Stochastic Relations: Foundations for Markov Transition Systems
暫譯: 隨機關係：馬可夫轉移系統的基礎
Doberkat, Ernst-Erich
- 出版商: CRC
- 出版日期: 2019-09-05
- 售價: $2,990
- 貴賓價: 9.5 折 $2,841
- 語言: 英文
- 頁數: 376
- 裝訂: Quality Paper - also called trade paper
- ISBN: 0367389118
- ISBN-13: 9780367389116
海外代購書籍(需單獨結帳)
商品描述
Collecting information previously scattered throughout the vast literature, including the author’s own research, Stochastic Relations: Foundations for Markov Transition Systems develops the theory of stochastic relations as a basis for Markov transition systems.
After an introduction to the basic mathematical tools from topology, measure theory, and categories, the book examines the central topics of congruences and morphisms, applies these to the monoidal structure, and defines bisimilarity and behavioral equivalence within this framework. The author views developments from the general theory of coalgebras in the context of the subprobability functor. These tools show that bisimilarity and behavioral and logical equivalence are the same for general modal logics and for continuous time stochastic logic with and without a fixed point operator.
With numerous problems and several case studies, this book is an invaluable study of an important aspect of computer science theory.
商品描述(中文翻譯)
收集了先前散佈在廣泛文獻中的資訊，包括作者自己的研究，隨機關係：馬可夫轉移系統的基礎 發展了隨機關係的理論，作為馬可夫轉移系統的基礎。
在介紹了來自拓撲學、測度論和範疇的基本數學工具後，本書探討了同餘和態射的核心主題，將這些應用於單元結構，並在此框架內定義了雙模擬性和行為等價。作者在子機率函子背景下，將一般的共代數理論的發展視為重要內容。這些工具顯示，對於一般的模態邏輯以及有無固定點運算子的連續時間隨機邏輯，雙模擬性和行為及邏輯等價是相同的。
本書包含大量問題和幾個案例研究，是計算機科學理論中一個重要方面的寶貴研究。
目錄大綱
Introduction. A Gentle Tutorial to All Things Considered. Stochastic Relations as Monads. Eilenberg–Moore Algebras for Stochastic Relations. The Existence of Semi-Pullbacks. Congruences and Bisimulations. Interpreting Modal and Temporal Logics. Appendix. Bibliography. Index.
目錄大綱(中文翻譯)
Introduction. A Gentle Tutorial to All Things Considered. Stochastic Relations as Monads. Eilenberg–Moore Algebras for Stochastic Relations. The Existence of Semi-Pullbacks. Congruences and Bisimulations. Interpreting Modal and Temporal Logics. Appendix. Bibliography. Index.
