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Cited by 12 publications
(24 citation statements)
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“…amount of communication produces a significant increase of the computational power of P systems. Contrarily to many other models, where P # is reached (see, for example, [1,2,4]), in this case we are only able to reach the conjecturally smaller complexity class P # ∥ . One interesting aspect of this result is that the construction used to build a system simulating a Turing machine remains practically unchanged with respect to the one employed for monodirectional P systems.…”
Section: Introductionmentioning
confidence: 89%
See 2 more Smart Citations
“…amount of communication produces a significant increase of the computational power of P systems. Contrarily to many other models, where P # is reached (see, for example, [1,2,4]), in this case we are only able to reach the conjecturally smaller complexity class P # ∥ . One interesting aspect of this result is that the construction used to build a system simulating a Turing machine remains practically unchanged with respect to the one employed for monodirectional P systems.…”
Section: Introductionmentioning
confidence: 89%
“…where the equality of the inclusions depends on the specific oracle chosen. As shown in [4], the complexity class P # [1] is the same as P # ∥ . That is, performing one oracle query or a polynomial number of them in parallel does not change the computational power of these systems, working with # oracles.…”
Section: Definitionmentioning
confidence: 99%
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“…The construction of P systems simulating Turing machines (TM) using as few membranes (or cells) as possible and limiting the depth of the system is one of the "tricks" that allowed the nesting of multiple machines to solve problems in large complexity classes. For example, nesting of non-deterministic machines (where the non-determinism was simulated by membrane division) and a counting mechanism allows to characterize P #P , the class of all problems solvable by a deterministic TM with access to a #P oracle [1,3]. The same ideas can be applied to tissue P systems [4], where the different communication topology makes even more important to keep TM simulations compact [2].…”
Section: Introductionmentioning
confidence: 99%
“…Furthermore, even with constant depth the currently known problems that can be solved all reside inside the counting hierarchy [3] and we conjecture this inclusion to actually be an upper bound on the computational power of constant depth P systems. Even in other models of P systems, like tissue P systems or depth 1 P systems with antimatter, the class P #P provides a strict upper bound on the computational power [5,4].…”
Section: Introductionmentioning
confidence: 99%