Time-Free Solution to Hamilton Path Problems Using P Systems withd-Division

Abstract

P systems withd-division are a particular class of distributed and parallel computing models investigated in membrane computing, which are inspired from the budding behavior of Baker’s yeast (a cell can generate several cells in one reproducing cycle). In previous works, such systems can theoretically generate exponential working space in linear time and thus provide a way to solve computational hard problems in polynomial time by a space-time tradeoff, where the precise execution time of each evolution rule, one time unit, plays a crucial role. However, the restriction that each rule has a precise same execution time does not coincide with the biological fact, since the execution time of biochemical reactions can vary because of external uncontrollable conditions. In this work, we consider timed P systems withd-division by adding a time mapping to the rules to specify the execution time for each rule, as well as the efficiency of the systems. As a result, a time-free solution to Hamiltonian path problem (HPP) is obtained by a family of such systems (constructed in a uniform way), that is, the execution time of the rules (specified by different time mappings) has no influence on the correctness of the solution.

Time‐Free Solution to 3‐Coloring Problem Using Tissue P Systems

“…The execution time of rules is determined by the time mapping e, thus it is possible that there exist one rule whose execution time is inherently exponential steps. The step is called a RSstep (rule starting step), if at this step at least one rules of system Π(e) starts its execution [34] . The RS-steps can be used to characterize how fast to solve a decision problem by using timed tissue P systems.…”

“…Therefore, it is natural to investigate P systems without the constrain on the execution time of rules [30−33] . Recently, several types of P systems have been considered by adding a time mapping to specify the execution time of each rule [34,35] . If for an arbitrary time mapping, a system always generates the same results, we say that it is time-free.…”

“…In Ref. [34], a family of time-free P systems with d division are constructed in a uniform way to solve Hamiltonian path problem (HPP). In Ref.…”

Implementation of Arithmetic Operations With Time-Free Spiking Neural P Systems

“…In [7], M. Cavaliere suggest a possible application of the notion of time-freeness to solutions of computational hard problems. A time-free solution to Hamilton Path Problems using membrane systems was proposed in [15]. Recently, timefreeness were introduced into SN P systems by Pan et al [13], where time-free SN P systems with extended rules (several spikes can be produced by a rule) are proved to be Turing complete.…”

Solving Multidimensional 0-1 Knapsack Problem with Time-Free Tissue P Systems

“…The concept of time-free was first introduced in [35]. In [36], a time-free solution to Hamilton Path Problems using cell-like P systems was investigated. In this work, we construct a family of time-free tissue P systems to solve another well-known NP-complete problem: the multidimensional 0-1 knapsack problem.…”