Verification of Information Flow Properties under Rational Observation

Information flow properties express the capability for an agent to infer information about secret behaviours of a partially observable system. In a language-theoretic setting, where the system behaviour is described by a language, we define the class of rational information flow properties (RIFP), where observers are modeled by finite transducers, acting on languages in a given family $\mathcal{L}$. This leads to a general decidability criterion for the verification problem of RIFPs on $\mathcal{L}$, implying PSPACE-completeness for this problem on regular languages. We show that most trace-based information flow properties studied up to now are RIFPs, including those related to selective declassification and conditional anonymity. As a consequence, we retrieve several existing decidability results that were obtained by ad-hoc proofs.Comment: 19 pages, 7 figures, version extended from AVOCS'201

Conjugacy and Equivalence of Weighted Automata and Functional Transducers

International audienceWe show that two equivalent K-automata are conjugate to a third one, when K is equal to B, N, Z, or any (skew) ¯eld and that the same holds true for functional tranducers as well

Algebraic Recognition of Regular Functions

We consider regular string-to-string functions, i.e. functions that are recognized by copyless streaming string transducers, or any of their equivalent models, such as deterministic two-way automata. We give yet another characterization, which is very succinct: finiteness-preserving functors from the category of semigroups to itself, together with a certain output function that is a natural transformation

On Equivalence and Uniformisation Problems for Finite Transducers

Transductions are binary relations of finite words. For rational transductions, i.e., transductions defined by finite transducers, the inclusion, equivalence and sequential uniformisation problems are known to be undecidable. In this paper, we investigate stronger variants of inclusion, equivalence and sequential uniformisation, based on a general notion of transducer resynchronisation, and show their decidability. We also investigate the classes of finite-valued rational transductions and deterministic rational transductions, which are known to have a decidable equivalence problem. We show that sequential uniformisation is also decidable for them

Logol : Modelling evolving sequence families through a dedicated constrained string language

The report reviews the key milestones that have been reached so far in applying formal languages to the analysis of genomic sequences. Then it introduces a new modelling language, Logol, that aims at expressing more easily complex structures on genomic sequences. It is based on a development of String Variable Grammars, a formal framework proposed by D. Searls

Fractal, group theoretic, and relational structures on Cantor space

Cantor space, the set of infinite words over a finite alphabet, is a type of metric space with a `self-similar' structure. This thesis explores three areas concerning Cantor space with regard to fractal geometry, group theory, and topology. We find first results on the dimension of intersections of fractal sets within the Cantor space. More specifically, we examine the intersection of a subset E of the n-ary Cantor space, C[sub]n with the image of another subset Funder a random isometry. We obtain almost sure upper bounds for the Hausdorff and upper box-counting dimensions of the intersection, and a lower bound for the essential supremum of the Hausdorff dimension. We then consider a class of groups, denoted by V[sub]n(G), of homeomorphisms of the Cantor space built from transducers. These groups can be seen as homeomorphisms that respect the self-similar and symmetric structure of C[sub]n, and are supergroups of the Higman-Thompson groups V[sub]n. We explore their isomorphism classes with our primary result being that V[sub]n(G) is isomorphic to (and conjugate to) V[sub]n if and only if G is a semiregular subgroup of the symmetric group on n points. Lastly, we explore invariant relations on Cantor space, which have quotients homeomorphic to fractals in many different classes. We generalize a method of describing these quotients by invariant relations as an inverse limit, before characterizing a specific class of fractals known as Sierpiński relatives as invariant factors. We then compare relations arising through edge replacement systems to invariant relations, detailing the conditions under which they are the same

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum