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

Issue title: SPECIAL ISSUE ON TRAJECTORIES OF LANGUAGE THEORY Dedicated to the memory of Alexandru Mateescu

Article type: Research Article

Authors: Vaida, Dragoş

Affiliations: Faculty of Mathematics and Computer Science Bucharest University Str. Academiei 14, 010014 Bucharest, Romania. dvaida@funinf.cs.unibuc.ro

Abstract: 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).

Keywords: Partial additive semantics, process algebra, semirings

Journal: Fundamenta Informaticae, vol. 73, no. 1-2, pp. 307-319, 2006