Logic Automata And Algorithms
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Logic, Automata, and Algorithms
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression.- Best operator approximation,- Non-Lagrange interpolation,- Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering
Finite Automata, Formal Logic, and Circuit Complexity
Author: Howard Straubing
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
The study of the connections between mathematical automata and for mal logic is as old as theoretical computer science itself. In the founding paper of the subject, published in 1936, Turing showed how to describe the behavior of a universal computing machine with a formula of first order predicate logic, and thereby concluded that there is no algorithm for deciding the validity of sentences in this logic. Research on the log ical aspects of the theory of finite-state automata, which is the subject of this book, began in the early 1960's with the work of J. Richard Biichi on monadic second-order logic. Biichi's investigations were extended in several directions. One of these, explored by McNaughton and Papert in their 1971 monograph Counter-free Automata, was the characterization of automata that admit first-order behavioral descriptions, in terms of the semigroup theoretic approach to automata that had recently been developed in the work of Krohn and Rhodes and of Schiitzenberger. In the more than twenty years that have passed since the appearance of McNaughton and Papert's book, the underlying semigroup theory has grown enor mously, permitting a considerable extension of their results. During the same period, however, fundamental investigations in the theory of finite automata by and large fell out of fashion in the theoretical com puter science community, which moved to other concerns.
Logic Synthesis for Control Automata
Author: Samary Baranov
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
Logic Synthesis for Control Automata provides techniques for logic design of very complex control units with hardly any constraints on their size, i.e. the number of inputs, outputs and states. These techniques cover all stages of control unit design, including: description of control unit behavior by using operator schemes of algorithms (binary decision trees) and various transformations of these descriptions -- composition, decomposition, minimization, etc.; synthesis of a control automaton (finite-state machine); synthesis of an automaton logic circuit: with matrix structure as a part of LSI or VLSI circuits; as multilevel circuit with logic gates; with standard LSI and VLSI circuits with and without memory. Each chapter contains many examples, illustrating the use of the models and methods described. Moreover, the special last chapter demonstrates in detail the whole design methodology presented in the previous chapters, through the examples of the logic design for a control unit. The models, methods and algorithms described in the book can be applied to a broad class of digital system design problems including design of complex controllers, robots, control units of computers and for designing CAD systems of VLSI circuits using FPGA, PLD and SIC technologies. Logic Synthesis for Control Automata is a valuable reference for graduate students, researchers and engineers involved in the design of very complex controllers, VLSI circuits and CAD systems. The inclusion of many examples and problems makes it most suitable for a course on the subject.