|
Stutter Bisimulation
In theoretical computer science, a stutter bisimulation''Principles of Model Checking'', by Christel Baier and Joost-Pieter Katoen, The MIT Press, Cambridge, Massachusetts. is defined in a coinductive manner, as is ''bisimulation''. Let TS=(S,Act,→,I,AP,L) be a transition system. A stutter bisimulation for TS is a binary relation In mathematics, a binary relation associates elements of one set, called the ''domain'', with elements of another set, called the ''codomain''. A binary relation over Set (mathematics), sets and is a new set of ordered pairs consisting of ele ... R on S such that for all (s1,s2) which is in R: # L(s1) = L(s2). # If s1' is in Post(s1) with (s1',s2) is not in R, then there exists a finite path fragment s2u1…uns2' with n≥0 and (s1,ui) is in R, and (s1',s2') is in R. # If s2' is in Post(s2) with (s1,s2') is not in R, then there exists a finite path fragment s1v1…vns1' with n≥0 and (vi,s2) is in R, and (s1',s2') is in R. References {{reflist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theoretical Computer Science
Theoretical computer science (TCS) is a subset of general computer science and mathematics that focuses on mathematical aspects of computer science such as the theory of computation, lambda calculus, and type theory. It is difficult to circumscribe the theoretical areas precisely. The Association for Computing Machinery, ACM's ACM SIGACT, Special Interest Group on Algorithms and Computation Theory (SIGACT) provides the following description: History While logical inference and mathematical proof had existed previously, in 1931 Kurt Gödel proved with his incompleteness theorem that there are fundamental limitations on what statements could be proved or disproved. Information theory was added to the field with a 1948 mathematical theory of communication by Claude Shannon. In the same decade, Donald Hebb introduced a mathematical model of Hebbian learning, learning in the brain. With mounting biological data supporting this hypothesis with some modification, the fields of n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Principles Of Model Checking
''Principles of Model Checking'' is a textbook on model checking, an area of computer science that automates the problem of determining if a machine meets specification requirements. It was written by Christel Baier and Joost-Pieter Katoen, and published in 2008 by MIT Press. Synopsis The introduction and first chapter outline the field of model checking: a model of a machine or process can be analysed to see if desirable properties hold. For instance, a vending machine might satisfy the property "the balance can never fall below €0,00". A video game might enforce the rule "if the player has 0 lives then the game ends in a loss". Both the vending machine and video game can be modelled as transition systems. Model checking is the process of describing such requirements in mathematical language, and automating proofs that the model satisfies the requirements, or discovery of counterexamples if the model is faulty. The second chapter focuses on creating an appropriate model for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Christel Baier
Christel Baier (born 26 September 1965) is a German theoretical computer scientist known for her work in model checking, temporal logic, and automata theory. She is a professor at TU Dresden, where she holds the chair for Algebraic and Logic Foundations of Computer Science in the Faculty of Computer Science. Baier is the editor-in-chief of ''Acta Informatica''. Education and career Baier earned a diploma in mathematics at the University of Mannheim in 1990, and stayed at the same university for graduate study in computer science, completing her Ph.D. there in 1994. Her dissertation, ''Transitionssystem- und Baum-Semantiken für CCS'', was supervised by Mila Majster-Cederbaum. She earned a habilitation at Mannheim in 1999. She became an associate professor for computer science at the University of Bonn in 1999, and moved to TU Dresden as a professor in 2006. Book With Joost-Pieter Katoen, Baier is coauthor of the book ''Principles of Model Checking'' (MIT Press, 2008). Recogni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joost-Pieter Katoen
Joost-Pieter Katoen (born October 6, 1964) is a Dutch theoretical computer scientist based in Germany. He is distinguished professor in Computer Science and head of the Software Modeling and Verification Group at RWTH Aachen University. Furthermore, he is part-time associated to the Formal Methods & Tools group at the University of Twente. Education Katoen received his master's degree with distinction in Computer Science from the University of Twente in 1987. In 1990, he was awarded a Professional Doctorate in Engineering from the Eindhoven University of Technology, and in 1996, he received his Ph.D. in computer science from the University of Twente. Research Katoen's main research interests are formal methods, computer aided verification, in particular model checking, concurrency theory, and semantics, in particular semantics of probabilistic programming languages. His research is largely tool and application oriented. Together with Christel Baier he wrote and published the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coinductive
In computer science, coinduction is a technique for defining and proving properties of systems of concurrent interacting objects. Coinduction is the mathematical dual to structural induction. Coinductively defined types are known as codata and are typically infinite data structures, such as streams. As a definition or specification, coinduction describes how an object may be "observed", "broken down" or "destructed" into simpler objects. As a proof technique, it may be used to show that an equation is satisfied by all possible implementations of such a specification. To generate and manipulate codata, one typically uses corecursive functions, in conjunction with lazy evaluation. Informally, rather than defining a function by pattern-matching on each of the inductive constructors, one defines each of the "destructors" or "observers" over the function result. In programming, co-logic programming (co-LP for brevity) "is a natural generalization of logic programming and coindu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bisimulation
In theoretical computer science a bisimulation is a binary relation between state transition systems, associating systems that behave in the same way in that one system simulates the other and vice versa. Intuitively two systems are bisimilar if they, assuming we view them as playing a ''game'' according to some rules, match each other's moves. In this sense, each of the systems cannot be distinguished from the other by an observer. Formal definition Given a labelled state transition system (S, \Lambda, →), where S is a set of states, \Lambda is a set of labels and → is a set of labelled transitions (i.e., a subset of S \times \Lambda \times S), a bisimulation is a binary relation R \subseteq S \times S, such that both R and its converse R^T are simulations. From this follows that the symmetric closure of a bisimulation is a bisimulation, and that each symmetric simulation is a bisimulation. Thus some authors define bisimulation as a symmetric simulation. Equivalentl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transition System
In theoretical computer science, a transition system is a concept used in the study of computation. It is used to describe the potential behavior of discrete systems. It consists of states and transitions between states, which may be labeled with labels chosen from a set; the same label may appear on more than one transition. If the label set is a singleton, the system is essentially unlabeled, and a simpler definition that omits the labels is possible. Transition systems coincide mathematically with abstract rewriting systems (as explained further in this article) and directed graphs. They differ from finite-state automata in several ways: * The set of states is not necessarily finite, or even countable. * The set of transitions is not necessarily finite, or even countable. * No "start" state or "final" states are given. Transition systems can be represented as directed graphs. Formal definition Formally, a transition system is a pair (S, \rightarrow) where S is a set of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Relation
In mathematics, a binary relation associates elements of one set, called the ''domain'', with elements of another set, called the ''codomain''. A binary relation over Set (mathematics), sets and is a new set of ordered pairs consisting of elements in and in . It is a generalization of the more widely understood idea of a unary function. It encodes the common concept of relation: an element is ''related'' to an element , if and only if the pair belongs to the set of ordered pairs that defines the ''binary relation''. A binary relation is the most studied special case of an Finitary relation, -ary relation over sets , which is a subset of the Cartesian product X_1 \times \cdots \times X_n. An example of a binary relation is the "divides" relation over the set of prime numbers \mathbb and the set of integers \mathbb, in which each prime is related to each integer that is a Divisibility, multiple of , but not to an integer that is not a multiple of . In this relation, for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
