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PL
Maszyna Turinga jest opracowanym przez Alana Turinga ideowym modelem programowania. Ten abstrakcyjny model urządzenia służył do zapisu i wykonania algorytmów. Niniejszy artykuł opisuje budowę i sposób działania maszyny Turinga oraz zasady zapisu algorytmów w postaci tabeli przejść. W artykule umieszczono przykład użycia symulatora maszyny Turinga do rozwiązania przykładowego zadania. Analiza zamieszczonego przykładu, pozwoli odbiorcy, na przyswojenie sposobu szukania rozwiązania problemu, dla ideowego modelu komputera, jakim jest maszyna Turinga.
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Content available Implementation of the Turing machine symulator
EN
This paper describes the process of designing and implementing a Turing machine simulator application. The created desktop application is distinguished from other solutions by the use of the latest technology and offline operating. The various stages of the project are described, such as defining requirements, creating UML diagrams, and prototyping the user interface. A MVVM architectural model used in building the application is presented. The issues of controls, data binding, and message passing found in the Avalonia package are addressed. The unit tests created and the exploratory tests performed are also described.
PL
Artykuł opisuje proces projektowania i implementacji aplikacji symulatora maszyny Turinga. Wytworzona aplikacja desktopowa wyróżnia się wśród innych rozwiązań zastosowaniem najnowszych technologii i brakiem konieczności połączenia z Internetem. Opisano poszczególne etapy projektu, takie jak zdefiniowanie wymagań, utworzenie diagramów UML, sporządzenie prototypu interfejsu użytkownika. Przedstawiony został wzorzec architektoniczny MVVM zastosowany podczas budowy aplikacji. Poruszono kwestie kontrolek, wiązania danych i przesyłania komunikatów występujące w pakiecie Avalonia. Opisano także utworzone testy jednostkowe i przeprowadzone testy eksploracyjne.
EN
In this paper, a dynamic model of computation based on the Universal Turing Machine is proposed. This model is capable of applying runtime code modifications for 3-symbol deterministic Turing Machines at runtime and requires a decomposition of the simulated machine into parts called subtasks. The algorithm for performing runtime changes is considered, and the ability to apply runtime changes is studied through computer simulations. Theoretical properties of the proposed model, including computational power as well as time and space complexity, are studied and proven. Connections between the proposed model and Oracle Machines are discussed. Moreover, a possible method of implementation in real-life systems is proposed.
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Content available remote Fuzzy and Intuitionistic Fuzzy Turing Machines
EN
First we define a new class of fuzzy Turing machines that we call Generalized Fuzzy Turing Machines. Our machines are equipped with rejecting states as well as accepting states. While we use a t-norm for computing degrees of accepting or rejecting paths, we use its dual t-conorm for computing the accepting or rejecting degrees of inputs. We naturally define when a generalized fuzzy Turing machine accepts or decides a fuzzy language. We prove that a fuzzy language L is decidable if and only if L and its complement are acceptable. Moreover, to each r.e. or co-r.e language L, we naturally correspond a fuzzy language which is acceptable by a generalized fuzzy Turing machine. A converse to this result is also proved. We also consider Atanasov’s intuitionistic fuzzy languages and introduce a version of fuzzy Turing machine for studying their computability theoretic properties.
EN
The goal of the presented paper is to provide an introduction to the basic computational models used in quantum information theory. We review various models of quantum Turing machine, quantum circuits and quantum random access machine (QRAM) along with their classical counterparts. We also provide an introduction to quantum programming languages, which are developed using the QRAM model. We review the syntax of several existing quantum programming languages and discuss their features and limitations.
EN
The aim of this paper is the development of foundations for evolutionary computations. To achieve this goal, a mathematical model of evolutionary automata is introduced and studied. The main classes of evolutionary automata considered in this paper are evolutionary Turing machines and evolutionary inductive Turing machines. Various subclasses and modes of evolutionary computation are defined. Problems of existence of universal objects in these classes are explored. Relations between Turing machines, inductive Turing machines, evolutionary Turing machines, and evolutionary inductive Turing machines are investigated.
7
Content available remote Modelling of Complex Systems: Systems as Dataflow Machines
EN
We develop a unified functional formalism for modelling complex systems, that is to say systems that are composed of a number of heterogeneous components, including typically software and physical devices. Our approach relies on non-standard analysis that allows us to model continuous time in a discrete way. Systems are defined as generalized Turing machines with temporized input, internal and output mechanisms. Behaviors of systems are represented by transfer functions. A transfer function is said to be implementable if it is associated with a system. This notion leads us to define a new class - which is natural in our framework - of computable functions on (usual) real numbers. We show that our definitions are robust: on one hand, the class of implementable transfer functions is closed under composition; on the other hand, the class of computable functions in our meaning includes analytical functions whose coefficients are computable in the usual way, and is closed under addition, multiplication, differentiation and integration. Our class of computable functions also includes solutions of dynamical and Hamiltonian systems defined by computable functions. Hence, our notion of system appears to take suitably into account physical systems.
