On determinism versus non-determinism and related problems

Paul, Wolfgang J.; Pippenger, Nicholas; Szemerédi, Endre; Trotter, William T.

doi:10.1109/sfcs.1983.39

Cited by 93 publications

(71 citation statements)

References 19 publications

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“…License or copyright restrictions may apply to redistribution; see https://www.ams.org/journal-terms-of-use (Kannan [11]) and NTIME2(«) % DTIME^«122) (Maass and Schorr [22]; here the lower bound also holds for 1-tape TM's with two-way input tape).…”

Section: Ntime2(«) % Dtime^«1 ')mentioning

confidence: 96%

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Combinatorial lower bound arguments for deterministic and nondeterministic Turing machines

Maass¹

1985

Trans. Amer. Math. Soc.

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Abstract.We introduce new techniques for proving quadratic lower bounds for deterministic and nondeterministic 1-tape Turing machines (all considered Turing machines have an additional one-way input tape). In particular, we derive for the simulation of 2-tape Turing machines by 1-tape Turing machines an optimal quadratic lower bound in the deterministic case and a nearly optimal lower bound in the nondeterministic case. This answers the rather old question whether the computing power of the considered types of Turing machines is significantly increased when more than one tape is used (problem Nos. 1 and 7 in the list of Duris, Galil, Paul, Reischuk [3]). Further, we demonstrate a substantial superiority of nondeterminism over determinism and of co-nondeterminism over nondeterminism for 1-tape Turing machines.1. Introduction and definitions. A major goal of computational complexity theory is the development of methods for proving optimal (or at least significant) lower bounds on the computation time for various abstract computer models. Such lower bounds are needed for the classification of mathematical problems according to their inherent computational complexity. But they are also of practical importance for the development of optimal computer hardware and software. Unfortunately the number of significant lower bound results in (machine based) complexity theory is very small. The "P = TV/5?" question is most prominent, but a closer look shows that nearly every question that requires a nontrivial lower bound argument for a general-purpose computer is open. Many of these questions are not related to nondeterminism, which suggests that there is more missing than just a single "trick".

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Section: Ntime2(«) % Dtime^«1 ')mentioning

confidence: 96%

“…(r(«)) consists of those languages whose complement is in NTIMEA(i(n)). The known separation results are NTIME2(«) g IJ DTIMEA(«(log*«)1/4) k>\ (Paul, Pippenger, Szemeredi and Trotter [22]),…”

mentioning

confidence: 99%

Combinatorial lower bound arguments for deterministic and nondeterministic Turing machines

Maass¹

1985

Trans. Amer. Math. Soc.

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“…In 1983, Paul, Pippenger, Szemeredi, and Trotter [PPST83] obtained the striking and deep result that DTIME(O(n)) = NTIME(O(n)).…”

Section: Linear Compression and Speedupmentioning

confidence: 99%

Turing and the development of computational complexity

Homer¹,

Selman²

2014

Turing's Legacy

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“…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 not to belong to NTLIN, nor even to linear time for NBMs of the stronger kind.…”

Section: Open Problems and Furthermentioning

confidence: 99%

“…This is not quite the same as polynomial vicinity-if t T , the machine within t steps could still address a number of registers that is exponential in t. The BM has polynomial vicinity under µ d (though not under µ log ), 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.…”

Section: Introduction This Paper Develops a New Theory Of Linear-timmentioning

confidence: 99%

Linear Time and Memory-Efficient Computation

Regan¹

1996

SIAM J. Comput.

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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.

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On determinism versus non-determinism and related problems

Cited by 93 publications

References 19 publications

Combinatorial lower bound arguments for deterministic and nondeterministic Turing machines

Combinatorial lower bound arguments for deterministic and nondeterministic Turing machines

Turing and the development of computational complexity

Linear Time and Memory-Efficient Computation

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