# On determinism versus non-determinism and related problems

@article{Paul1983OnDV, title={On determinism versus non-determinism and related problems}, author={Wolfgang J. Paul and Nicholas Pippenger and Endre Szemer{\'e}di and William T. Trotter}, journal={24th Annual Symposium on Foundations of Computer Science (sfcs 1983)}, year={1983}, pages={429-438} }

We show that, for multi-tape Turing machines, non-deterministic linear time is more powerful than deterministic linear time. We also discuss the prospects for extending this result to more general Turing machines.

## 131 Citations

Alternating time versus deterministic time: a separation

- Computer Science[1993] Proceedings of the Eigth Annual Structure in Complexity Theory Conference
- 1993

It is shown that only two alternations are sufficient to achieve a log*t(n) speed-up of deterministic Turing machines and that for each time-constructible function t(n), two alternation are strictly more powerful than deterministic time.

Speedup of Determinism by Alternation for Multidimensional Turing Machines

- Computer ScienceTheor. Comput. Sci.
- 1994

Two tapes versus one for off-line Turing machines

- Computer Sciencecomputational complexity
- 2005

We prove the first superlinear lower bound for a concrete, polynomial time recognizable decision problem on a Turing machine with one work tape and a two-way input tape (also called off-line 1-tape…

On relationships between complexity classes of Turing machines

- Business, Computer Science
- 2017

Classes of time and space complexity of Turing machines are defined, and relationships between them are discussed. New relationships between the defined complexity classes are described.

Two tapes are better than one for off-line Turing machines

- Computer ScienceSTOC
- 1987

This work proves the first superlinear lower bound for a concrete decision problem in P on a Turing machine with one work tape and a two-way input tape and shows for off-line Turing machines that 2 tapes are better than 1 and that 3 pushdown stores arebetter than 2.

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- Computer ScienceSOFSEM
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This paper discusses the computational complexity of one-tape Turing machines of various machine types that halt in time O(n), where the running time of a machine is defined as the height of its computation tree.

Shrinking Multi-pushdown Automata

- Computer ScienceFCT
- 2005

The expressive power of shrinking pushdown automata with more than two pushdown stores is studied, obtaining a close correspondence to linear time-bounded multi-tape Turing machines.

Quadratic lower bounds for deterministic and nondeterministic one-tape turing machines

- Computer ScienceSTOC '84
- 1984

New techniques for proving quadratic lower bounds for deterministic and nondeterministic l-tape Turing machines (all considered Turing machines have an additional oneway input tape) are introduced and a substantial superiority of nondeterminism over determinism and of co-nond determinism over nond determinism for l-Tape TM's is demonstrated.

Relations among simultaneous complexity classes of nondeterministic and alternating Turing machines

- Computer ScienceActa Informatica
- 2005

It is established in this paper that computations by tree-size and space simultaneously bounded ATMs roughly correspond to Computations by time and space simultaneous bounded nondeterministic TMs (NTMs).

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