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On the power of membrane dissolution in polarizationless P systems with active membranes

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Abstract

It is known that dissolution rules are necessary in polarizationless P systems with active membranes to solve problems beyond \(\mathbf {AC^0}\) using reasonable tight uniformity conditions (Murphy and Woods, Fundam Inf Series 134:129–152, 2014). On the other hand, no solutions of such problems exist using only dissolution rules. In this paper, we show that the \(\mathbf {NL}\)-complete reachability problem can be solved in polynomial time by polarizationless P systems with active membranes using only dissolution rules under a suitable uniformity condition.

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References

  • Alhazov A, Martín-Vide C, Pan L (2003) Solving a \(\rm PSPACE\)-complete problem by P systems with restricted active membranes. Fundam Inf Series 58:67–77

    MATH  Google Scholar 

  • Alhazov A, Pérez-Jiménez MJ (2007) Uniform solution of QSAT using polarizationless active membranes. In: International conference on machines, computations and universality, pp 122-133

  • Gazdag Z, Hajagos K, Iván Sz (2021) On the power of P systems with active membranes using weak non-elementary membrane division. J Membr Comput 3:258–269

  • Gazdag Z, Gutiérrez-Naranjo MA (2014) Solving the ST-connectivity problem with pure membrane computing techniques. In: Gheorghe, M., Rozenberg, G., Salomaa, A., Sosík, P., Zandron, C. (Eds.) Membrane Computing: 15th International Conference, LNCS vol. 8961, pp 215–228

  • Gazdag Z, Kolonits G (2019) A new method to simulate restricted variants of polarizationless P systems with active membranes. J Membr Comput 1(4):251–261

  • Gensler HJ (2002) Introduction to Logic. Routledge, London

    Book  MATH  Google Scholar 

  • Gutierrez-Naranjo MA, Perez-Jimenez MJ, Riscos-Núñez A, Romero-Campero FJ (2006) On the power of dissolution in P systems with active membranes. In: Freund, R., Păun, Gh., Rozenberg, G., Salomaa, A. (Eds.) Membrane computing: 6th international workshop, LNCS vol. 3850, pp 224–240

  • Jones ND (1975) Space-bounded reducibility among combinatorial problems. J Comput Syst Sci 11(1):68–85

    Article  MathSciNet  MATH  Google Scholar 

  • Krishna SN, Rama R (1999) A variant of P systems with active membranes: solving NP-complete problems. Roman J Inf Sci Technol 2(4):357–367

    Google Scholar 

  • Leporati A, Manzoni L, Mauri G, Porreca AE, Zandron C (2014) Simulating elementary active membranes, with an application to the P conjecture. In: M. Gheorghe, G. Rozenberg, A. Salomaa, P. Sosík, C. Zandron (Eds.) Membrane Computing – 15th international conference, CMC15, LNCS vol. 8961, pp 284–299

  • Leporati A, Manzoni L, Mauri G, Porreca AE, Zandron C (2017) Solving a special case of the P conjecture using dependency graphs with dissolution. In: Gheorghe, M., Rozenberg, G., Salomaa, A., Zandron, C. (Eds.) Membrane Computing: 18th international conference, LNCS vol. 10725, pp 196-213

  • Murphy N, Woods D (2007) Active membrane systems without charges and using only symmetric elementary division characterise P. In: Eleftherakis, G., Kefalas, P., Păun, Gh., Rozenberg, G., Salomaa, A. (Eds.) Membrane Computing: 8th international workshop, LNCS vol. 4860, pp 367–384

  • Murphy N, Woods D (2008) A characterisation of NL using membrane systems without charges and dissolution. In: Calude, C.S., da Costa, J.F.G., Freund, R., Oswald, M., Rozenberg, G. (Eds.) Unconventional Computing: 7th International Conference, LNCS vol. 5204, pp 164–176

  • Murphy N, Woods D (2009) On acceptance conditions for membrane systems: characterisations of \(\mathbf{L}\) and \(\mathbf{NL}\). In Neary, T., Woods, D., Seda, T., Murphy, N., (Eds)., Proceedings of the international workshop on the complexity of simple programs, Cork, Ireland, Vol. 1 of Electronic proceedings in theoretical computer science., Open Publishing Association, pp 172–184

  • Murphy N, Woods D (2014) Uniformity is weaker than semi-uniformity for some membrane systems. Fundam Inf Series 134(1–2):129–152

    MathSciNet  MATH  Google Scholar 

  • Orellana-Martín D, Riscos-Núnez A (2020) Seeking computational efficiency boundaries: the Păun’s conjecture. J Membr Comput 2:323–331

    Article  MathSciNet  MATH  Google Scholar 

  • Păun Gh (2001) P systems with active membranes: attacking NP-complete problems. J Automata, Lang Comb Series 6(1):75–90

    MathSciNet  MATH  Google Scholar 

  • Păun Gh (2005) Further twenty six open problems in membrane computing. In: Third brainstorming week on membrane computing, pp. 249–262. Fénix Editora, Sevilla

  • Păun Gh, Rozenberg G, Salomaa A (eds) (2010) The Oxford Handbook of Membrane Computing. Oxford University Press, Oxford, England

    MATH  Google Scholar 

  • Pérez-Jiménez MJ, Romero-Jiménez Á, Sancho-Caparrini F (2006) A polynomial complexity class in P systems using membrane division. J Autom Lang Comb 11(4):423–434

    MathSciNet  MATH  Google Scholar 

  • Salomaa A (1973) Formal Languages. Academic Press, New York, London

    MATH  Google Scholar 

  • Sosík P (2003) The computational power of cell division in P systems. Natural Computing series 2(3):287–298

    Article  MATH  Google Scholar 

  • Sosík P (2019) P systems attacking hard problems beyond NP: a survey. J Membr Comput 1:198–208

    Article  MathSciNet  MATH  Google Scholar 

  • Sosík P, Rodríguez-Patón A (2007) Membrane computing and complexity theory: a characterization of PSPACE. J Comput Syst Sci Series 73(1):137–152

  • Woods D, Murphy N, Pérez-Jiménez MJ, Riscos-Núnez A (2009) Membrane dissolution and division in P. In: Calude, C.S., da Costa, J.F.G., Dershowitz, N., Freire, E., Rozenberg, G. (Eds.) Unconventional Computation: 8th international conference, LNCS vol. 5715, pp 262–276

  • Zandron C, Ferretti C, Mauri G (2001) Solving NP-complete problems using P systems with active membranes. In: Unconventional models of computation, UMC’2K: Proceedings of the Second international conference on unconventional models of computation. Springer London, London, pp 289–301

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Acknowledgements

We thank the anonymous reviewers for their constructive comments, which helped us to improve the manuscript. This research was supported by project TKP2021-NVA-09, implemented with the support provided by the Ministry of Innovation and Technology of Hungary from the National Research, Development and Innovation Fund, financed under the TKP2021-NVA funding scheme.

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  1. Institute of Informatics, University of Szeged, Árpád tér 2, Szeged, H-6720, Hungary

    Zsolt Gazdag & Károly Hajagos

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  1. Zsolt Gazdag
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  2. Károly Hajagos
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Correspondence to Zsolt Gazdag.

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Gazdag, Z., Hajagos, K. On the power of membrane dissolution in polarizationless P systems with active membranes. Nat Comput 22, 95–104 (2023). https://doi.org/10.1007/s11047-022-09926-x

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