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

On the invertibility of finite state machines

Structural properties of finite state machines invertible with delay

A General Notion of Useful Information

In this paper we introduce a general framework for defining the depth of a sequence with respect to a class of observers. We show that our general framework captures all depth notions introduced in complexity theory so far. We review most such notions, show how they are particular cases of our general depth framework, and review some classical results about the different depth notions

Dimension Extractors and Optimal Decompression

A *dimension extractor* is an algorithm designed to increase the effective dimension -- i.e., the amount of computational randomness -- of an infinite binary sequence, in order to turn a "partially random" sequence into a "more random" sequence. Extractors are exhibited for various effective dimensions, including constructive, computable, space-bounded, time-bounded, and finite-state dimension. Using similar techniques, the Kucera-Gacs theorem is examined from the perspective of decompression, by showing that every infinite sequence S is Turing reducible to a Martin-Loef random sequence R such that the asymptotic number of bits of R needed to compute n bits of S, divided by n, is precisely the constructive dimension of S, which is shown to be the optimal ratio of query bits to computed bits achievable with Turing reductions. The extractors and decompressors that are developed lead directly to new characterizations of some effective dimensions in terms of optimal decompression by Turing reductions.Comment: This report was combined with a different conference paper "Every Sequence is Decompressible from a Random One" (cs.IT/0511074, at http://dx.doi.org/10.1007/11780342_17), and both titles were changed, with the conference paper incorporated as section 5 of this new combined paper. The combined paper was accepted to the journal Theory of Computing Systems, as part of a special issue of invited papers from the second conference on Computability in Europe, 200