|
Semi-deterministic Büchi Automaton
In automata theory, a semi-deterministic Büchi automaton (also known as Büchi automaton deterministic in the limit, or limit-deterministic Büchi automaton) is a special type of Büchi automaton. In such an automaton, the set of states can be partitioned into two subsets: one subset forms a deterministic automaton and also contains all the accepting states. For every Büchi automaton, a semi-deterministic Büchi automaton can be constructed such that both recognize the same ω-language. But, a deterministic Büchi automaton may not exist for the same ω-language. Motivation In standard model checking against linear temporal logic (LTL) properties, it is sufficient to translate an LTL formula into a non-deterministic Büchi automaton. But, in probabilistic model checking, LTL formulae are typically translated into deterministic Rabin automata (DRA), as for instance in the PRISM tool. However, a fully deterministic automaton is not needed. Indeed, semi-deterministic Büchi a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Automata Theory
Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them. It is a theory in theoretical computer science. The word ''automata'' comes from the Greek word αὐτόματος, which means "self-acting, self-willed, self-moving". An automaton (automata in plural) is an abstract self-propelled computing device which follows a predetermined sequence of operations automatically. An automaton with a finite number of states is called a Finite Automaton (FA) or Finite-State Machine (FSM). The figure on the right illustrates a finite-state machine, which is a well-known type of automaton. This automaton consists of states (represented in the figure by circles) and transitions (represented by arrows). As the automaton sees a symbol of input, it makes a transition (or jump) to another state, according to its transition function, which takes the previous state and current input symbol as its arguments. Automata theo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Aided Verification
In computer science, the International Conference on Computer-Aided Verification (CAV) is an annual academic conference on the theory and practice of computer-aided formal analysis of software and hardware systems, broadly known as formal methods. It is one of the highest-ranked conferences in computer science. Among the important results originally published in CAV are breakthrough techniques in model checking, such as Counterexample-Guided Abstraction Refinement (CEGAR) and partial order reduction. The first CAV was held in 1989 in Grenoble, France. The CAV proceedings (1989-present) are published by Springer Science+Business Media and are open access. See also * List of computer science conferences * Symposium on Logic in Computer Science * European Joint Conferences on Theory and Practice of Software External links *bibliography for CAVat DBLP DBLP is a computer science bibliography website. Starting in 1993 at Universität Trier in Germany, it grew from a small co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lecture Notes In Computer Science
''Lecture Notes in Computer Science'' is a series of computer science books published by Springer Science+Business Media since 1973. Overview The series contains proceedings, post-proceedings, monographs, and Festschrifts. In addition, tutorials, state-of-the-art surveys, and "hot topics" are increasingly being included. The series is indexed by DBLP. See also *''Monographiae Biologicae'', another monograph series published by Springer Science+Business Media *''Lecture Notes in Physics'' *''Lecture Notes in Mathematics'' *''Electronic Workshops in Computing ''Electronic Workshops in Computing'' (eWiC) is a publication series by the British Computer Society. The series provides free online access for conferences and workshops in the area of computing. For example, the EVA London Conference proceeding ...'', published by the British Computer Society References External links * Publications established in 1973 Computer science books Series of non-fiction books Springer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Büchi Automaton
In computer science and automata theory, a deterministic Büchi automaton is a theoretical machine which either accepts or rejects infinite inputs. Such a machine has a set of states and a transition function, which determines which state the machine should move to from its current state when it reads the next input character. Some states are accepting states and one state is the start state. The machine accepts an input if and only if it will pass through an accepting state infinitely many times as it reads the input. A non-deterministic Büchi automaton, later referred to just as a Büchi automaton, has a transition function which may have multiple outputs, leading to many possible paths for the same input; it accepts an infinite input if and only if some possible path is accepting. Deterministic and non-deterministic Büchi automata generalize deterministic finite automata and nondeterministic finite automata to infinite inputs. Each are types of ω-automata. Büchi automata rec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partition Of A Set
In mathematics, a partition of a set is a grouping of its elements into non-empty subsets, in such a way that every element is included in exactly one subset. Every equivalence relation on a set defines a partition of this set, and every partition defines an equivalence relation. A set equipped with an equivalence relation or a partition is sometimes called a setoid, typically in type theory and proof theory. Definition and Notation A partition of a set ''X'' is a set of non-empty subsets of ''X'' such that every element ''x'' in ''X'' is in exactly one of these subsets (i.e., ''X'' is a disjoint union of the subsets). Equivalently, a family of sets ''P'' is a partition of ''X'' if and only if all of the following conditions hold: *The family ''P'' does not contain the empty set (that is \emptyset \notin P). *The union of the sets in ''P'' is equal to ''X'' (that is \textstyle\bigcup_ A = X). The sets in ''P'' are said to exhaust or cover ''X''. See also collectively exhaus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ω-language
