition. Proof. The... |

17 |
Reversal complexity
- Chen, Yap
- 1991
(Show Context)
Citation Context ...e, but we do not pursue space complexity further in this paper. The pass count appears to be sandwiched between two measures of reversals for multitape Turing machines, namely the now-standard one of =-=[59, 35, 16]-=-, and the stricter notion of [43] which essentially counts keeping a TM head stationary as a reversal. Definition 2.8. For any memory cost functionsand recursive function t : N! N, DTIME[t] stands for... |

15 |
Real-time Simulation of Multihead Tape Units
- Fischer, Meyer, et al.
- 1972
(Show Context)
Citation Context ...nt = f x 1 # : : : #xm , y 1 # : : : #ym : (9i; j) x i = y j g: (d) Triangle: L \Delta = fA : A is the adjacency matrix of an undirected graph that contains a triangleg. 31 L pat belongs to DLIN (see =-=[25, 23]-=-), and was recently shown not to be solvable by a one-way non-sensing multihead DFA [42]. L dup and L int can be solved in linear time by a RAM or RAM-TM that treats list elements as cell addresses. L... |

15 |
Some results concerning linear iterative (systolic) arrays
- Ibarra, Palis
- 1985
(Show Context)
Citation Context ...s on its own output, a form generally known as a "cascading finite automaton" (CFA). Up to small technical differences, CFAs are comparable to the one-way "sweeping automata" studi=-=ed by Ibarra et.al. [39, 41, 40, 37, 38, 15]-=-. These papers characterize both one-way and two-way arrays of identical finite-state machines in terms of these and other automata and language classes. The following shows that the BM can be regarde... |

14 |
On the power of one-way communication
- Chang, Ibarra, et al.
- 1988
(Show Context)
Citation Context ...s on its own output, a form generally known as a "cascading finite automaton" (CFA). Up to small technical differences, CFAs are comparable to the one-way "sweeping automata" studi=-=ed by Ibarra et.al. [39, 41, 40, 37, 38, 15]-=-. These papers characterize both one-way and two-way arrays of identical finite-state machines in terms of these and other automata and language classes. The following shows that the BM can be regarde... |

14 |
Nearly-linear time
- Gurevich, Shelah
- 1989
(Show Context)
Citation Context |

12 |
Random-access stored-program machines, an approach to programming languages
- Elgot, Robinson
- 1964
(Show Context)
Citation Context ...t cost functions1 that we consider, many interesting nonregular languages and functions are computable in linear time. Previous models. It has long been realized that the standard unit-cost RAM model =-=[21, 31, 18] is too po-=-werful for many practical purposes. Feldman and Shapiro [22] contend that realistic models M, both sequential and parallel, should have a property they call "polynomial vicinity" which we st... |

12 |
k one-way heads cannot do string matching
- Jiang, Li
- 1993
(Show Context)
Citation Context ...: A is the adjacency matrix of an undirected graph that contains a triangleg. 31 L pat belongs to DLIN (see [25, 23]), and was recently shown not to be solvable by a one-way non-sensing multihead DFA =-=[42]-=-. L dup and L int can be solved in linear time by a RAM or RAM-TM that treats list elements as cell addresses. L \Delta is not believed to be solvable in linear time on a RAM at all. The best method k... |

11 |
Characterizations and computational complexity of systolic trellis automata
- Ibarra, Kim
- 1984
(Show Context)
Citation Context |

9 |
An information-theoretic approach to time bounds for on-line computation
- Paul, Seiferas, et al.
- 1981
(Show Context)
Citation Context ...ctive than the older concept given by d-dimensional Turing machines. For d ? 1 we suspect that it is noticeably more restrictive. The d-dimensional tape reduction theorem of Paul, Seiferas, and Simon =-=[58]-=- gives t 0 (n) roughly equal to t(n) 1+1=d , and when ported to a BM, incurs memory access charges close to t(n) 1+2=d . Intuitively, the problem is that a d-dimensional TM can change the direction of... |

