Finite-state Sequential Machine Research Articles

FPGA Technology and Sequential Finite State Machine Method

<em>The implementation of complex control algorithms on an FPGA</em> (Field programmable gate arrays)<em> is still at a basic level. There is no fixed method to develop algorithms on these devices because of their general characteristics. Therefore, the design engineers are still on the way to find the good approaches to optimize the implementation of algorithms on FPGAs [1-7]. This paper presents and demonstrates a sequential finite state machine design method that can solve the issue of optimal usage of the limited resources on an FPGA.</em>

Reverse engineering concurrent UML state machines using black box testing and genetic programming

This paper presents a technique for reverse engineering, a software system generated from a concurrent unified modeling language state machine implementation. In its first step, a primitive sequential finite-state machine (FSM) is deduced from a sequence of outputs emitted from black box tests applied to the systems’ input interface. Next, we provide an algorithmic technique for decomposing the sequential primitive FSM into a set of concurrent (orthogonal) primitive FSMs. Lastly, we show a genetic programming machine learning technique for discovering local variables, actions performed on local and non-binary output variables, and two types of intra-FSM loops, called counting-loops and while-loops.

EXIT chart analysis of nonlinear turbo coding over GF(4)

The behaviour of nonlinear turbo codes that use nonlinear finite state sequential machines (FSSMs), designed over the finite field GF(4), as constituent encoders is studied. These FSSMs show a nonzero output for the all-zero input case. The state-transitions structure and the randomness of the output for the all-zero input response of these FSSMs are studied for different initial state conditions. A relationship is found between these two characteristics and the BER performance or, equivalently, the form of the extrinsic information transfer chart of the corresponding turbo code. It is found that FSSMs with responses of the form of long closed cycles, and good randomness properties of the corresponding output are the best options as constituent encoders of nonlinear turbo codes designed over GF(4). A coefficient called the random behaviour coefficient is defined, to provide a quantitative measure of the behaviour of these FSSMs as constituent encoders of a turbo code.

Construction of FSSM Modeled Encoders to Meet Specific Spectral Requirements

In digital transmission and storage systems, sequences must have attributes that comply with the physical characteristics of the channel. These channel constraints can often be satisfied through constrained sequence coding techniques which avoid use of sequences that violate the given channel constraints. In the design of a constrained code, it is usually helpful to consider the PSD of the encoded sequence in order to ensure that PSD requirements are met, and to obtain an indication of bandwidth, response at dc, average power peaks, and other spectral characteristics of interest. In this paper, we introduce an approach for the construction of finite-state sequential machine (FSSM) modeled encoders to satisfy spectral requirements. This approach involves construction of either a Mealy or a Moore FSSM to represent the encoder, and evaluation of the state transition probabilities and codeword values such that the PSD of the designed code meets a predefined spectral shape. Examples in this paper demonstrate the usefulness of this approach.

State verification for synchronous circuits

This paper presents the techniques of implicit traversing and state verification for sequential finite state machines (FSMs) based of on the state collapsing of state transition graph(STG). The problems of state designing are described. In order to achieve high state enumeration coverage, heuristic knowledge is proposed.

On Encoding and Decoding with Two-Way Head Machines

Ziv and Lempel investigated the encoding power of finite state machines with respect to given individual sequences. Motivated by the study of various kinds of machines as recognizers of formal languages (cf. Hopcroft and Ullman, 1979, "Introduction to Automata Theory, Languages, and Computation," Addison-Wesley, Reading, MA), we compare the encoding and decoding power of finite state sequential machines and the following extensions thereof. First, we show that, with a forward moving head, the best compression ratio achievable for a given sequence, to be decoded by a finite state decoder, is the same as the best ratio attainable for that sequence when encoded by a finite state information lossless encoder. Second, we prove that we can not gain in compression by allowing a finite state encoder to move its head back and forth on an input sequence, even if the decoder has unrestricted power. However, better compression can be achieved for specific infinite sequences using an unrestricted encoder and a two-way finite state decoder.

