Methods for relativizing properties of codes

The usual setting for information transmission systems assumes that all words over the source alphabet need to be encoded. The demands on encodings of messages with respect to decodability, error-detection, etc. are thus relative to the whole set of words. In reality, depending on the information source, far fewer messages are transmitted, all belonging to some specific language. Hence the original demands on encodings can be weakened, if only the words in that language are to be considered. This leads one to relativize the properties of encodings or codes to the language at hand. We analyse methods of relativization in this sense. It seems there are four equally convincing notions of relativization. We compare those. Each of them has their own merits for specific code properties. We clarify the differences between the four approaches. We also consider the decidability of relativized properties. If P is a property defining a class of codes and L is a language, one asks, for a given language C, whether C satisfies P relative to L. We show that in the realm of regular languages this question is mostly decidable

Application and implementation of transducer tools in answering certain questions about regular languages

121 leaves : ill. ; 29 cm.Includes abstract.Includes bibliographical references (leaves 117-121).In this research, we investigate, refine, and implement algorithmic tools that allow us to answer decision questions about regular languages. We provide a thorough presentation of existing algorithmic tools to answer the satisfaction questions of whether a given language satisfies a given property described by an input-preserving transducer, which is equivalent to the question of whether a given language is error-detecting for the channel realized by the same input-preserving transducer; whether a given language is error-correcting for the channel realized by an input-preserving transducer; whether a given regular language satisfies the code property. In the process, we give a thorough presentation of an existing algorithm to decide whether a transducer is functional and an algorithm about how to translate a normal form transducer into a real-time transducer. We also introduce our method to provide counterexamples in cases where the answers to the satisfaction questions are negative. In addition, we discuss our new method to estimate the edit distance of a regular language by the error-correction property, which is much faster than the existing method of computing the edit distance via error-detection. Finally, we deliver an open implementation of these algorithms and methods via a web interface – I-LaSer, and add the implementation of transducer classes into our copy of the FAdo libraries

Implementation of Code Properties via Transducers

The FAdo system is a symbolic manipulator of formal language objects, implemented in Python. In this work, we extend its capabilities by implementing methods to manipulate transducers and we go one level higher than existing formal language systems and implement methods to manipulate objects representing classes of independent languages (widely known as code properties). Our methods allow users to define their own code properties and combine them between themselves or with fixed properties such as prefix codes, suffix codes, error detecting codes, etc. The satisfaction and maximality decision questions are solvable for any of the definable properties. The new online system LaSer allows one to query about a code property and obtain the answer in a batch mode. Our work is founded on independence theory as well as the theory of rational relations and transducers, and contributes with improved algorithms on these objects

A system for describing and deciding properties of regular languages using input altering transducers

ii, 94 leaves : ill. ; 29 cm.Includes abstract.Includes bibliographical references (leaves 92-94).We present a formal method for describing and deciding code related properties of regular languages using input altering transducers. We also provide an implementation of that method in the form of a web application. We introduce the concept of an input altering transducer. We show how to use such transducers to describe properties of languages and present examples of transducers describing some well known properties (like suffix codes, prefix codes, infix codes, solid codes, and others). We discuss some limitations of our method. In particular, all properties that can be described using input altering transducers are 3-independence properties. We also give an example of a 3-independence property that cannot be represented using a transducer. We explain how our method is a specialisation of a more general method based on language in-equations. We also discuss the relation between our method and a method that uses sets of trajectories to describe properties. In particular, we show how, for any given set of trajectories describing some property, to build an input altering transducer describing the same property. We introduce the concept of counterexample, which is a pair of words that, if a given language does not belong to a given property, illustrate that fact. We show how we can incorporate extracting such counterexample into our method. Finally, we provide some details on the implementation and usage of the web application that was built as a part of this research

A note on autodense related languages

In this paper, some algebraic properties of autodense languages and pure autodense languages are studied. We also investigate the algebraic properties concerning anti-autodense languages. The family of anti-autodense languages contains infix codes, comma-free codes, and some subfamilies of new codes which are anti-autodense prefix codes, anti-autodense suffix codes and anti-autodense codes. The relationships among these subfamilies of new codes are investigated. The characterization of L (n) , n a parts per thousand yen 2, which are anti-autodense is studied