WMC 2005: Membrane Computing pp 144-158 | Cite as
On the Computational Power of the Mate/Bud/Drip Brane Calculus: Interleaving vs. Maximal Parallelism
Abstract
Brane calculi are a family of biologically inspired process calculi proposed in [3] for modeling the interactions of dynamically nested membranes. In [3] two basic calculi are proposed. Mate/Bud/Drip (MBD) is one of such basic calculi, and its primitives are inspired by membrane fusion and fission.
In this paper we investigate the expressiveness of MBD w.r.t. its ability to act as a computational device. In particular, we compare the expressiveness of two different semantics for MBD: the standard interleaving semantics – where a single interaction is executed at each computational step – and the maximal parallelism semantics – according to which a computational step is composed of a maximal set of independent interactions.
For the interleaving semantics, we show a nondeterministic encoding of Register Machines in MBD, that preserves the existence of a terminating computation, but that could introduce additional divergent (i.e., infinite) computations.
For the maximal parallelism semantics, we provide a deterministic encoding of Register Machines, which preserves both the existence of a terminating computation and the existence of a divergent computation.
The impossibilty of providing a deterministic encoding under the interleaving semantics is a consequence of the decidability of the existence of a divergent computation proved in [1].
Keywords
Parallel Composition Computational Step Register Membrane Program Counter Register MachinePreview
Unable to display preview. Download preview PDF.
References
- 1.Busi, N., Gorrieri, R.: On the computational power of brane calculi. In: Proc. Third Workshop on Computational Methods in Systems Biology (CMSB 2005), Edinburgh, Scotland (2005)Google Scholar
- 2.Busi, N., Zavattaro, G.: Deciding reachability in mobile ambients. In: Sagiv, M. (ed.) ESOP 2005. LNCS, vol. 3444, pp. 248–262. Springer, Heidelberg (2005)CrossRefGoogle Scholar
- 3.Cardelli, L.: Brane calculi – Interactions of biological membranes. In: Danos, V., Schachter, V. (eds.) CMSB 2004. LNCS (LNBI), vol. 3082, pp. 257–278. Springer, Heidelberg (2005)CrossRefGoogle Scholar
- 4.Cardelli, L., Gordon, A.D.: Mobile ambients. Theoretical Computer Science 240(1), 177–213 (2000)MATHCrossRefMathSciNetGoogle Scholar
- 5.Cardelli, L., Păun, G.: An universality result for a (mem)brane calculus based on mate/drip operations. International Journal of Foundations of Computer Science (to appear)Google Scholar
- 6.Freund, R.: Asynchronous P Systems and P Systems Working in the Sequential Mode. In: Mauri, G., Păun, G., Jesús Pérez-Jímenez, M., Rozenberg, G., Salomaa, A. (eds.) WMC 2004. LNCS, vol. 3365, pp. 36–62. Springer, Heidelberg (2005)CrossRefGoogle Scholar
- 7.Minsky, M.L.: Computation: Finite and Infinite Machines. Prentice-Hall, Englewood Cliffs (1967)MATHGoogle Scholar
- 8.Păun, G.: Computing with membranes. Journal of Computer and System Sciences 61(1), 108–143 (2000)MATHCrossRefMathSciNetGoogle Scholar
- 9.Păun, G.: Membrane Computing. An Introduction. Springer, Berlin (2002)MATHGoogle Scholar
- 10.Regev, A., Panina, E.M., Silverman, W., Cardelli, L., Shapiro, E.: BioAmbients: An abstraction for biological compartments. Theoretical Computer Science 325(1), 141–167 (2004)MATHCrossRefMathSciNetGoogle Scholar
- 11.Reisig, W.: Petri Nets: An Introduction. Springer, Berlin (1985)MATHGoogle Scholar
- 12.Shepherdson, J.C., Sturgis, J.E.: Computability of recursive functions. Journal of the ACM 10, 217–255 (1963)MATHCrossRefMathSciNetGoogle Scholar