Space complexity equivalence of P systems with active membranes and Turing machines

AbstractThe first definition of space complexity for P systems was based on a hypothetical real implementation by means of biochemical materials, and thus it assumes that every single object or membrane requires some constant physical space. This is equivalent to using a unary encoding to represent multiplicities for each object and membrane. A different approach can also be considered, having in mind an implementation of P systems in silico; in this case, the multiplicity of each object in each membrane can be stored using binary numbers, thus reducing the amount of needed space. In this paper, we give a formal definition for this alternative space complexity measure, we define the corresponding complexity classes and we compare such classes both with standard space complexity classes and with complexity classes defined in the framework of P systems considering the original definition of space.

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A Linear-Time Solution to the Knapsack Problem Using P Systems with Active Membranes

Membrane Computing - Lecture Notes in Computer Science ◽

10.1007/978-3-540-24619-0_19 ◽

2004 ◽

pp. 250-268 ◽

Cited By ~ 34

Author(s):

Mario J. Pérez-Jiménez ◽

Agustin Riscos-Núñez

Keyword(s):

Knapsack Problem ◽

Linear Time ◽

P Systems ◽

Time Solution ◽

Active Membranes

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P Systems with Active Membranes, Without Polarizations and Without Dissolution: A Characterization of P

Lecture Notes in Computer Science - Unconventional Computation ◽

10.1007/11560319_11 ◽

2005 ◽

pp. 105-116 ◽

Cited By ~ 7

Author(s):

Miguel A. Gutiérrez-Naranjo ◽

Mario J. Pérez-Jiménez ◽

Agustín Riscos-Núñez ◽

Francisco J. Romero-Campero

Keyword(s):

P Systems ◽

Active Membranes

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TWO TOPICS CONCERNING TWO-DIMENSIONAL AUTOMATA OPERATING IN PARALLEL

International Journal of Pattern Recognition and Artificial Intelligence ◽

10.1142/s0218001492000126 ◽

1992 ◽

Vol 06 (02n03) ◽

pp. 211-225 ◽

Cited By ~ 1

Author(s):

KATSUSHI INOUE ◽

ITSUO SAKURAMOTO ◽

MAKOTO SAKAMOTO ◽

ITSUO TAKANAMI

Keyword(s):

Turing Machine ◽

Finite Automata ◽

Space Complexity ◽

Two Dimensional ◽

Turing Machines ◽

Small Space ◽

Bottom Up ◽

Constructible Function ◽

Deterministic Turing Machine ◽

Alternating Turing Machines

This paper deals with two topics concerning two-dimensional automata operating in parallel. We first investigate a relationship between the accepting powers of two-dimensional alternating finite automata (2-AFAs) and nondeterministic bottom-up pyramid cellular acceptors (NUPCAs), and show that Ω ( diameter × log diameter ) time is necessary for NUPCAs to simulate 2-AFAs. We then investigate space complexity of two-dimensional alternating Turing machines (2-ATMs) operating in small space, and show that if L (n) is a two-dimensionally space-constructible function such that lim n → ∞ L (n)/ loglog n > 1 and L (n) ≤ log n, and L′ (n) is a function satisfying L′ (n) =o (L(n)), then there exists a set accepted by some strongly L (n) space-bounded two-dimensional deterministic Turing machine, but not accepted by any weakly L′ (n) space-bounded 2-ATM, and thus there exists a rich space hierarchy for weakly S (n) space-bounded 2-ATMs with loglog n ≤ S (n) ≤ log n.

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