scholarly journals Formalization of the class of problems solvable by a nondeterministic turing machine

1997 ◽  
Vol 33 (5) ◽  
pp. 635-640
Author(s):  
A. D. Plotnikov
Keyword(s):  
Turing Machine ◽  
Nondeterministic Turing Machine

Membership Problem for Two-Dimensional General Row Jumping Finite Automata

2020 ◽  
Vol 31 (04) ◽  
pp. 527-538
Author(s):  
Grzegorz Madejski ◽  
Andrzej Szepietowski
Keyword(s):  
Computational Model ◽  
Turing Machine ◽  
Finite Automaton ◽  
Finite Automata ◽  
The Other ◽  
Membership Problem ◽  
Two Dimensional ◽  
Np Complete ◽  
Nondeterministic Turing Machine ◽  
Membership Problems

Two-dimensional general row jumping finite automata were recently introduced as an interesting computational model for accepting two-dimensional languages. These automata are nondeterministic. They guess an order in which rows of the input array are read and they jump to the next row only after reading all symbols in the previous row. In each row, they choose, also nondeterministically, an order in which segments of the row are read. In this paper, we study the membership problem for these automata. We show that each general row jumping finite automaton can be simulated by a nondeterministic Turing machine with space bounded by the logarithm. This means that the fixed membership problems for such automata are in NL, and so in P. On the other hand, we show that the uniform membership problem is NP-complete.

scholarly journals Testing a new idea to solve the P = NP problem with mathematical induction

2015 ◽  
Author(s):  
Yubin Huang
Keyword(s):  
Computer Science ◽  
Turing Machine ◽  
Open Problem ◽  
Mathematical Induction ◽  
Basic Knowledge ◽  
Mathematical Methods ◽  
Filter Function ◽  
Nondeterministic Turing Machine ◽  
Np Problem ◽  
Computation Path

Background. P and NP are two classes (sets) of languages in Computer Science. An open problem is whether P = NP. This paper tests a new idea to compare the two language sets and attempts to prove that these two language sets consist of same languages by elementary mathematical methods and basic knowledge of Turing machine. Methods. By introducing a filter function C(M,w) that is the number of configurations which have more than one children (nondeterministic moves) in the shortest accept computation path of a nondeterministic Turing machine M for input w, for any language L(M) ∈ NP, we can define a series of its subsets, Li(M) = {w | w ∈ L(M) ∧ C(M,w) ≤ i}, and a series of the subsets of NP as Li = {Li(M) | ∀M ∙ L(M) ∈ NP}. The nondeterministic multi-tape Turing machine is used to bridge two language sets Li and Li+1, by simulating the (i+1)-th nondeterministic move deterministically in multiple work tapes, to reduce one (the last) nondeterministic move. Results. The main result is that, with the above methods, the language set Li+1, which seems more powerful, can be proved to be a subset of Li. This result collapses Li ⊆ P for all i ∈ N. With NP = ⋃i∈NLi, it is clear that NP ⊆ P. Because by definition P ⊆ NP, we have P = NP. Discussion. There can be other ways to define the subsets Li and prove the same result. The result can be extended to cover any sets of time functions C, if ∀f ∙ f ∈ C ⇒ f2 ∈ C, then DTIME(C) = NTIME(C). This paper does not show any ways to find a solution in P for the problem known in NP.

scholarly journals Testing a new idea to solve the P = NP problem with mathematical induction

2015 ◽  
Author(s):  
Yubin Huang
Keyword(s):  
Computer Science ◽  
Turing Machine ◽  
Open Problem ◽  
Mathematical Induction ◽  
Basic Knowledge ◽  
Mathematical Methods ◽  
Filter Function ◽  
Nondeterministic Turing Machine ◽  
Np Problem ◽  
Computation Path

Background. P and NP are two classes (sets) of languages in Computer Science. An open problem is whether P = NP. This paper tests a new idea to compare the two language sets and attempts to prove that these two language sets consist of same languages by elementary mathematical methods and basic knowledge of Turing machine. Methods. By introducing a filter function C(M,w) that is the number of configurations which have more than one children (nondeterministic moves) in the shortest accept computation path of a nondeterministic Turing machine M for input w, for any language L(M) ∈ NP, we can define a series of its subsets, Li(M) = {w | w ∈ L(M) ∧ C(M,w) ≤ i}, and a series of the subsets of NP as Li = {Li(M) | ∀M ∙ L(M) ∈ NP}. The nondeterministic multi-tape Turing machine is used to bridge two language sets Li and Li+1, by simulating the (i+1)-th nondeterministic move deterministically in multiple work tapes, to reduce one (the last) nondeterministic move. Results. The main result is that, with the above methods, the language set Li+1, which seems more powerful, can be proved to be a subset of Li. This result collapses Li ⊆ P for all i ∈ N. With NP = ⋃i∈NLi, it is clear that NP ⊆ P. Because by definition P ⊆ NP, we have P = NP. Discussion. There can be other ways to define the subsets Li and prove the same result. The result can be extended to cover any sets of time functions C, if ∀f ∙ f ∈ C ⇒ f2 ∈ C, then DTIME(C) = NTIME(C). This paper does not show any ways to find a solution in P for the problem known in NP.

THE SIMULATION OF TWO-DIMENSIONAL ONE-MARKER AUTOMATA BY THREE-WAY TURING MACHINES

1989 ◽  
Vol 03 (03n04) ◽  
pp. 393-404 ◽  
Author(s):  
AKIRA ITO ◽  
KATSUSHI INOUE ◽  
ITSUO TAKANAMI
Keyword(s):  
Turing Machine ◽  
Two Dimensional ◽  
Turing Machines ◽  
Nondeterministic Turing Machine ◽  
Necessary And Sufficient ◽  
Sufficient Space

We denote a two-dimensional deterministic (nondeterministic) one-marker automaton by 2-DM1 (2-NM1), and a three-way two-dimensional deterministic (nondeterministic) Turing machine by TR2-DTM (TR2-NTM). In this paper, we show that the necessary and sufficient space for TR2-NTMs to simulate 2-DM1s (2-NM1s) is n log n (n2), and the necessary and sufficient space for TR2-DTMs to simulate 2-DM1s (2-NM1s) is 2O(n log n) (2 O(n2)), where n is the number of columns of rectangular input tapes.

SOFTWARE PROGRAMMABLE MODULE BASED ON TURING MACHINE

2016 ◽  
Vol 21 (97) ◽  
pp. 87-91
Author(s):  
Victor A. Krisilov ◽  
◽  
Gleb E. Romanov ◽  
Nikolaj I. Sinegub ◽  
◽  
...  
Keyword(s):  
Turing Machine
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