EN
In this paper three models of polymorphic viruses are presented. These models had to capture self-reproduction, evolution and damaging payload of polymorphic viruses. They have been derived using a formal model of Evolutionary Computation the Evolutionary Turing Machine, cellular space models, and the $-calculus process algebra for problem solving. Some preliminary results associated with these models are discussed.
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Content available remote Funkcje normalne jako nowy model definiowania funkcji obliczalnych
PL
Artykuł prezentuje nową metodę definiowania funkcji obliczalnych. Metoda jest formalizacją tradycyjnego zapisu funkcji i pozwala na określanie funkcji w sposób intuicyjny. W systemie funkcji rekursywnych Hilberta nie wszystkie odwzorowania, które mają łatwe algorytmy obliczania, mogą być równie łatwo zdefiniowane formalnie, czego przykładem jest funkcja Ackermanna. Funkcje normalne są pozbawione tej wady.
EN
Report sets new method of defining computable functions. This is formalization of traditional function descriptions, so it allows to define functions in very intuitive way. Discovery of Ackermann function proved that not all functions that can be easily computed can be so easily described with Hilbert's system of recursive functions. Normal functions lack this disadvantage.
11
Content available remote Generowanie maszyn Turinga poprzez zastosowanie nowych modeli obliczeniowych
PL
Dla każdego problemu obliczalnego istnieje algorytm jego rozwiązania, który może być przedstawiony w postaci konkretnej maszyny Turinga. Ze względu na prostotę tej maszyny programy są bardzo skomplikowane i nieprzejrzyste. Dlatego tworzy się inne modele obliczenia, na których można szybko i łatwo zapisywać algorytmy związane z danym typem problemu, a następnie symuluje się działanie tych modeli na maszynie Turinga. Niniejszy artykuł przedstawia metodologię znajdowania modelu obliczeniowego pasującego do danego typu problemów i przekształcenie go w odpowiednią maszynę Turinga na przykładzie obliczeń na liczbach naturalnych.
EN
For each problem that can be solved there exists algorithm, which can be described with a program of Turing machine. Because this is very simple model programs tend to be very complicated and hard to analyse by human. The best practice to solve given type of problems is to define a new model of computation that allows for quick and easy programming, and then to emulate its operation with Turing machine. This article shows how to define most suitable model for computation on natural numbers and defines Turing machine that emulates its operation.
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Content available remote Simulating Turing Machines by P Systems with External Output
EN
In [3] a variant of the computation model introduced by Gh. Pun in [1] is considered: membrane systems with external output, which were proven to be universal, in the sense that they are able to generate all Parikh images of recursively enumerable languages. Here we give another proof of the universality of this model. The proof is carried out associating to each deterministic Turing machine a P system with external output that simulates its running. Thus, although we work with symbol-objects, we get strings as a result of computations, and in this way we generate directly all recursively enumerable languages, instead of their images through Parikh mapping, as it is done in [3].
13
Content available remote Thue specifications, infinite graphs and synchronized product
EN
This paper presents some formal verification-oriented results about the class of graphs associated with Thue specifications. It is shown that this class is closed, up to isomorphism, under synchronized product. It is also established that every rational graph with no edge labeled by the empty word is isomorphic to the graph of a Thue specification. A consequence of this result is that the first-order theory of the graphs of Thue specifications is undecidable. Connections between graphs of Thue specifications and those of Turing machines are finally investigated. The main result is that the graph of each Thue specification is observationally equivalent to that of a Turing machine but the reverse does not hold.
14
Content available remote Relative cost random access machines
EN
The purpose of a model of computation is to provide the algorithm designer a device for run-ning algorithms. It should be conceptually clear to let him or her concentrate at the algo-rithmic ideas for solving the problem. At the same time it should be concrete enough to give a realistic estimate on the use resources, when the algorithm is executed on a real computer. In this paper we analyze some weaknesses of existing models of computation, namely sequential access machine and random access machine and propose a new cost model, called relative cost random access machine, which solves some contradictions between these models. The new model actually only generalizes the way of counting the complexity, and includes se-quential access machines and random access machines as special cases. At the same time, it is flexible enough to characterize the cost of memory access in current computers.
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