2020, Volume 9
2019, Volume 8
2018, Volume 7
2017, Volume 6
2016, Volume 5
2015, Volume 4
2014, Volume 3
2013, Volume 2
2012, Volume 1

Volume 3, Issue 6, December 2014, Page: 295-302
Multisorted Tree Algebra
Erick Patrick Zobo, Department of Computer Sciences and Education Technologies (DITE), University of Yaounde I Yaounde, Cameroon
Marcel Fouda Ndjodo, Department of Computer Sciences and Education Technologies (DITE), University of Yaounde I Yaounde, Cameroon
Received: Nov. 24, 2014;       Accepted: Dec. 5, 2014;       Published: Dec. 16, 2014
DOI: 10.11648/j.acm.20140306.12      View  2848      Downloads  192
This paper introduces basic concepts describing a hierarchical algebraic structure called multisorted tree algebra. This structure is constructed by placing multisorted algebra at the bottom of a hierarchy and placing at other intermediate nodes the aggregation of algebras placed at their immediate subordinate nodes. These constructions are different from the one of subalgebras, homomorphic images and product algebras used to characterize varieties in universal algebra theory. The resulting hierarchical algebraic structures cannot be easily classified in common universal algebra varieties. The aggregation method and the fundamental properties of the aggregated algebras have been presented with an illustrative example. Multisorted tree algebras spans multisorted algebra concepts and can be used as modelling framework for building hierarchical abstract data types for information processing in organizations.
Multisorted Algebra, Hierarchy, Aggregation, Abstract Data Type
To cite this article
Erick Patrick Zobo, Marcel Fouda Ndjodo, Multisorted Tree Algebra, Applied and Computational Mathematics. Vol. 3, No. 6, 2014, pp. 295-302. doi: 10.11648/j.acm.20140306.12
K. D. . S. L. Wismath, Universal Algebra and Applications in Theoretical Computer Science, CRC, 2002.
S. Burris. . H. P. Shankappanavar, A Course in Universal Algebra, the millenium edition Edition, Springer-Verlag, ewkiss/univ-algebra.pdf, 1981.
W. Wechler, Universal Algebra for Computer Scientists, Springer-Verlag, 1992.
C. Oriat, Etude des speci_cations modulaires: constructions de colimites _nies, diagrammes, isomorphismes, Informatique, Institut National Polytechnique de Grenoble, Laboratoire Logiciels Systmes et Rseaux (LSR-IMAG) (janvier 1996).
A. Mucka. al., Many-sorted and single-sorted algebras, Algebra Universalis 69 (2013) 171{190.
J. A. Goguen, Hidden algebraic engineering, in: C. Nahaniv (Ed.), Conference on semi groups and algebraic engineering, University Aisu, 1997.
J. Goguen, Hidden algebra for software engineering, in: Proc. Conf. Discrete Mathematics and Theoretical Computer Science, Vol. 21 of Australian Computer Science Communications, 1999, pp. 35{59.
J. Stell, A framework for order-sorted algebra, in: H. Kirchner, C. Ringeissen (Eds.), Algebraic Methodology and Software Technology, Vol. 2422 of Lecture Notes in Computer Science, Springer Berlin Heidelberg, 2002, pp. 396{411.
J. J. M. M. Rutten, Universal coalgebra: a theory of systems (2000).
G. Rosu, Hidden logic, Phd, University of California, San Diego (2000).
T. V. Zandt, Real-time hierarchical resource allocation,
M. W. A. Knapp, A formal approach to object-oriented software engineering, Theoretical ComputerScience 285 (2002) 519{560.
T. V. Zandt, Hierarchical computation of the resource allocation problem, European Economic Review39 (1995) 700{708.
F. H. Trinkl, Hierarchical resource allocation decisions, Policy Sciences 4 (1973) 211{221.
J. G. . G. Malcom, A hidden agenda, Theoretical Computer science 245 (2000) 55{101.
M. Barr, C. Wells, Category Theory for Computer Science, Pintice-Hall International, 1990.
J. L. Fiadeiro, Cathegories for software engineering, Springer, 2005.
G. Manzonetto, A. Salibra, From -calculus to universal algebra and back, in: MFCS08, volume 5162 of LNCS, 2008, pp. 479{490.
V. Capretta, Universal algebra in type theory, in: Theorem Proving in Higher Order Logics, 12th International Conference, TPHOLs '99, volume 1690 of LNCS, Springer-Verlag, 1999, pp. 131{148.
J. V. Guttag, Abstract data types and the development of data structures, Communication of the ACM6 (1977) 396{404.
J. A. Goguen, G. Malcolm, Software Engineering with OBJ: algebraic specification in action, Vol. Advances in Formal Methods, Kluwer Academic Publishers, 2000.
Browse journals by subject