Zur Beschreibung von Petri-Netzen als Abtastsystem

Petri nets provide a tool for modelling discrete-event systems. Usually the properties of the net are investigated via graph theoretical analysis. In this paper it is shown that an arithmetic version of Shegalkin polynomials proposed by D. Franke for modelling sequential finite state machines is also suitable for a vector representation of the over-all behaviour of a Petri net. This allows to model the behaviour of a Petri net as a generally multilinear classical discrete-time system

Organizations as Teams of Automata

This paper examines the impact of "bounded rationality" on the internal structure of the firm. No specific internal organization nor any ad hoc "cost of organization" is presumed. Finite state sequential machines (automata) are the primitive model of individual constituents of a firm, each having limited capacities for computation and communication. The main results are (1) that arbitrarily complex machines may be simulated by certain two-state machines and very restricted products; and (2) that upper bound on the number of components (i.e., the cost) required to simulate a complex behavior is at best logarithmic, and at worst linear, in the number of states in the target. Journal of Economic Literature Classification Number: 022.

Electromagnetic launcher control using finite state machines

The authors show the continued viability of sequential finite state machines (FSMs) as a means to control the sequencing of electromagnetic launcher (EML) systems. While computer-controlled sequencing is an attractive alternative, FSMs are easy to design, inexpensive, and reliable. Several FSM controllers are currently in use for the long duration EML experiments at the Hypervelocity Research Facility, Eglin Air Force Base, Florida. The authors discuss basic system design, with reference to design procedure and systems interfacing. Flexibility and the fail-safe nature of the FSM (i.e., system interrupt capability) are also discussed. Where requirements include repeatability, reliability, ease of operation, relatively low cost, and flexibility, the FSM is presented as a reasonable alternative to more expensive computer-based systems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Elaborated rank order processors

The author discusses an elaborated rank order processor, which admits constants as operands and preliminary operations on input variables (e.g. negation) so that the processor is also implementable in bit-serial, most significant bit leading, terms. The theory for the special case in which the constant 0 and the operation negation are admitted and a realization in finite autoregressive form exists is discussed. Input/output relations are expressible with a finite-state sequential machine with ternary inputs and outputs; that machine is only a mathematical construct and need not represent an actual device. The question of root signals is examined theoretically and by example. An example showing a bandpass effect is presented, and computer programs for doing the relevant calculations pertaining to finite automata and simulations are offered. A part of a theory for general elaboration is also presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Ancillary channel of optical fibre communication systems based on 1B2B code redundancy

A method of 1B2B code modification, enabling the use of their high redundancy for ancillary channel insertion is suggested. The finite state sequential machine representations of the derived codes, their spectra and the basic structure of the encoder and decoder are given.

The ESTEREL language

The authors present the basics of the ESTEREL reactive model of synchronous parallel systems. The ESTEREL programming style, based on instantaneous communications and decisions, is illustrated through the example of a mouse handler. The ESTEREL formal semantics is described, and it is shown how programs can be compiled into finite state sequential machines for efficient execution. The implementation is described with the ESTEREL environment, including simulation, and verification and validation tools. Some ESTEREL uses in various contexts are reported. >

Regular sets and rank order processors

Rank order processors (ROPs) can be specified in terms of regular sets and consequently studied as finite-state automata or sequential machines. A necessary and sufficient condition for a regular set to represent an ROP is given. Examples are given to illustrate the advantages of such a specification in terms of a primary focus on root signals and input-output relations. One result is a practical equivalent of the recursive median smoother that is easier to compute. Another is a demonstration that some ROPs, although not implementable as finite autoregressive algorithms involving only the input-output signal values, are implementable as finite state sequential machines, e.g. those with a modified stack filter structure. The demonstration is constructive and coincidentally shows how the idea of a nondeterministic automaton relates to the subject matter. >

Decomposition and factorization of sequential finite state machines

Algorithms are proposed for decomposing a finite-state machine into smaller interacting machines so as to optimize area and performance of the eventual logic implementation. Cascade decomposition algorithms, which decompose a given machine into independent and dependent components, have been proposed in the past. The authors propose a more powerful form of decomposition where both components of the decomposed machine interact with each other. Experimental results indicate that this decomposition technique for state machine decomposition is superior to cascade decomposition techniques. It is the premise of this study that optimal state assignment corresponds to finding an optimal multiple general decomposition of a finite-state machine. State assignment techniques that target two-level and multilevel implementations based on state machine factorization algorithms followed by state assignment algorithms are presented. It is rigorously proved that one-hot encoding a nontrivially factored machine is guaranteed to produce a better result than one-hot encoding the original machine for the two-level case.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Data structure of Huffman codes and its application to efficient encoding and decoding (Corresp.)

