Note on Some Order Properties Related to Processes Semantics (I)

• Autorzy: Vaida D.
• Języki publikacji: EN

Abstrakty

EN

This note begins a study of some elementary properties related to the order structures applied in the algebraic approach to processes semantics. The support examples come from the partially additive semantics developed by Steenstrup (1985) and Manes and Arbib (1986) and from process algebra of Baeten and Weijland (1990). The main sources for the algebraic theory are F.A.Smith (1966) and Golan (1999). We show that different properties can be extended to partially additive distributive algebras more general than sum-ordered partial semirings. One establishes that the support examples constitute multilattices, in the sense of Benado (1955). By the examples, the ordering considered, and the references, this preliminary study is related to Rudeanu et al. (2004) and to the algebraic approach to languages due to Mateescu, e.g., (1996), (1989), (1994).

Słowa kluczowe

EN

partial additive semantics; process algebras; semiring

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2006
• Tom: Vol. 73, nr 1-2
• Strony: 307--319
• Opis fizyczny: bibliogr. 23 poz.

Twórcy

autor

Vaida D.

• Faculty of Mathematics and Computer Science, Bucharest University, Str. Academiei 14, 010014 Bucharest, Romania [e-mail],

Bibliografia

• [1] J.C.M. Baeten, W.P. Weijland: Process Algebra. Cambridge, Cambridge Univ. Press (Cambridge Tracts in Theoretical Computer Science), 1990.
• [2] M. Benado: Les ensembles partiellement ordonnés et le théoréme de raffinement de Schreier, II (Theorie des multistructures). Czechoslovak Math., 5 (1955), 308-344.
• [3] G. Birkhoff: Lattice Theory. Amer. Math. Soc., Providence, R.I., 1967 (third ed., third printing, 1973).
• [4] P. Bottoni, S. Levialdi, D. Vaida: Ordered structures for visual data: An algebraic-oriented approach to visual interaction. Rapporto di Ricerca, SI 2000/08, Dipartimento di Scienze dell'Informazione, Universita degli Studi La Sapienza, Roma, 2000.
• [5] W.H. Cornish, A.S.A. Noor: Standard elements in a near lattice. Bull. Austral. Math. Soc., 26 (1980) 185-213.
• [6] L. Fuchs: Partially Ordered Algebraic Systems. International Series of Monographs on Pure and Applied Mathematics, vol. 28, Pergamon Press, Oxford/London/New York/Paris, 1963.
• [7] J.S. Golan: Semirings and their Applications. Kluwer Academic Publishers, Dordrecht/Boston/London, 1999.
• [8] J.S. Golan, A. Mateescu, D. Vaida: Semirings and parallel composition of processes. Journal of Automata, Languages and Combinatorics, 1 (1996), 199-217.
• [9] U. Hebisch, H.J. Weinert: Semirings - Algebraic Theory and Applications in Computer Science. Ser. Alg., vol. 5, World Sci., Singapore, 1996.
• [10] W. Kuich, A. Salomaa: Semirings, Automata, Languages. EATCS Monographs on Theoretical Computer Science no. 5, Springer-Verlag, Berlin, 1986.
• [11] E.G. Manes, M.A. Arbib: Algebraic Approach to Program Semantics. Springer-Verlag, Berlin, 1986.
• [12] E.G. Manes, D.B. Benson: The inverse semigroup of a sum-ordered semiring. Semigroup Forum, 31 (1985), 129-152.
• [13] A. Mateescu: Marcus contextual grammars with shuffled contexts. In Mathematical Aspects of Natural and Formal Languages (Gh. P˘aun, ed.),World Scientific Publ. Co. Singapore, 1994, 273-284.
• [14] A. Mateescu, D. Vaida: Structuri matematice discrete. Editura Academiei, Bucures¸ti (Preface S. Marcus), Gramatici Van Wijngaarden, 1989, 73-298.
• [15] A. Mateescu, D. Vaida: Limbaje formale s¸i tehnici de compilare - Aplicat¸ii ale algebrelor multisortate în informatică (Caietul I). Universitatea din Bucureşti, Bucureşti, 1982.
• [16] A. Mateescu, D. Vaida: Limbaje formale s¸i tehnici de compilare - Nedecidabilitate ˆın teoria limbajelor. Semantica part¸ial aditiv˘a (Caietul III, Partea I). Universitatea din Bucures¸ti, Bucureşti, 1989.
• [17] S. Rudeanu: Axiomele laticilor s¸i ale algebrelor Booleene. Ed. Academiei Române, Bucharest, 1963.
• [18] S. Rudeanu, D. Vaida: Semirings in operations research and computer science: More algebra. Fundamenta Informaticae, 61 (2004), 61-85.
• [19] F.A. Smith: A structure theory for a class of lattice-ordered semirings. Fund. Math., 59 (1966), 49-64.
• [20] M.E. Steenstrup: Sum-Ordered Partial Semirings. PhD Thesis, University of Massachusetts, Boston, February, 1985.
• [21] D. Vaida: On partially additive semirings and applications. Mult.-Val. Logic, 6 (2001), 251-266.
• [22] D. Vaida: Note on more general setting for complemented elements (I) (Remarks from Semirings Theory). Manuscript, 2005.
• [23] A. Vescan: Elemente de teoria laticelor s¸i aplicat¸ii. Editura Dacia, Cluj-Napoca, 1984.