Topic
Semiring
About: Semiring is a research topic. Over the lifetime, 1685 publications have been published within this topic receiving 19849 citations. The topic is also known as: rig.
Papers published on a yearly basis
1 / 2
Papers
Book•
14 Mar 2014
TL;DR: In this paper, the authors define Hemirings and semirings as "sets and relations with values with values in a semiring" and define a set of conditions on semimodal construction.
Abstract: Preface. 1. Hemirings and semirings: definitions and examples. 2. Sets and relations with values in a semiring. 3. Building new semirings from old. 4. Some conditions on semirings. 5. Complemented elements in semirings. 6. Ideals in semirings. 7. Prime and semiprime ideals in semirings. 8. Factor semirings. 9. Morphisms of semirings. 10. Kernels of morphisms. 11. Semirings of fractions. 12. Euclidean semirings. 13. Additively-regular semirings. 14. Semimodules over semirings. 15. Factor semimodules. 16. Some constructions for semimodules. 17. Free, projective, and injective semimodules. 18. Localization of semimodules. 19. Linear algebra over a semiring. 20. Partially-ordered semirings. 21. Lattice-ordered semirings. 22. Complete semirings. 23. Complete semimodules. 24. CLO-semirings. 25. Fixed points of affine maps. References. Index of applications. Index of terminology.
1,268 citations
[...]
TL;DR: This paper initiates the study of soft semirings by using the soft set theory, and the notions of soft Semirings, soft subsemirings,soft ideals, idealistic softSemirings and soft semiring homomorphisms are introduced, and several related properties are investigated.
Abstract: Molodtsov introduced the concept of soft sets, which can be seen as a new mathematical tool for dealing with uncertainty. In this paper, we initiate the study of soft semirings by using the soft set theory. The notions of soft semirings, soft subsemirings, soft ideals, idealistic soft semirings and soft semiring homomorphisms are introduced, and several related properties are investigated.
657 citations
Journal Article•
TL;DR: A generic algorithm for finding single-source shortest distances in a weighted directed graph when the weights satisfy the conditions of the general semiring framework is given.
Abstract: We define general algebraic frameworks for shortest-distance problems based on the structure of semirings. We give a generic algorithm for finding single-source shortest distances in a weighted directed graph when the weights satisfy the conditions of our general semiring framework. The same algorithm can be used to solve efficiently classical shortest paths problems or to find the k-shortest distances in a directed graph. It can be used to solve single-source shortest-distance problems in weighted directed acyclic graphs over any semiring. We examine several semirings and describe some specific instances of our generic algorithms to illustrate their use and compare them with existing methods and algorithms. The proof of the soundness of all algorithms is given in detail, including their pseudocode and a full analysis of their running time complexity.
330 citations
17 Jun 1991
TL;DR: By using monadic second-order logic and semiring homomorphisms, this work describes in a single formalism a large class of functions on graphs that can be computed recursively on the derivation trees of these graphs.
Abstract: Every graph generated by a hyperedge replacement graph-grammar can be represented by a tree, namely the derivation tree of the derivation sequence that produced it. Certain functions on graphs can be computed recursively on the derivation trees of these graphs. By using monadic second-order logic and semiring homomorphisms, we describe in a single formalism a large class of such functions. Polynomial and even linear algorithms can be constructed for some of these functions. We unify similar results obtained by Takamizawa et al. (1982), Bern et al. (1987), Arnborg et al. (1991) and Habel et al. (1989).
194 citations
Journal Article•
[...]
TL;DR: This work synthesizes work on parsing algorithms, deductive parsing, and the theory of algebra applied to formal languages into a general system for describing parsers that allows a single, simple representation to be used for describing Parsers that compute recognition, derivation forests, Viterbi, n-best, inside values, and other values.
Abstract: We synthesize work on parsing algorithms, deductive parsing, and the theory of algebra applied to formal languages into a general system for describing parsers. Each parser performs abstract computations using the operations of a semiring. The system allows a single, simple representation to be used for describing parsers that compute recognition, derivation forests, Viterbi, n-best, inside values, and other values, simply by substituting the operations of different semirings. We also show how to use the same representation, interpreted differently, to compute outside values. The system can be used to describe a wide variety of parsers, including Earley's algorithm, tree adjoining grammar parsing, Graham Harrison Ruzzo parsing, and prefix value computation.
187 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 32 |
| 2024 | 43 |
| 2023 | 92 |
| 2022 | 151 |
| 2021 | 79 |
| 2020 | 104 |