8 |
A Natural NP-Complete Problem with a Nontrivial Lower Bound
- Grandjean
- 1988
(Show Context)
Citation Context ...reover, they require only O(log n) bits of nondeterminism. Open Problem 2. Is NTLIN 6= TLIN? For reasonablesand time bounds t, is there a general separation of NTIME[t(n)] from DTIME[t(n)]? Grandjean =-=[27, 28]-=- shows that a few NP-complete languages are also hard for NLIN under TM linear time reductions, and hence by the theorem of [56] lie outside DLIN, not to mention TLIN. However, these languages seem no... |

8 |
Data structures for distributed counting
- Furer
- 1984
(Show Context)
Citation Context ...esults on memory-efficiency are in Section 5. The second main result of this paper, in Section 6, shows that like the RAM but unlike what is known for the standard multitape Turing machine model (see =-=[36, 24]-=-), the BM carries only a constant factor overhead for universal simulation. The universal BM given is efficient under any µd, while separate constructions work for µlog. In consequence, for any fixed ... |

7 |
Lower bounds for data structure problems on RAMs
- Ben-Amram, Galil
- 1991
(Show Context)
Citation Context ...es of Schonhage and others [45, 66, 67, 49, 10], we move straight to a model that uses "random-access addressing," a mechanism usually considered stronger than pointers (for in-depth compari=-=sons, see [9, 10] and also [68]). The-=- following BM form is based on a random-access Turing machine (RAM-TM; cf. "RTM" in [30] and "indexing TM" in [14, 64, 8]), and is closest to the BT. Definition 3.5. A RAM-BM has o... |

7 |
On similarity and duality of computation (i
- Hong
- 1984
(Show Context)
Citation Context ...e, but we do not pursue space complexity further in this paper. The pass count appears to be sandwiched between two measures of reversals for multitape Turing machines, namely the now-standard one of =-=[59, 35, 16]-=-, and the stricter notion of [43] which essentially counts keeping a TM head stationary as a reversal. Definition 2.8. For any memory cost functionsand recursive function t : N! N, DTIME[t] stands for... |

6 |
Real-time simulation of concatenable double-ended queues by double-ended queues
- Kosaraju
- 1979
(Show Context)
Citation Context ... and has constantfactor overheads in all measures, by remarks following Definition 3.1. It is interesting to ask whether the above can be extended to a linear simulation of a concatenable buffer (cf. =-=[46]-=-), but this appears to run into problems related to the nonlinear lower bounds for the Touch Problem in [2]. The proof gives w 0 (n) = O(w(n) + n) and R 0 (n) = O(R(n) log s(n)). For -acc 0 , the char... |

6 |
Simulations among multidimensional Turing machines
- Loui
- 1980
(Show Context)
Citation Context ... [18]. So do the random-access Turing machine (RAM-TM) forms described in [30, 26, 7, 14, 64], and TMs with tree-structured tapes (see [57, 63, 51, 52]). Turing machines with d-dimensional tapes (see =-=[31, 60, 50]) hav-=-e vicinity O(t d ), regardless of the number of such tapes or number of heads on each tape, even with head-to-head jumps allowed. The standard TM model, with d = 1, has linear vicinity. The "RAM ... |

5 | Fast simulation of Turing machines by random access machines
- Katajainen, Leeuwen, et al.
- 1988
(Show Context)
Citation Context ...(n)]. (b) D log TIME[t(n)] ` RAM-TIME log [t(n) log t(n)]. Proof. Straightforward simulations give these bounds. (The extra log t(n) factor in (b) dominates a factor of log log n that was observed by =-=[44]-=- for the simulation of a TM (or RAM-TM) by a log-cost RAM.) For quasilinear time, i.e. time qlin = n(log n) O(1) , the extra log n factors in Theorem 7.1 and Proposition 7.6 do not matter. Following S... |