In formal language theory within theoretical computer science, an infinite word is an infinite-length sequence (specifically, an ω-length sequence) of symbols, and an ω-language is a set of infinite words. Here, ω refers to the first ordinal number, the set of natural numbers. Formal definition Let Σ be a set of symbols (not necessarily finite). Following the standard definition from formal language theory, Σ* is the set of all ''finite'' words over Σ. Every finite word has a length, which is a natural number. Given a word ''w'' of length ''n'', ''w'' can be viewed as a function from the set → Σ, with the value at ''i'' giving the symbol at position ''i''. The infinite words, or ω-words, can likewise be viewed as functions from \mathbb to Σ. The set of all infinite words over Σ is denoted Σω. The set of all finite ''and'' infinite words over Σ is sometimes written Σ∞ or Σ≤ω. Thus an ω-language ''L'' over Σ is a subset of Σω. Operations Some common ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Model Checking
In computer science, model checking or property checking is a method for checking whether a finite-state model of a system meets a given specification (also known as correctness). This is typically associated with hardware or software systems, where the specification contains liveness requirements (such as avoidance of livelock) as well as safety requirements (such as avoidance of states representing a system crash). In order to solve such a problem algorithmically, both the model of the system and its specification are formulated in some precise mathematical language. To this end, the problem is formulated as a task in logic, namely to check whether a structure satisfies a given logical formula. This general concept applies to many kinds of logic and many kinds of structures. A simple model-checking problem consists of verifying whether a formula in the propositional logic is satisfied by a given structure. Overview Property checking is used for verification when two desc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Temporal Logic
In logic, linear temporal logic or linear-time temporal logic (LTL) is a modal temporal logic with modalities referring to time. In LTL, one can encode formulae about the future of paths, e.g., a condition will eventually be true, a condition will be true until another fact becomes true, etc. It is a fragment of the more complex CTL*, which additionally allows branching time and quantifiers. Subsequently, LTL is sometimes called ''propositional temporal logic'', abbreviated ''PTL''. In terms of expressive power, linear temporal logic (LTL) is a fragment of first-order logic. LTL was first proposed for the formal verification of computer programs by Amir Pnueli in 1977. Syntax LTL is built up from a finite set of propositional variables ''AP'', the logical operators ¬ and ∨, and the temporal modal operators X (some literature uses O or N) and U. Formally, the set of LTL formulas over ''AP'' is inductively defined as follows: * if p ∈ ''AP'' then p is an LTL formula; * if ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PRISM Model Checker
PRISM is a probabilistic model checker, a formal verification software tool for the modelling and analysis of systems that exhibit probabilistic behaviour.Kwiatkowska, M.; Norman, G.; Parker, D. "Probabilistic model checking in practice: Case studies with PRISM". ''ACM SIGMETRICS Performance Evaluation Review'', 32(4), pages 16–21. One source of such systems is the use of randomization, for example in communication protocols like Bluetooth and FireWire, or in security protocols such as Crowds and Onion routing. Stochastic behaviour also arises in many other computer systems, for example due to equipment failures or unpredictable communication delays. Yet another class of systems amenable to this kind of analysis are biochemical reaction networks. PRISM can be used to analyse several different types of probabilistic models, including discrete-time Markov chains, continuous-time Markov chains, Markov decision processes and probabilistic extensions of the timed automata formalis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Power Set
In mathematics, the power set (or powerset) of a set is the set of all subsets of , including the empty set and itself. In axiomatic set theory (as developed, for example, in the ZFC axioms), the existence of the power set of any set is postulated by the axiom of power set. The powerset of is variously denoted as , , , \mathbb(S), or . The notation , meaning the set of all functions from S to a given set of two elements (e.g., ), is used because the powerset of can be identified with, equivalent to, or bijective to the set of all the functions from to the given two elements set. Any subset of is called a ''family of sets'' over . Example If is the set , then all the subsets of are * (also denoted \varnothing or \empty, the empty set or the null set) * * * * * * * and hence the power set of is . Properties If is a finite set with the cardinality (i.e., the number of all elements in the set is ), then the number of all the subsets of is . This fact as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kőnig's Lemma
Kőnig's lemma or Kőnig's infinity lemma is a theorem in graph theory due to the Hungarian mathematician Dénes Kőnig who published it in 1927. It gives a sufficient condition for an infinite graph to have an infinitely long path. The computability aspects of this theorem have been thoroughly investigated by researchers in mathematical logic, especially in computability theory. This theorem also has important roles in constructive mathematics and proof theory. Statement of the lemma Let G be a connected, locally finite, infinite graph. This means that every two vertices can be connected by a finite path, the graph has infinitely many vertices, and each vertex is adjacent to only finitely many other vertices. Then G contains a ray: a simple path (a path with no repeated vertices) that starts at one vertex and continues from it through infinitely many vertices. A useful special case of the lemma is that every infinite tree contains either a vertex of infinite degree or an in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
.jpg "Click for more on -> Model Checking")
