Journal Article10.1137/0206035
Linear-Time Computation by Nondeterministic Multidimensional Iterative Arrays
15
TL;DR: It is shown by simulation that every language accepted within time $n^d$ by a nondeter-ministic one-dimensional Turing machine is accepted in linear time by an iterative array of nondeterministic d-dimensional iterative arrays, which is precisely Karp’s class NP.
read more
Abstract: It is shown by simulation that every language accepted within time $n^d$ by a nondeter-ministic one-dimensional Turing machine is accepted in linear time by a nondeterministic d-dimensional iterative array. Conversely, every language accepted in linear time by such an iterative array is accepted within time $n^{d+1}$ by a nondeterministic one-dimensional Turing machine. It follows that the class of languages accepted in linear time by nondeterministic multidimensional iterative arrays is precisely Karp’s class NP, that nondeterministic $(d + 2)$-dimensional iterative arrays are more powerful than nondeterministic d-dimensional iterative arrays, and that nondeterministic two-dimensional iterative arrays are more powerful than the entire class of nondeterministic multidimensional Turing machines. Related deterministic results are surveyed and summarized for comparison.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Iterative Arrays with Small Time Bounds
Thomas Buchholz,Andreas Klein,Martin Kutrib +2 more
- 01 Sep 2000
TL;DR: In this paper, the authors investigated deterministic iterative arrays with small time bounds between real-time and linear-time, and showed that there exists an infinite dense hierarchy of strictly included complexity classes in that range.
Iterative arrays with limited nondeterministic communication cell
Thomas Buchholz,Andreas Klein,Martin Kutrib +2 more
- 01 Jul 2003
TL;DR: In this article, it is shown that for sub-logarithmic limits there exists an infinite hierarchy of properly included real-time language families, and several closure properties of these families are proved.
Regular biosequence pattern matching with cellular automata
TL;DR: This work suggests it is possible by presenting a systematic approach for creating 1D linear cellular automata that in parallel can locate all starting positions of complete matches to a given PROSITE pattern in a string.
16
•Journal Article
Iterative arrays with small time bounds
TL;DR: It is shown that there exists an infinite dense hierarchy of strictly included complexity classes in that range of deterministic iterative arrays and the result closes the last gap in the time hierarchy of IAs.
13
Iterative Arrays with a Wee Bit Alternation
Thomas Buchholz,Andreas Klein,Martin Kutrib +2 more
- 30 Aug 1999
TL;DR: It is shown that alternation is strictly more powerful than nondeterminism and for sublogarithmic limits there exist infinite hierarchies of properly included alternating language families that are closed under boolean operations.
References
Reducibility Among Combinatorial Problems.
Richard M. Karp
- 01 Jan 1972
TL;DR: Throughout the 1960s I worked on combinatorial optimization problems including logic circuit design with Paul Roth and assembly line balancing and the traveling salesman problem with Mike Held, which made me aware of the importance of distinction between polynomial-time and superpolynomial-time solvability.
13.6K
Separating Nondeterministic Time Complexity Classes
TL;DR: The strongest known dmgonalization results for both deterministic and nondetermlmstlc time complexity classes are reviewed and orgamzed for comparison with the results of the new padding technique.
A hierarchy for nondeterministic time complexity
TL;DR: This paper proves the following theorem: For any real numbers r"1, r"2, [email protected]?r"1 , where r is the number of real numbers and 𝕂 is the inequality between real numbers.
140
A One-Dimensional Real-Time Iterative Multiplier
TL;DR: The class of one-dimensional, real-time, iterative, discrete-state automata is described and it is shown that serial multiplication can be carried out by such a sequential switching network.
106