Implementation of Code Properties via Transducers

Konstantinidis, Stavros; Meijer, Casey; Moreira, Nelma; Reis, Rui L.

doi:10.1007/978-3-319-40946-7_16

Cited by 3 publications

(8 citation statements)

References 19 publications

(34 reference statements)

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“…All main algorithmic tools have been implemented over the years in the Python package FAdo [1,5,10]. Many aspects of the new module FAdo.codes are presented in [10]. Here we present methods of that module pertaining to generating codes.…”

Section: Implementation and Usementioning

confidence: 99%

“…Our motivation for considering a randomized algorithm is that embedding a given er -detecting block code C into a maximal er -detecting block code is a computationally hard problem-this is shown in Section 4. In Section 5, we discuss with examples some capabilities of the new module codes.py in the open source software package FAdo [1,5,10]. In Section 6, we discuss a few more points on channel modelling and present some tests of the randomized algorithm on various error specifications.…”

Section: Introductionmentioning

confidence: 99%

“…In[10], the authors implement the Python class ErrDetectProp. An object of this class is initialized using an error specification er , like del 1 , and 'represents' all languages that are er -detecting.…”

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confidence: 99%

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Randomized generation of error control codes with automata and transducers

Konstantinidis

Moreira

Reis

2018

RAIRO-Theor. Inf. Appl.

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We introduce the concept of an f -maximal error-detecting block code, for some parameter f in (0,1), in order to formalize the situation where a block code is close to maximal with respect to being error-detecting. Our motivation for this is that it is computationally hard to decide whether an error-detecting block code is maximal. We present an output-polynomial time randomized algorithm that takes as input two positive integers N, and a specification of the errors permitted in some application, and generates an error-detecting, or error-correcting, block code of length that is 99%-maximal, or contains N words with a high likelihood. We model error specifications as (nondeterministic) transducers, which allow one to represent any rational combination of substitution and synchronization errors. We also present some elements of our implementation of various error-detecting properties and their associated methods. Then, we show several tests of the implemented randomized algorithm on various error specifications. A methodological contribution is the presentation of how various desirable error combinations can be expressed formally and processed algorithmically.Mathematics Subject Classification. 68Q45, 68W20, 94A40, 94B25.

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Section: Implementation and Usementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Randomized generation of error control codes with automata and transducers

Konstantinidis

Moreira

Reis

2018

RAIRO-Theor. Inf. Appl.

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“…Remark 5. In [25], the independence described by an input-preserving transducer t is called an error-detecting property. Specifically, t can be viewed as a communication channel such that, if v ∈ t(u) and v = u then we have a channel error.…”

Section: T-independent Languages: Classic and Antimorphicmentioning

confidence: 99%

“…, or a triple of None's if the transducer t is functional. This algorithm is a witness version, [25], of the decision algorithm for transducer functionality in [2,1]. 3.…”

Section: Tnfunctw() Returns Either a Triplementioning

confidence: 99%

Applications of Transducers in Independent Languages, Word Distances, Codes

Konstantinidis¹

2017

Descriptional Complexity of Formal Systems

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A (nondeterministic) transducer t is an operator mapping an input word to a set of possible output words. A few types of transducers are important in this work: input-altering, input-preserving, and inputdecreasing. Two words are t-dependent, if one is the output of t when the other one is used as input. A t-independent language is one containing no two t-dependent words. Examples of independent languages are found in noiseless coding theory, noisy coding theory and DNA computing. We discuss how the above transducer types can provide elegant solutions to some cases of the following broad problems: (i) computing two minimum distance witness words of a given regular language; (ii) computing witness words for the non-satisfaction, or non-maximality, of a given regular language with respect to the independence specified by a given transducer t; (iii) computing, for any given t and language L, a maximal t-independent language containing L; (iv) computing, for any given positive integer n and transducer t, a t-independent language of n words. The descriptional complexity cost of converting between transducer types is discussed, when this conversion is possible. We also explore methods of defining more independences in a way that some of the above problems can still be computed.

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Channels with Synchronization/Substitution Errors and Computation of Error Control Codes

Konstantinidis¹,

Moreira²,

Reis³

2016

Preprint

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We introduce the concept of an f -maximal errordetecting block code, for some parameter f between 0 and 1, in order to formalize the situation where a block code is close to maximal with respect to being error-detecting. Our motivation for this is that constructing a maximal error-detecting code is a computationally hard problem. We present a randomized algorithm that takes as input two positive integers N, ℓ, a probability value f , and a specification of the errors permitted in some application, and generates an error-detecting, or errorcorrecting, block code having up to N codewords of length ℓ. If the algorithm finds less than N codewords, then those codewords constitute a code that is f -maximal with high probability. The error specification (also called channel) is modelled as a transducer, which allows one to model any rational combination of substitution and synchronization errors. We also present some elements of our implementation of various error-detecting properties and their associated methods. Then, we show several tests of the implemented randomized algorithm on various channels. A methodological contribution is the presentation of how various desirable error combinations can be expressed formally and processed algorithmically. 1 The general definition of transducer allows two alphabets: the input and the output alphabet. Here, however, we assume that both alphabets are the same.

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Implementation of Code Properties via Transducers

Cited by 3 publications

References 19 publications

Randomized generation of error control codes with automata and transducers

Randomized generation of error control codes with automata and transducers

Applications of Transducers in Independent Languages, Word Distances, Codes

Channels with Synchronization/Substitution Errors and Computation of Error Control Codes

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