Abstract
Multisets are the fundamental data structure of P systems. In this paper we relate P systems with the language and theory for multisets presented in [9.] This allows us, on the one hand, to define and implement P systems using multiset constraints in a constraint logic programming framework, and, on the other hand, to define and implement constraint solving procedures used to test multiset constraint satisfiability in terms of P systems with active membranes. While the former can be exploited to provide a precise formulation of a P system, as well as a working implementation of it, based on a first-order theory, the latter provides a way to obtain a P system for a given problem (in particular, NP problems) starting from a rather natural encoding of its solution in terms of multiset constraints.
Partially supported by MURST project Certificazione automatica di programmi mediante interpretazione astratta.
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
K. R. Apt. From Logic Programming to Prolog. International Series in Computer Science. Prentice Hall, 1997.
P. Arenas-Sánchez, F. J. López-Fraguas, M. Rodríguez-Artalejo Embedding Multiset Constraints into a Lazy Functional Logic LanguageIn C. Palamidessi, H. Glaser, K. Meinke, editors, Principles of Declarative Programming, LNCS 1490, Springer-Verlag, pp. 429–444, 1998.
J. Bănatre and D. Le Métayer. Programming by Multiset Transformation. Communications of the ACM, 36(1):98–111. January 1993.
G. Berry and G. Boudol. The Chemical Abstract Machine. Theoretical Computer Science, vol. 96 (1992) 217–248.
J.-P. Bodeveix, C. Percebois, S. Majoul. An Object-Oriented Coordination Model based on Multiset Rewriting. In Proc. of Ninth International Conference on Parallel and Distributed Computing Systems. Dijon, France, 1996.
I. Cervesato, N. Durgin, P. Lincoln, J. Mitchell, and A. Scedrov. Relating Strands and Multiset Rewriting for Security Protocol Analysis In P. Syverson, ed., 13th IEEE Computer Security Foundations Workshop—CSFW’00, pp. 35–51, 2000.
P. Ciancarini, D. Fogli, and M. Gaspari. A Logic Language Based on GAMMA-like Multiset Rewriting. In R. Dyckho., H. Herre, P. Schroeder-Heister eds., Extensions of Logic Programming, 5th International Workshop, LNCS 1050, 1996, pp. 83–101.
E. Dantsin and A. Voronkov. A Nondeterministic Polynomial-Time Unification Algorithm for Bags, Sets and Trees. In W. Thomas ed., Foundations of Software Science and Computation Structure, LNCS Vol. 1578, pages 180–196, 1999.
A. Dovier, A. Policriti, and G. Rossi. A uniform axiomatic view of lists, multisets, and sets, and the relevant unification algorithms. Fundamenta Informaticae, 36(2/3):201–234, 1998.
A. Dovier, C. Piazza, and G. Rossi. A uniform approach to constraintsolving for lists, multisets, compact lists, and sets. Technical Report, Dipartimento di Matematica, Universit`a di Parma, no. 235, July 2000 (available at http://prmat.math.unipr.it/-gianfr/PAPERS/RRPR235.ps).
A. Dovier, E. G. Omodeo, E. Pontelli, and G. Rossi. log: A Language for Programming in Logic with Finite Sets. Journal of Logic Programming, 28(1):1–44, 1996.
A. Dovier, C. Piazza, E. Pontelli, and G. Rossi. Sets and constraint logic programming. ACM Transaction on Programming Language and Systems (TOPLAS), 22(5) 2000, pp. 861–931.
G. Gupta and E. Pontelli. Optimization Schemas for Parallel Implementation of Nondeterministic Languages. Int. Parallel Proc. Symposium, IEEE, pp. 428–435, 1997.
C. Hankin, D. Le Métayer, and D. Sands. A Parallel Programming Style and Its Algebra of Programs. In Proc. Conf. on Parallel Architecture and Languages Europe (PARLE 93), vol. 694 of LNCS, 367–378, Springer-Verlag, Berlin, 1993.
J. Herbrand. Recherches sur la theorie de la demonstration. Master’s thesis, Universit’e de Paris, 1930. Also in Ecrits logiques de Jacques Herbrand, PUF, Paris, 1968.
J. Jaffar and M. J. Maher. Constraint Logic Programming: A Survey. Journal of Logic Programming, 19-20:503–581, 1994.
J. Jaffar, M. J. Maher, K. Marriott, and P. J. Stuckey. The Semantics of Constraint Logic Programs. Journal of Logic Programming 37 (1–3), 1–46, 1998.
K. Marriott, B. Meyer, and K. B. Wittenburg. A survey of visual language specification and recognition. In K. Marriott and B. Meyer, editors, Visual Language Theory pages 5–85, Springer, 1998.
A. Mal’cev. Axiomatizable Classes of Locally Free Algebras of Various Types. In The Metamathematics of Algebraic Systems, Collected Papers, Ch. 23. North Holland, 1971.
A. Martelli and U. Montanari. An efficient unification algorithm. ACM Transactions on Programming Languages and Systems 4 (1982), 258–282.
G. Păun. Computing with Membranes. Journal of Computer and System Science, 61(1):108–143, 2000.
G. Păun. Attacking NP Complete Problems. Journal of Automata, Languages and Combinatorics, 6(1):75–90, 2001.
G. Rossi. The Languages CLP(SET) and CLP(BAG) User Manuals and Running Interpreters. In http://prmat.math.unipr.it/-gianfr/setlog.Home.html.
A. Tzouvaras. The Linear Logic of Multisets. Logic Journal of the IGPL, Vol. 6, No. 6, pp. 901–916, 1998.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dovier, A., Piazza, C., Rossi, G. (2001). Multiset Constraints and P Systems. In: Calude, C.S., PĂun, G., Rozenberg, G., Salomaa, A. (eds) Multiset Processing. WMC 2000. Lecture Notes in Computer Science, vol 2235. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45523-X_6
Download citation
DOI: https://doi.org/10.1007/3-540-45523-X_6
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43063-6
Online ISBN: 978-3-540-45523-3
eBook Packages: Springer Book Archive