Non-Closure Properties of Multi-Inkdot Nondeterministic Turing Machines with Sublogarithmic Space

2020 ◽  
Vol E103.A (10) ◽  
pp. 1234-1236
Author(s):  
Tsunehiro YOSHINAGA ◽  
Makoto SAKAMOTO
Keyword(s):  
Turing Machines ◽  
Closure Properties ◽  
Sublogarithmic Space

Preface

1997 ◽  
Vol 11 (07) ◽  
pp. 1023-1024
Author(s):  
Serge Miguet ◽  
Annick Montanvert ◽  
P. S. P. Wang
Keyword(s):  
Finite State Machine ◽  
Finite Automata ◽  
Upper Bounds ◽  
Two Dimensional ◽  
Turing Machines ◽  
Closure Properties ◽  
Working Space ◽  
Finite State ◽  
The Individual ◽  
Alternating Turing Machines

Several nonclosure properties of each class of sets accepted by two-dimensional alternating one-marker automata, alternating one-marker automata with only universal states, nondeterministic one-marker automata, deterministic one-marker automata, alternating finite automata, and alternating finite automata with only universal states are shown. To do this, we first establish the upper bounds of the working space used by "three-way" alternating Turing machines with only universal states to simulate those "four-way" non-storage machines. These bounds provide us a simplified and unified proof method for the whole variants of one-marker and/or alternating finite state machine, without directly analyzing the complex behavior of the individual four-way machine on two-dimensional rectangular input tapes. We also summarize the known closure properties including Boolean closures for all the variants of two-dimensional alternating one-marker automata.

Closure properties of the classes of sets recognized by space-bounded two-dimensional probabilistic turing machines

1999 ◽  
Vol 115 (1-4) ◽  
pp. 61-81 ◽  
Author(s):  
Tokio Okazaki ◽  
Katsushi Inoue ◽  
Akira Ito ◽  
Yue Wang
Keyword(s):  
Two Dimensional ◽  
Turing Machines ◽  
Closure Properties

scholarly journals Some properties of one-pebble Turing machines with sublogarithmic space

2005 ◽  
Vol 341 (1-3) ◽  
pp. 138-149 ◽  
Author(s):  
Atsuyuki Inoue ◽  
Akira Ito ◽  
Katsushi Inoue ◽  
Tokio Okazaki
Keyword(s):  
Turing Machines ◽  
Sublogarithmic Space

scholarly journals Languages recognized by nondeterministic quantum finite automata

2010 ◽  
Vol 10 (9&10) ◽  
pp. 747-770
Author(s):  
Abuzer Yakaryilmaz ◽  
A.C. Cem Say
Keyword(s):  
Finite Automaton ◽  
Finite Automata ◽  
Space Complexity ◽  
Complexity Classes ◽  
Language Recognition ◽  
Closure Properties ◽  
Quantum Finite Automata ◽  
Sublogarithmic Space

The nondeterministic quantum finite automaton (NQFA) is the only known case where a one-way quantum finite automaton (QFA) model has been shown to be strictly superior in terms of language recognition power to its probabilistic counterpart. We give a characterization of the class of languages recognized by NQFAs, demonstrating that it is equal to the class of exclusive stochastic languages. We also characterize the class of languages that are recognized necessarily by two-sided error by QFAs. It is shown that these classes remain the same when the QFAs used in their definitions are replaced by several different model variants that have appeared in the literature. We prove several closure properties of the related classes. The ramifications of these results about classical and quantum sublogarithmic space complexity classes are examined.

Nonclosure Properties of Two-Dimensional One-Marker Automata

1997 ◽  
Vol 11 (07) ◽  
pp. 1025-1050 ◽  
Author(s):  
Akira Ito ◽  
Katsushi Inoue ◽  
Yue Wang
Keyword(s):  
Finite State Machine ◽  
Finite Automata ◽  
Upper Bounds ◽  
Two Dimensional ◽  
Turing Machines ◽  
Closure Properties ◽  
Working Space ◽  
Finite State ◽  
The Individual ◽  
Alternating Turing Machines

Several nonclosure properties of each class of sets accepted by two-dimensional alternating one-marker automata, alternating one-marker automata with only universal states, nondeterministic one-marker automata, deterministic one-marker automata, alternating finite automata, and alternating finite automata with only universal states are shown. To do this, we first establish the upper bounds of the working space used by "three-way" alternating Turing machines with only universal states to simulate those "four-way" non-storage machines. These bounds provide us a simplified and unified proof method for the whole variants of one-marker and/or alternating finite state machine, without directly analyzing the complex behavior of the individual four-way machine on two-dimensional rectangular input tapes. We also summarize the known closure properties including Boolean closures for all the variants of two-dimensional alternating one-marker automata.

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