State Sequential Machine Research Articles

Implementation of Sequential Machine for Encryption of Textual Information

Cryptography is a secured transfer of information between users to avoid leakage of information. Research of techniques for cryptography using public key is done to have a need of great computational power besides being highly complex and time consuming for obtaining the key. Neural networks are found to have an edge over these shortcomings for obtaining the keys. In this paper, n – state sequential machine is used to examine Artificial Neural Network as a toll for cryptography. The results thereby obtained demonstrate the use of artificial neural network for cryptography.

Implementation of Sequential Machine for Encryption of Textual Information

Cryptography is a secured transfer of information between users to avoid leakage of information. Research of techniques for cryptography using public key is done to have a need of great computational power besides being highly complex and time consuming for obtaining the key. Neural networks are found to have an edge over these shortcomings for obtaining the keys. In this paper, n – state sequential machine is used to examine Artificial Neural Network as a toll for cryptography. The results thereby obtained demonstrate the use of artificial neural network for cryptography.

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.

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.

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.

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. >

Machine Models for Cognitive Science

Introduction. During the past two decades philosophers of psychology have considered a large variety of computational models for philosophy of mind and more recently for cognitive science. Among the suggested models are computer programs, Turing machines, pushdown automata, linear bounded automata, finite state automata and sequential machines. Many philosophers have found finite state automata models to be the most appealing, for various reasons, although there has been no shortage of defenders of programs and Turing machines. A paper by Arthur Burks (1973) convinced me long ago that “all natural human functions” are, or can be fruitfully modeled to be, finite state automata with output. Further work in the field has reinforced this conviction. There is room, however, for the use of any of the above models in philosophy of mind and in the ongoing development of cognitive science.

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.

Large state sequential machine realization with minimum ROM capacity

Sequential machines of all types can be implemented using ROMs for the combinational circuit portion of the realization. When large state sequential machines are to be implemented, the capacity of ROMs needed will also be large. A given machine can be implemented by decomposing it in either serial or parallel form (Hartmanis 1960). It is shown in this paper that when a machine M is decomposed under certain prescribed conditions, there is always a saving (gain) in the ROM capacity, compared with the memory capacity needed when the machine is realized without decomposition. A set of formulae for gains associated with serial and parallel decompositions of a p-state machine M is presented. This is followed by an approximate cost analysis.

Modelling of recursive games of survival as finite state sequential machines and solutions by fictitious play

Fictitious play has been used effectively to solve extended games. In this work, recursive games of survival are investigated by fictitious play. The game is modelled as a finite state sequential machine with each component game representing a different state. Two types of algorithms are proposed to generate the desired behaviour strategy solutions.Two examples are investigated and the corresponding solutions compared.

The upper bound of K in K-lossless sequential machines

A sequential machine is said to be k -lossless if k is the least integer such that the initial state and the first k outputs uniquely determine the initial input. For n -state machines the upper bound of k is 1/2 n ( n − 1) + 1 and the lower bound of k is 1. In this paper it will be shown that there exists an n -state {1\2 n ( n − 1) + 1}-lossless sequential machine with 3 input symbols and 6 output symbols. This problem is related to the computation capability of n -state sequential machines.

Uniform Synthesis of Sequential Circuits†

In this paper we consider the synthesis of sequential machines by networks of a fixed module with delay. We show that every binary input n state sequential machine has an isomorphic realization using at most p copies of a module with 2r + 1 inputs, where p is the smaller of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">${2r \over 2r - 1} (n^{1+log r^2} + 4n^{1+log r^4)$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$r2^[n/r]$</tex> . ([x] is the smallest integer ≧ x.)

Complexity of ideals in finite semigroups and finite-state machines

# G (S) denotes the complexity of a finite semigroup as introduced by Krohn and Rhodes. IfI is a maximal ideal or maximal left ideal of a semigroupS, then# G (I) ⩽ # G (S) ⩽ # G (I) + 1. Thus, ifV is an ideal ofS with# G (S) = n ⩾ k = # G (V), then there is a chain of ideals ofS $$V = V_k \subset V_{k + 1} \subset ... \subset V_n \subseteq S$$ with# G (V j ) =j, i.e., complexity is continuous with respect to ideals. Given a representation ofS as a subsemigroup ofF R (Q), all mappings on the setQ(e.g., as the semigroup of a finite state sequential machine with statesQ) a rank ideal consists of all elements ofS whose range contains no more thank elements for some fixed integerk. The above result also applies to rank ideals. Existing results on complexity are reviewed in the language of finite-state sequential machines.

Finite state transformations

A notion of index is defined for transformations which map n -tuples of words into m -tuples of words, and it is proved that the transformations of finite index are precisely those which are affected by finite state sequential machines, provided these are allowed to have certain unusual features. Further conditions are formulated which, together with the finite index requirement, characterize the transformations which can be effected by finite state sequential machines of the usual sort.

Symbolic analysis of a decomposition of information processing machines

In this paper we study the problem of replacing (decomposing) a complex finite state sequential machine by several simpler ones which operate in parallel and yield the same result. In the first part, we give the necessary mathematical background and results. In the second part, we apply these results and derive the necessary and sufficient conditions for the existence of a decomposition for a given machine. If a decomposition exists then the required simpler machines which have to be connected in parallel are given.

A Synthesis Technique for Minimal State Sequential Machines

A method is presented which always yields a minimal state sequential machine satisfying a prescribed finite set of input-output sequences. An application is made to the case where a given sequential machine is to be reduced, by the merging technique, to a machine having the smallest number of states possible. Numerous examples are given.