Abstract
We introduce a new model of membrane computing system (or P system), called signaling P system. It turns out that signaling systems are a form of P systems with promoters that have been studied earlier in the literature. However, unlike non-cooperative P systems with promoters, which are known to be universal, non-cooperative signaling systems have decidable reachability properties. Our focus in this paper is on verification problems of signaling systems; i.e., algorithmic solutions to a verification query on whether a given signaling system satisfies some desired behavioral property. Such solutions not only help us understand the power of “maximal parallelism” in P systems but also would provide a way to validate a (signaling) P system in vitro through digital computers when the P system is intended to simulate living cells. We present decidable and undecidable properties of the model of non-cooperative signaling systems using proof techniques that we believe are new in the P system area. For the positive results, we use a form of “upper-closed sets” to serve as a symbolic representation for configuration sets of the system, and prove decidable symbolic model-checking properties about them using backward reachability analysis. For the negative results, we use a reduction via the undecidability of Hilbert’s Tenth Problem. This is in contrast to previous proofs of universality in P systems where almost always the reduction is via matrix grammar with appearance checking or through Minsky’s two-counter machines. Here, we employ a new tool using Diophantine equations, which facilitates elegant proofs of the undecidable results. With multiplication being easily implemented under maximal parallelism, we feel that our new technique is of interest in its own right and might find additional applications in P systems.
The work by Cheng Li and Zhe Dang was supported in part by NSF Grant CCF-0430531. The work by Oscar H. Ibarra was supported in part by NSF Grants CCR-0208595 and CCF-0430945.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alur, R., Dill, D.L.: A theory of timed automata. TCS 126(2), 183–235 (1994)
Ardelean, I.I., Cavaliere, M., Sburlan, D.: Computing using signals: From cells to P Systems. In: Second Brainstorming Week on Membrane Computing, Sevilla, Spain, February 2-7, pp. 60–73 (2004)
Becker, W.M., Kleinsmith, L.J., Hardin, J.: The World of the Cell, 5th edn. Benjamin Cummings, San Francisco (2003)
Bottoni, P., Martin-Vide, C., Paun, G., Rozenberg, G.: Membrane systems with promoters/inhibitors. Acta Informatica 38(10), 695–720 (2002)
Bultan, T., Gerber, R., Pugh, W.: Model-checking concurrent systems with unbounded integer variables: symbolic representations, approximations, and experimental results. TOPLAS 21(4), 747–789 (1999)
Clarke, E.M., Emerson, E.A., Sistla, A.P.: Automatic verification of finite-state concurrent systems using temporal logic specifications. TOPLAS 8(2), 244–263 (1986)
Clarke, E.M., Grumberg, O., Peled, D.A.: Model Checking. MIT Press, Cambridge (1999)
Dang, Z., Ibarra, O.H., Li, C., Xie, G.: On model-checking of P systems (2005) (submitted)
Esparza, J.: Decidability and complexity of Petri net problems - an introduction. In: Petri Nets, pp. 374–428 (1996)
Freund, R., Kari, L., Oswald, M., Sosik, P.: Computationally universal P systems without priorities: two catalysts are sufficient (2003), Available at http://psystems.disco.unimib.it
Freund, R., Paun, G.: On deterministic P systems (2003), Available at http://psystems.disco.unimib.it
Ibarra, O.H.: The number of membranes matters. In: Martín-Vide, C., Mauri, G., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2003. LNCS, vol. 2933, pp. 218–231. Springer, Heidelberg (2004)
Ibarra, O.H., Dang, Z., Egecioglu, O.: Catalytic P systems, semilinear sets, and vector addition systems. Theoretical Computer Science 312(2-3), 379–399 (2004)
Ibarra, O.H., Yen, H., Dang, Z.: The power of maximal parallelism in P systems. In: Calude, C.S., Calude, E., Dinneen, M.J. (eds.) DLT 2004. LNCS, vol. 3340, pp. 212–224. Springer, Heidelberg (2004)
Ito, M., Martin-Vide, C., Paun, G.: A characterization of Parikh sets of ET0L languages in terms of P systems. In: Words, Semigroups, and Transducers, pp. 239–254. World Scientific, Singapore
Martin-Vide, C., Paun, G.: Computing with membranes (P systems): universality results. In: Margenstern, M., Rogozhin, Y. (eds.) MCU 2001. LNCS, vol. 2055, pp. 82–101. Springer, Heidelberg (2001)
Matiyasevich, Y.V.: Hilbert’s Tenth Problem. MIT Press, Cambridge (1993)
Paun, G.: Computing with membranes. JCSS 61(1), 108–143 (2000)
Paun, G.: Membrane Computing: An Introduction. Springer, Heidelberg (2002)
Paun, G., Rozenberg, G.: A guide to membrane computing. TCS 287(1), 73–100 (2002)
Sosik, P.: P systems versus register machines: two universality proofs. In: Păun, G., Rozenberg, G., Salomaa, A., Zandron, C. (eds.) WMC 2002. LNCS, vol. 2597, pp. 371–382. Springer, Heidelberg (2003)
Sosik, P., Freund, R.: P systems without priorities are computationally universal. In: Păun, G., Rozenberg, G., Salomaa, A., Zandron, C. (eds.) WMC 2002. LNCS, vol. 2597, pp. 400–409. Springer, Heidelberg (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Li, C., Dang, Z., Ibarra, O.H., Yen, HC. (2005). Signaling P Systems and Verification Problems. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds) Automata, Languages and Programming. ICALP 2005. Lecture Notes in Computer Science, vol 3580. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11523468_118
Download citation
DOI: https://doi.org/10.1007/11523468_118
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-27580-0
Online ISBN: 978-3-540-31691-6
eBook Packages: Computer ScienceComputer Science (R0)