Abstract
A class of P systems, called EOP systems, with symbol objects processed by evolution rules distributed alongside the transitions of an Eilenberg machine, is introduced. A parallel variant of EOP systems, called EOPP systems, is also defined and the power of both EOP and EOPP systems is investigated in relationship with three parameters: number of membranes, states and set of distributed rules. It is proven that the family of Parikh sets of vectors of numbers generated by EOP systems with one membrane, one state and one single set of rules coincides with the family of Parikh sets of context-free languages. The hierarchy collapses when at least one membrane, two states and four sets of rules are used and in this case a characterization of the family of Parikh sets of vectors associated with ET0L languages is obtained. It is also shown that every EOP system may be simulated by an EOPP system and EOPP systems may be used for solving NP-complete problems. In particular linear time solutions are provided for the SAT problem.
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References
Bălănescu, T., Gheorghe, M., Holcombe, M., Ipate, F.: Eilenberg P systems. In: Păun, G., Rozenberg, G., Salomaa, A., Zandron, C. (eds.) WMC 2002. LNCS, vol. 2597, pp. 43–57. Springer, Heidelberg (2003)
Bălănescu, T., Cowling, T., Georgescu, H., Gheorghe, M., Holcombe, M., Vertan, C.: Communicating stream X-machines systems are no more than X-machines. J. Universal Comp. Sci. 5, 494–507 (1997)
Calude, C., Păun, G.: Computing with Cells and Atoms. Taylor and Francis, London (2000)
Csuhaj-Varju, E., Dassow, J., Kelemen, J., Păun, G.: Grammar Systems. Gordon & Breach, London (1994)
Dassow, J., Păun, G.: Regulated Rewriting in Formal Language Theory. Springer, Berlin (1989)
Eilenberg, S.: Automata, Languages and Machines. Academic Press, New York (1974)
Ferretti, C., Mauri, G., Păun, G., Zandron, C.: On three variants of rewriting P systems. In: Martin-Vide, C., Păun, G. (eds.) Pre-proceedings of Workshop on Membrane Computing (WMC-CdeA2001), Curtea de Argeş, Romania, August 2001, pp. 63–76 (2001), Theor. Comp. Sci. (to appear)
Gheorghe, M.: Generalised stream X-machines and cooperating grammar systems. Formal Aspects of Computing 12, 459–472 (2000)
Holcombe, M.: X-machines as a basis for dynamic system specification. Software Engineering Journal 3, 69–76 (1998)
Holcombe, M., Ipate, F.: Correct Systems Building a Business Process Solution. Applied Computing Series. Springer, Berlin (1998)
Krishna, S.N., Rama, R.: P systems with replicated rewriting. Journal of Automata, Languages and Combinatorics 6, 345–350 (2001)
Păun, G.: Computing with membranes. Journal of Computer System Sciences 61, 108–143 (1998), and Turku Center for Computer Science, TUCS Report 208, http://www.tucs.fi
Păun, G.: Membrane computing. An Introduction. Springer, Berlin (2002)
Rozenberg, G., Salomaa, A.: The Mathematical Theory of L Systems. Academic Press, New York (1980)
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Bernardini, F., Gheorghe, M., Holcombe, M. (2003). Eilenberg P Systems with Symbol-Objects. In: Jonoska, N., Păun, G., Rozenberg, G. (eds) Aspects of Molecular Computing. Lecture Notes in Computer Science, vol 2950. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24635-0_4
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DOI: https://doi.org/10.1007/978-3-540-24635-0_4
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