Adding modular predicates to first-order fragments

We investigate the decidability of the definability problem for fragments of first order logic over finite words enriched with modular predicates. Our approach aims toward the most generic statements that we could achieve, which successfully covers the quantifier alternation hierarchy of first order logic and some of its fragments. We obtain that deciding this problem for each level of the alternation hierarchy of both first order logic and its two-variable fragment when equipped with all regular numerical predicates is not harder than deciding it for the corresponding level equipped with only the linear order and the successor. For two-variable fragments we also treat the case of the signature containing only the order and modular predicates.Relying on some recent results, this proves the decidability for each level of the alternation hierarchy of the two-variable first order fragmentwhile in the case of the first order logic the question remains open for levels greater than two.The main ingredients of the proofs are syntactic transformations of first order formulas as well as the algebraic framework of finite categories

Aperiodic Two-way Transducers and FO-Transductions

Deterministic two-way transducers on finite words have been shown by Engelfriet and Hoogeboom to have the same expressive power as MSO-transductions. We introduce a notion of aperiodicity for these transducers and we show that aperiodic transducers correspond exactly to FO-transductions. This lifts to transducers the classical equivalence for languages between FO-definability, recognition by aperiodic monoids and acceptance by counter-free automata

Two-variable first order logic with modular predicates over words

We consider first order formulae over the signature consisting of the symbols of the alphabet, the symbol < (interpreted as a linear order) and the set MOD of modular numerical predicates. We study the expressive power of FO 2 [<, MOD], the two-variable first order logic over this signature, interpreted over finite words. We give an algebraic characterization of the corresponding regular languages in terms of their syntactic morphisms and we also give simple unambiguous regular expressions for them. It follows that one can decide whether a given regular language is captured by FO 2 [<, MOD]. Our proofs rely on a combination of arguments from semigroup theory (stamps), model theory (Ehrenfeucht-Fraïssé games) and combinatorics

On Reversible Transducers

Deterministic two-way transducers define the robust class of regular functions which is, among other good properties, closed under composition. However, the best known algorithms for composing two-way transducers cause a double exponential blow-up in the size of the inputs. In this paper, we introduce a class of transducers for which the composition has polynomial complexity. It is the class of reversible transducers, for which the computation steps can be reversed deterministically. While in the one-way setting this class is not very expressive, we prove that any two-way transducer can be made reversible through a single exponential blow-up. As a consequence, we prove that the composition of two-way transducers can be done with a single exponential blow-up in the number of states. A uniformization of a relation is a function with the same domain and which is included in the original relation. Our main result actually states that we can uniformize any non-deterministic two-way transducer by a reversible transducer with a single exponential blow-up, improving the known result by de Souza which has a quadruple exponential complexity. As a side result, our construction also gives a quadratic transformation from copyless streaming string transducers to two-way transducers, improving the exponential previous bound

Rankers over infinite words

We consider the fragments FO2, the intersection of Sigma2 and FO2, the intersection of Pi2 and FO2, and Delta2 of first-order logic FO[<] over finite and infinite words. For all four fragments, we give characterizations in terms of rankers. In particular, we generalize the notion of a ranker to infinite words in two possible ways. Both extensions are natural in the sense that over finite words, they coincide with classical rankers and over infinite words, they both have the full expressive power of FO2. Moreover, the first extension of rankers admits a characterization of the intersection of Sigma2 and FO2 while the other leads to a characterization of the intersection of Pi2 and FO2. Both versions of rankers yield characterizations of the fragment Delta2. As a byproduct, we also obtain characterizations based on unambiguous temporal logic and unambiguous interval temporal logic

The Herschel-Heterodyne Instrument for the Far-Infrared (HIFI): instrument and pre-launch testing

This paper describes the Heterodyne Instrument for the Far-Infrared (HIFI), to be launched onboard of ESA's Herschel Space Observatory, by 2008. It includes the first results from the instrument level tests. The instrument is designed to be electronically tuneable over a wide and continuous frequency range in the Far Infrared, with velocity resolutions better than 0.1 km/s with a high sensitivity. This will enable detailed investigations of a wide variety of astronomical sources, ranging from solar system objects, star formation regions to nuclei of galaxies. The instrument comprises 5 frequency bands covering 480-1150 GHz with SIS mixers and a sixth dual frequency band, for the 1410-1910 GHz range, with Hot Electron Bolometer Mixers (HEB). The Local Oscillator (LO) subsystem consists of a dedicated Ka-band synthesizer followed by 7 times 2 chains of frequency multipliers, 2 chains for each frequency band. A pair of Auto-Correlators and a pair of Acousto-Optic spectrometers process the two IF signals from the dual-polarization front-ends to provide instantaneous frequency coverage of 4 GHz, with a set of resolutions (140 kHz to 1 MHz), better than < 0.1 km/s. After a successful qualification program, the flight instrument was delivered and entered the testing phase at satellite level. We will also report on the pre-flight test and calibration results together with the expected in-flight performance

Convertisseur analogique-numérique delta-sigma

The invention relates on a sigma delta digital to analog converter, digitally sequenced by a clock, comprising a main line and a feedback line, the main line comprising: an input port, a linear filter G(z) and a multibit quantifier, a digital to analog converter, an output port, and the feedback line comprising a correcting memory table, able to process a correcting signal, and an adder able to subtract said correcting signal from an input signal, wherein the correcting memory table time cycle is k times greater than the clock time cycle

Dispositif amplificateur de radiofréquence et dispositif de configuration, procédés d'amplification et de configuration associés

L‘invention concerne un procédé de configuration d'une fonction de division (SPF) d'un diviseur de déphasage (OTS) d'un dispositif radiofréquence d'amplification (RFA), dans lequel un signal de bande de base d'entrée (IBS) est décomposé en un premier signal déphasé (FOS) et un second signal déphasé (SOS), lesdits premier (FOS) et second (SOS) signaux déphasés correspondant au signal de bande de base d'entrée (IBS) dans un diagramme "I/Q", ledit procédé comprenant l'étape consistant à: - déterminer une première règle (R1) en fonction d‘au moins un des critères de la liste de critères (LC) représentatifs des caractéristiques du dispositif radiofréquence d'amplification (RFA), - configurer la fonction de division (SPF) avec la première règle (R1) à veiller à ce que la différence de phase (DP) entre le premier signal déphasé (FOS) et le second signal déphasé (SOS) est inférieure à un premier seuil (TH1)

Logics for word transductions with synthesis

We introduce a logic, called LT, to express properties of transductions, i.e. binary relations from input to output (finite) words. In LT, the input/output dependencies are modelled via an origin function which associates to any position of the output word, the input position from which it originates. LT is well-suited to express relations (which are not necessarily functional), and can express all regular functional transductions, i.e. transductions definable for instance by deterministic two-way transducers. Despite its high expressive power, LT has decidable satisfiability and equivalence problems, with tight non-elementary and elementary complexities, depending on specific representation of LT-formulas. Our main contribution is a synthesis result: from any transduction R defined in LT, it is possible to synthesise a regular functional transduction f such that for all input words u in the domain of R, f is defined and (u, f(u)) R. As a consequence, we obtain that any functional transduction is regular iff it is LT-definable. We also investigate the algorithmic and expressiveness properties of several extensions of LT, and explicit a correspondence between transductions and data words. As a side-result, we obtain a new decidable logic for data words.SCOPUS: cp.pinfo:eu-repo/semantics/publishe