Time-freeness and clock-freeness and related concepts in P systems

Abstract : In the majority of models of P systems, rules are applied at the ticks of a global clock and their products are introduced into the system for the following step. In timed P systems, different integer durations are statically assigned to rules; time-free P systems are P systems yielding the same languages independently of these durations. In clock-free P systems, durations are real and are assigned to individual rule applications; thus, different applications of the same rule may last for a different amount of time. In this paper, we formalise timed, time-free, and clock-free P system within a framework for generalised parallel rewriting. We then explore the relationship between these variants of semantics. We show that clock-free P systems cannot efficiently solve intractable problems. Moreover, we consider un-timed systems where we collect the results using arbitrary timing functions as well as un-clocked P systems where we take the union over all possible per-instance rule durations. Finally, we also introduce and study mode-free P systems, whose results do not depend on the choice of a mode within a fixed family of modes, and compare mode-freeness with clock-freeness.
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https://hal.archives-ouvertes.fr/hal-01893373
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Submitted on : Thursday, October 11, 2018 - 12:45:39 PM
Last modification on : Friday, January 3, 2020 - 8:59:08 PM

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Artiom Alhazov, Rudolf Freund, Sergiu Ivanov, Linqiang Pan, Bosheng Song. Time-freeness and clock-freeness and related concepts in P systems. Theoretical Computer Science, Elsevier, 2020, 805, pp.127--143. ⟨10.1016/j.tcs.2018.09.009⟩. ⟨hal-01893373⟩

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