The data structure of Huffman codes and its application to efficient encoding and decoding of Huffman codes are studied in detail. The tree structure is presented by a two-dimensional array which can be applied for the decoding of Huffman codes as a state transition table of the finite-state decoding automaton. Inversion produces a one-dimensional state transition table of the semiautonomous finite-state sequential machine which can be used as a Huffman encoder with a push-down stack. The encoding and decoding procedures are simple and efficient. It is not only possible to implement by simple hardware but is also applicable to software implementation.

Power spectral density of digital continuous phase modulation with correlated data symbols. Part 1: Autocorrelation function method

A general method for computing the power spectral density (PSD) of an encoded, continuous phase modulated (CPM) signal with correlated data symbols is presented in the paper. The encoder is a finite-state sequential machine which introduces correlation between symbols transmitted in different time slots. The method used is the so-called autocorrelation function method, in which the autocorrelation functon is first computed and then numerically Fourier-transformed to obtain the PSD. A key result is that the autocorrelation function is obtained via a recursive equation that is in keeping with the assumed Markov property of the data source. The computational complexity of the present method is linear in the length of the baseband pulse, and this enables one to calculate the PSD of CPM signals with a long pulse length. Our primary goal is to specifically consider the PSD of convolutionally encoded CPM signals. However, our algorithm is presented in a general format and numerical results are included for a wide class of digital CPM signals.

Power spectral density of digital continuous phase modulation with correlated data symbols. Part 2: Rowe-Prabhu method

An extension of the Rowe-Prabhu method is presented for finding the power spectral density (PSD) of continuous phase modulated (CPM) signals with correlated data symbols. Correlation between symbols in different time slots is introduced by an encoder which is represented as a finite-state sequential machine. This structure simplifies any procedure for the spectral analysis of modulated signals with correlated data symbols, including the Rowe-Prabhu method. For instance, it allows a sequential computation of some of the matrices needed for this spectral analysis technique. The PSD is expressed in a compact, Hermitian matrix form that is suitable for numerical computation by a digital computer. Examples for convolutionally encoded CPM are given for the purposes of illustration, as treating such signals was the primary motivation in developing the spectral analysis algorithm that is presented in the paper.

Signature Testing of Sequential Machines

A new approach to the testing of sequential machines is presented which employs signature analysis. In the conventional scheme of testing sequential finite state machines, distinguishing and transfer sequences are used. For the purposes of testing sequential machines by signature analysis, a signature distinguishing sequence is defined. An algorithm for augmenting a sequential machine by introducing an extra input is presented. This yields a sequential machine that has a signature distinguishing sequence. The additional cost in terms of the chip area for a programmable logic array (PLA) implementation is calculated.

Invited paper Analysis of codes and spectra calculations

Abstract The paper deals with the statistical analysis of the several kinds of signals encountered in digital transmission systems in which the data are coded by a line coder before being transmitted. In the preliminary sections, models of signals and systems are formulated. In particular, a general model is presented in which a line coder is split into three parts : a serial-to-parallel conversion, a finite-state sequential machine, and a parallel-to-serial conversion, where the fundamental coding function is described by a finite-state machine operating on blocks of source-symbols to produce blocks of code-symbols. On the basis of this model, the complete statistics of the coded sequence are evaluated in terms of the source probabilities. In the final part, consideration is given to spectral analysis, where both the continuous and the discrete part (spectral lines) of the spectral densities are calculated in closed form. The results obtained have a general validity and can be used for any line coding sc...

Spectral Analysis of Functions of Markov Chains with Applications

This paper deals with the spectral analysis of digital processes obtained through memoryless functions of stationary Markov chains. Under the assumption that the Markov chain is ergodic, not necessarily acyclic, closed form formulas are derived for both the discrete part (spectral lines) and the continuous part of the spectral density. The results are applied at the output of a finite state sequential machine driven by a stationary Markov chain, which represents a general model of several situations of engineering interest. Finally, the theory is used to evaluate the spectrum of encoded and modulated digital signals.