First-order definable string transformations

The connection between languages defined by computational models and logic for languages is well-studied. Monadic second-order logic and finite automata are shown to closely correspond to each-other for the languages of strings, trees, and partial-orders. Similar connections are shown for first-order logic and finite automata with certain aperiodicity restriction. Courcelle in 1994 proposed a way to use logic to define functions over structures where the output structure is defined using logical formulas interpreted over the input structure. Engelfriet and Hoogeboom discovered the corresponding "automata connection" by showing that two-way generalised sequential machines capture the class of monadic-second order definable transformations. Alur and Cerny further refined the result by proposing a one-way deterministic transducer model with string variables---called the streaming string transducers---to capture the same class of transformations. In this paper we establish a transducer-logic correspondence for Courcelle's first-order definable string transformations. We propose a new notion of transition monoid for streaming string transducers that involves structural properties of both underlying input automata and variable dependencies. By putting an aperiodicity restriction on the transition monoids, we define a class of streaming string transducers that captures exactly the class of first-order definable transformations.Comment: 31 page

COMPUTER SIMULATION AND COMPUTABILITY OF BIOLOGICAL SYSTEMS

The ability to simulate a biological organism by employing a computer is related to the ability of the computer to calculate the behavior of such a dynamical system, or the "computability" of the system.* However, the two questions of computability and simulation are not equivalent. Since the question of computability can be given a precise answer in terms of recursive functions, automata theory and dynamical systems, it will be appropriate to consider it first. The more elusive question of adequate simulation of biological systems by a computer will be then addressed and a possible connection between the two answers given will be considered. A conjecture is formulated that suggests the possibility of employing an algebraic-topological, "quantum" computer (Baianu, 1971b) for analogous and symbolic simulations of biological systems that may include chaotic processes that are not, in genral, either recursively or digitally computable. Depending on the biological network being modelled, such as the Human Genome/Cell Interactome or a trillion-cell Cognitive Neural Network system, the appropriate logical structure for such simulations might be either the Quantum MV-Logic (QMV) discussed in recent publications (Chiara, 2004, and references cited therein)or Lukasiewicz Logic Algebras that were shown to be isomorphic to MV-logic algebras (Georgescu et al, 2001)

Dynamic systems as tools for analysing human judgement

With the advent of computers in the experimental labs, dynamic systems have become a new tool for research on problem solving and decision making. A short review on this research is given and the main features of these systems (connectivity and dynamics) are illustrated. To allow systematic approaches to the influential variables in this area, two formal frameworks (linear structural equations and finite state automata) are presented. Besides the formal background, it is shown how the task demands of system identification and system control can be realized in these environments and how psychometrically acceptable dependent variables can be derived

A state of a dynamic computational structure distributed in an environment: a model and its corollaries

Currently there is great interest in computational models consisting of underlying regular computational environments, and built on them distributed computational structures. Examples of such models are cellular automata, spatial computation and space-time crystallography. For any computational model it is natural to define a functional equivalence of different but related computational structures. In the finite automata theory an example of such equivalence is automata homomorphism and, in particular, automata isomorphism. If we continue to stick to the finite automata theory, a fundamental question arise, what a state of a distributed computational structure is. This work is devoted to particular solution of the issue.Comment: 11 pages, 5 figure

Метод синтезу моделей станів об’єктів програмного забезпечення автоматизованої системи обробки цифрових зображень

This article proposes a method for the synthesis of the behavior of software objects models (SOM) for the developed object-oriented software systems for automated digital image processing in order to avoid systemic and algorithmic errors in the design phase of a software system, as well as to reduce the time of its development. The process of constructing the SOM proceeding from its finite-state representation is viewed from the standpoint of abstract synthesis of an automata’s finite state. Thus, the specialties of the synthesis of finite automaton SOM, the construction of the map defining a plurality of channels management class of objects, the order to bring it to an automata, the construction of the canonical set of events and their regular expressions to display defining a plurality of channels management of software objects class for object oriented software system are considered and justified. Переважна більшість даних, які обробляються сучасними інфокомунікаційними системами, є графічними. Істотна частка з них – цифрові зображення, які характеризуються великими обсягами. Таким чином, виникає потреба їх представлення у компактному вигляді, що забезпечить зменшення навантаження на канали зв’язку, підвищення оперативності доставки та скорочення обсягів пам’яті, необхідної для зберігання даних. Вирішенням цієї проблеми є розроблення з використанням об’єктно- орієнтованої технології автоматизованої системи обробки цифрових зображень (АСОЗ), на етапі проектування якої постає актуальна задача побудови моделей поведінки екземплярів класів об’єктно- орієнтованого програмного забезпечення (ООПЗ) задля уникнення системних та алгоритмічних помилок, а також скорочення часу розроблення. Тож, мета роботи полягає в розробленні метода синтезу моделей станів програмних об’єктів об’єктно-орієнтованого програмного забезпечення АСОЗ. Процес побудови моделі станів програмних об’єктів (МСО) ООПЗ, виходячи з її скінченно- автоматного представлення, розглянуто з погляду абстрактного синтезу скінченного автомата. У роботі викладені й обґрунтовані особливості синтезу скінченно-автоматної МСО ООПЗ, побудова відображення, яке визначає множину каналів керування класу об’єктів, та порядок приведення його до автоматного виду, а також побудова канонічної множини подій і їх регулярних виразів для відображення, яке визначає множину каналів керування класу програмних об’єктів. На основі отриманих результатів дослідження запропоновано метод синтезу моделей станів програмних об’єктів ООПЗ. Запропонований метод забезпечує формалізацію процесу визначення станів та їх взаємозв’язків у життєвому циклі екземпляра класу ООПЗ, а також дозволяє зменшити трудомісткість процесу розробки динамічної компоненти комплексної моделі ООПЗ під час її проектування на логічному рівні

Cryptautomata: definition, cryptanalysis, example

This conference paper is an extended abstract of a recent article in Prikladnaya Diskretnaya Matematika (2017, No.36), where we presented the definition of the cryptautomata and described some cryptanalysis techniques for them. In cryptosystems, the cryptautomata are widely used as its primitives including cryptographic generators, s-boxes, filters, combiners, key hash functions as well as symmetric and public-key ciphers, and digital signature schemes. A cryptautomaton is defined as a class C of automata networks of a fixed structure N constructed by means of the series, parallel, and feedback connection operations over initial finite automata (finite state machines) with transition and output functions taken from some predetermined functional classes. A cryptautomaton key can include initial states, transition and output functions of some components in N. Choosing a certain key k produces a certain network Nk from C to be a new cryptographic algorithm. In case of invertibility of Nk, this algorithm can be used for encryption. The operation (functioning) of any network Nk in the discrete time is described by the canonical system of equations of its automaton. The structure of Nk is described by the union of canonical systems of equations of its components. The cryptanalysis problems for a cryptautomaton are considered as the problems of solving the operational or structural system of equations of Nk with the corresponding unknowns that are key k variables and (or) plaintexts (input sequences). For solving such a system E, the method DSS is used. It is the iteration of the following three actions: 1) E is Divided into subsystems E' and E ", where E' is easy solvable; 2) E' is Solved; 3) the solutions of E' are Substituted into E'' by turns. The definition and cryptanalysis of a cryptautomaton are illustrated by giving the example of the autonomous alternating control cryptautomaton. It is a generalization of the LFSR-based cryptographic alternating step generator. We present a number of attacks on this cryptautomaton with the states or output functions of its components as a key