Logic Meets Algebra: the Case of Regular Languages

The study of finite automata and regular languages is a privileged meeting point of algebra and logic. Since the work of Buchi, regular languages have been classified according to their descriptive complexity, i.e. the type of logical formalism required to define them. The algebraic point of view on automata is an essential complement of this classification: by providing alternative, algebraic characterizations for the classes, it often yields the only opportunity for the design of algorithms that decide expressibility in some logical fragment. We survey the existing results relating the expressibility of regular languages in logical fragments of MSO[S] with algebraic properties of their minimal automata. In particular, we show that many of the best known results in this area share the same underlying mechanics and rely on a very strong relation between logical substitutions and block-products of pseudovarieties of monoid. We also explain the impact of these connections on circuit complexity theory.Comment: 37 page

Development of a versatile vaccination platform based on papaya mosaic virus (PapMV) nanoparticles

Over the past years, virus-like particles (VLPs) have shown great potential as highly immunogenic subunit vaccines. These non-infectious viral structures mimic the native pathogen’s organisation and conformation. VLPs contain highly repetitive and ordered viral epitopes leading to B cell activation through receptor cross-linking. By displaying heterologous epitopes on VLPs, one can mount an immune response against a different pathogen. These chimeric VLPs serve as presentation scaffold and can sometimes act as adjuvant to boost the immune response. However, VLP assembly can be affected by large epitope insertions altering intra or extra protein interactions impacting its conformation. Even if the insertion is successful, the epitopes have to be exposed at the particle surface to induce an immune response. To circumvent this problem, we have developed a new vaccine platform based on PapMV nanoparticules and sortase A (SrtA) transpeptidase. SrtA catalyzes the covalent conjugation of target antigenic epitopes to already assembled PapMV VLPs harbouring the SrtA recognition motif LPETG. Successful SrtA conjugations were achieved with peptides derived from Influenza (M2e) and HIV (T20). SrtA conjugated PapMV nanoparticles induce strong humoral responses in mice against both M2e and T20 peptides. PapMV-M2e vaccinated mice were protected against a lethal dose of Influenza H1N1 (A/WSN/33). Sera from PapMV-T20 vaccinated mice did not reduce in vitro HIV infection even with the high presence of specific antibodies. This new PapMV-SrtA platform eliminates the need for genetic fusion of the coat protein that can be difficult, time consuming and, sometime, unrealizable. The modification of PapMV VLP post-assembly facilitates its use in the rapid development of new vaccines by changing the nature of the target epitopes conjugated. This could be particularly useful when developing a pandemic vaccine or personalised vaccine for cancer therapy

A Type System for Privacy Properties (Technical Report)

Mature push button tools have emerged for checking trace properties (e.g. secrecy or authentication) of security protocols. The case of indistinguishability-based privacy properties (e.g. ballot privacy or anonymity) is more complex and constitutes an active research topic with several recent propositions of techniques and tools. We explore a novel approach based on type systems and provide a (sound) type system for proving equivalence of protocols, for a bounded or an unbounded number of sessions. The resulting prototype implementation has been tested on various protocols of the literature. It provides a significant speed-up (by orders of magnitude) compared to tools for a bounded number of sessions and complements in terms of expressiveness other state-of-the-art tools, such as ProVerif and Tamarin: e.g., we show that our analysis technique is the first one to handle a faithful encoding of the Helios e-voting protocol in the context of an untrusted ballot box

Regular languages in NC1

We give several characterizations, in terms of formal logic, semigroup theory, and operations on languages, of the regular languages in the circuit complexity class AC0, thus answering a question of Chandra, Fortune, and Lipton. As a by-product, we are able to determine effectively whether a given regular language is in AC0 and to solve in part an open problem originally posed by McNaughton. Using recent lower-bound results of Razborov and Smolensky, we obtain similar characterizations of the family of regular languages recognized by constant-depth circuit families that include unbounded fan-in mod p addition gates for a fixed prime p along with unbounded fan-in boolean gates. We also obtain logical characterizations for the class of all languages recognized by nonuniform circuit families in which mod m gates (where m is not necessarily prime) are permitted. Comparison of this characterization with our previous results provides evidence for a conjecture concerning the regular languages in this class. A proof of this conjecture would show that computing the bit sum modulo p, where p is a prime not dividing m, is not AC0-reducible to addition mod m, and thus that MAJORITY is not AC0-reducible to addition mod m.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/30017/1/0000385.pd

Imre Simon: an exceptional graduate student

This short note reviews the main contributions of the Ph.D. thesis of Imre Simon. His graduate work had major impact on algebraic theory of automata and thirty years later we are in a good position to appreciate how sensitive he was in selecting good problems, and how clever in solving them

A Note on MOD p - MOD m Circuits

Introduction An outstanding problem in circuit complexity concerns the computing power of constant-depth circuit families in which the output of each gate depends on the sum, modulo m; of its input bits. It is conjectured that such circuits require exponential size to compute the AND function of the inputs and to compute the sum, modulo q; of the inputs, where q is a prime that does not divide m: Several papers have concentrated on a special subclass of these circuits--- those in which there is a single layer of MODm gates connected to the inputs, followed by a fixed number of layers of MOD p k-gates, where p is prime. (We may always assume that p does not divide m; for if pjm; then we can construct an equivalent circuit with MODm p -gate