Algebraic approaches to program semantics
Algebraic approaches to program semantics
Process algebra
The theory of semirings with applications in mathematics and theoretical computer science
The theory of semirings with applications in mathematics and theoretical computer science
Fuzzy sets and fuzzy logic: theory and applications
Fuzzy sets and fuzzy logic: theory and applications
Journal of the ACM (JACM)
Sum-ordered partial semirings
Note on Some Order Properties Related to Processes Semantics (I)
Fundamenta Informaticae - SPECIAL ISSUE ON TRAJECTORIES OF LANGUAGE THEORY Dedicated to the memory of Alexandru Mateescu
Enhancing constraints manipulation in semiring-based formalisms
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
Open bisimulation for the concurrent constraint pi-calculus
ESOP'08/ETAPS'08 Proceedings of the Theory and practice of software, 17th European conference on Programming languages and systems
Invertible matrices and semilinear spaces over commutative semirings
Information Sciences: an International Journal
CC-Pi: a constraint language for service negotiation and composition
Rigorous software engineering for service-oriented systems
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We undertake an axiomatic study of certain semirings and related structures that occur in operations research and computer science. We focus on the properties A,I,U,G,Z,L that have been used in the algebraic study of path problems in graphs and prove that the only implications linking the above properties are essentially those already known. On the other hand we extend those implications to the framework of left and right variants of A,I,U,G,Z,L, and we also prove two embedding theorems. Further generalizations refer mainly to semiring-like algebras with a partially defined addition, which is needed in semantics. As suggested by idempotency (I) and absorption (A), we also examine in some detail the connections between semirings and distributive lattices, which yield new systems of axioms for the latter.