Symbolic Manipulation of Code Properties

Abstract

The FAdo system is a symbolic manipulator of formal languages 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 to query about code properties 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 improveded algorithms on these objects.

Embedding rationally independent languages into maximal ones

“…, q − 1}, for some integer q ≥ 2. Thus, u ≺ v means that, either u is shorter, or u and v are of the same length and, for the first position in which they differ, the symbol of u at that position is smaller than that of v. All the examples presented below have been confirmed using the well-maintained Python package FAdo [7], which was recently updated to include a module on codes described by input-altering transducers [12].…”