Canonical forms for information-lossless finite-state logical machines

"March 25, 1959"--Cover. "Reprinted from the Transactions of the 1959 International Symposium on Circuit and Information Theory."Bibliography: p. 51.Army Signal Corps Contract DA36-039-sc-78108. Dept. of the Army Task 3-99-06-108 and Project 3-99-00-100.David A. Huffman

Early pioneers to reversible computation

Reversible computing is one of the most intensively developing research areas nowadays. We present a survey of less known or forgotten papers to show that a transfer of ideas between different disciplines is possible

On-line diagnosis of unrestricted faults

A formal model for the study of on-line diagnosis is introduced and used to investigate the diagnosis of unrestricted faults. A fault of a system S is considered to be a transformation of S into another system S' at some time tau. The resulting faulty system is taken to be the system which looks like S up to time tau, and like S' thereafter. Notions of fault tolerance error are defined in terms of the resulting system being able to mimic some desired behavior as specified by a system similar to S. A notion of on-line diagnosis is formulated which involves an external detector and a maximum time delay within which every error caused by a fault in a prescribed set must be detected. It is shown that if a system is on-line diagnosable for the unrestricted set of faults then the detector is at least as complex, in terms of state set size, as the specification. The use of inverse systems for the diagnosis of unrestricted faults is considered. A partial characterization of those inverses which can be used for unrestricted fault diagnosis is obtained

Finite-State Dimension and Lossy Decompressors

This paper examines information-theoretic questions regarding the difficulty of compressing data versus the difficulty of decompressing data and the role that information loss plays in this interaction. Finite-state compression and decompression are shown to be of equivalent difficulty, even when the decompressors are allowed to be lossy. Inspired by Kolmogorov complexity, this paper defines the optimal *decompression *ratio achievable on an infinite sequence by finite-state decompressors (that is, finite-state transducers outputting the sequence in question). It is shown that the optimal compression ratio achievable on a sequence S by any *information lossless* finite state compressor, known as the finite-state dimension of S, is equal to the optimal decompression ratio achievable on S by any finite-state decompressor. This result implies a new decompression characterization of finite-state dimension in terms of lossy finite-state transducers.Comment: We found that Theorem 3.11, which was basically the motive for this paper, was already proven by Sheinwald, Ziv, and Lempel in 1991 and 1995 paper

Normal numbers and finite automata

We give an elementary and direct proof of the following theorem: A real number is normal to a given integer base if, and only if, its expansion in that base is incompressible by lossless finite-state compressors (these are finite automata augmented with an output transition function such that the automata input–output behaviour is injective; they are also known as injective finite-state transducers). As a corollary we obtain V.N. Agafonov’s theorem on the preservation of normality on subsequences selected by finite automata.Fil: Becher, Veronica Andrea. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Heiber, Pablo Ariel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Normal numbers and finite automata

We give an elementary and direct proof of the following theorem: A real number is normal to a given integer base if, and only if, its expansion in that base is incompressible by lossless finite-state compressors (these are finite automata augmented with an output transition function such that the automata input–output behaviour is injective; they are also known as injective finite-state transducers). As a corollary we obtain V.N. Agafonov’s theorem on the preservation of normality on subsequences selected by finite automata.Fil: Becher, Veronica Andrea. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Heiber, Pablo Ariel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Cryptanalytic concept of finite automaton invertibility with finite delay

The automaton invertibility with a finite delay plays a very important role in the analysis and synthesis of finite automata cryptographic systems. The automaton cryptanalitic invertibility with a finite delay т is studied in the paper. From the cryptanalyst's point of view, this notion means the theoretical possibility for recovering, under some conditions, a prefix a of a length n in an unknown input sequence ab of an automaton from its output sequence 7 of the length n + т and perhaps an additional information such as parameters т and n, initial (q), intermediate (в) or final (t) state of the automaton or the suffix b of the length т in the input sequence. The conditions imposed on the recovering algorithm require for prefix a to be arbitrary and may require for the initial state q and suffix b to be arbitrary or existent, that is, the variable a is always bound by the universal quantifier and each of variables q and b may be bound by any of quantifiers — universal (V) or existential (3) one. The variety of information, which can be known to a cryptanalyst, provides many different types of the automaton invertibility and, respectively, many different classes of invertible automata. Thus, in the paper, an invertibility with a finite delay т of a finite automaton A is the ability of this automaton to resist recovering or, on the contrary, to allow precise determining any input word a of a length n for the output word у being the result of transforming by the automaton A in its initial state q the input word ab with the b of length т and with the known n, т, A, 7 and и C {b, q, в, t} where q and b may be arbitrary or some elements in their sets and в and t are respectively intermediate and final states of A into which A comes from q under acting of input words a and ab respectively. According to this, the automaton A is called invertible with a delay т if there exists a function f (y,u) and a triplet of quantifiers к e {Q1x1Q2X2Q3X3 : QiXi e {Vq, 3q, Va, Vb, 3b}, i = j ^ Xi = Xj} such that x [f(y,u) = a]; in this case f is called a recovering function, (к, u) — an invertibility type, к — an invertibility degree, u — an invertibility order of the automaton A and 3f K[f (y, u) = a] — an invertibility condition of type (к, u) for the automaton A. So, 208 different types of the automaton A invertibility are defined at all. The well known types of (strong) invertibility and weak invertibility described for finite automata earlier by scientists (D. A. Huffman, A. Gill, Sh. Even, A. A. Kurmit, Z. D. Dai, D. F. Ye, K. Y. Lam, R. Tao and many others) in our theory belong to types (VqVaVb, 0 ) and (VqVaVb, {q}) respectively. For every invertibility type, we have defined a class of automata with this type of invertibility and described the inclusion relation on the set of all these classes. It has turned out that the graph of this relation is the union of twenty nine lattices with thirteen of them each containing sixteen classes and sixteen lattices each containing thirteen classes. To solve the scientific problems (invertability tests, synthesis of inverse automata and so on) related to the different and concrete invertibility classes, we hope to continue these investigations

Perfectly Balanced Functions in Symbolic Dynamics

In the present paper we study properties of perfectly balanced Boolean functions. Based on the concept of Boolean function barrier, we propose a novel approach to construct large classes of perfectly balanced Boolean functions