2015
DOI: 10.3233/fi-2015-1201
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Abstract: Polynomial-time P systems with active membranes characterise PSPACE by exploiting membranes nested to a polynomial depth, which may be subject to membrane division rules. When only elementary (leaf) membrane division rules are allowed, the computing power decreases to P PP = P #P , the class of problems solvable in polynomial time by deterministic Turing machines equipped with oracles for counting (or majority) problems. In this paper we investigate a variant of intermediate power, limiting membrane nesting (h… Show more

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Cited by 25 publications
(21 citation statements)
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“…The resulting simulation is also efficient, requiring a slowdown of only a constant multiplicative factor. However, some problems remain open, and the most prominent one is to study if the construction presented in [1] can be replicated for systems with charges, possibly adding an additional nesting level to accommodate for the different TM simulation technique. Such a result would show that even without charges the entire counting hierarchy can be computed in constant depth.…”
Section: Discussionmentioning
confidence: 99%
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“…The resulting simulation is also efficient, requiring a slowdown of only a constant multiplicative factor. However, some problems remain open, and the most prominent one is to study if the construction presented in [1] can be replicated for systems with charges, possibly adding an additional nesting level to accommodate for the different TM simulation technique. Such a result would show that even without charges the entire counting hierarchy can be computed in constant depth.…”
Section: Discussionmentioning
confidence: 99%
“…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%
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“…In fact, depth 1 systems have been proved [2] to be limited to solve in polynomial time the problems in P #P , a class which is conjecturally smaller than PSPACE. 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: 88%
“…On the other hand, confluent P systems working with membrane structure of nesting depth 1 are known to solve exactly the problems in PP = #P [12,37]. The last result was generalized in [13], where it has been shown that constant-depth confluent P systems solve the problems in the counting hierarchy in polynomial time and, more precisely, that depth−k P systems solve the problems in C k P in polynomial time, where C k P is the k− th level of the hierarchy.…”
mentioning
confidence: 99%