Understanding the complexity of #SAT using knowledge compilation

Two main techniques have been used so far to solve the #P-hard problem #SAT. The first one, used in practice, is based on an extension of DPLL for model counting called exhaustive DPLL. The second approach, more theoretical, exploits the structure of the input to compute the number of satisfying assignments by usually using a dynamic programming scheme on a decomposition of the formula. In this paper, we make a first step toward the separation of these two techniques by exhibiting a family of formulas that can be solved in polynomial time with the first technique but needs an exponential time with the second one. We show this by observing that both techniques implicitely construct a very specific boolean circuit equivalent to the input formula. We then show that every beta-acyclic formula can be represented by a polynomial size circuit corresponding to the first method and exhibit a family of beta-acyclic formulas which cannot be represented by polynomial size circuits corresponding to the second method. This result shed a new light on the complexity of #SAT and related problems on beta-acyclic formulas. As a byproduct, we give new handy tools to design algorithms on beta-acyclic hypergraphs

Enumerating models of DNF faster: breaking the dependency on the formula size

In this article, we study the problem of enumerating the models of DNF formulas. The aim is to provide enumeration algorithms with a delay that depends polynomially on the size of each model and not on the size of the formula, which can be exponentially larger. We succeed for two subclasses of DNF formulas: we provide a constant delay algorithm for $k$-DNF with fixed $k$ by an appropriate amortization method and we give a quadratic delay algorithm for monotone formulas. We then focus on the \emph{average delay} of enumeration algorithms and show how to obtain a sublinear delay in the formula size

Finzioni e funzioni del sogno : la costante onirico-ideologica nella lirica occitana tra cinque e novecento

L'articolo prende in esame gli autori occitani moderni e contemporanei che hanno utilizzato sistematicamente il tema poetico del sogno attribuendogli la funzione ideologica di strumento per la rivendicazione politico-letteraria di riscoperta ed esaltazione del passato, specificamente dell'eredità trobadorica, in quanto epoca d'oro dell'indipendenza linguistica, economica e artistica del Midi della Francia. Da Jean de Nostredame, precursore erudito della rinascenza provenzale del XVI secolo, fino al contemporaneo Max Rouquette, passando per l'opera mediatrice primo ottocentesca di Fabre d'Olivet e il patriottismo sentimentale di Frédéric Mistral (Premio Nobel per la Letteratura nel 1904), l'analisi sincronica e diacronica del presente contributo evidenzia le caratteristiche fondamentali di ciascun autore in rapporto alla tendenza generale di una poesia «impegnata», dove l'elemento onirico è usato come parentesi meta-narrativa all'interno del discorso poetico, concepito per accogliere le riflessioni del poeta sulla sua missione nella e per la Storia, in forma di immagine atemporale, collettiva, universalizzante.This essay studies the Provençal authors who systematically exploited the dream motif for ideological purposes, taking on the legacy of the Troubadours in order to reassert the strong sense of linguistic and literary commonality between regions in Southern France, which creates difficult issues of competition between the literature in the Provençal mother tongue and the homogenizing power of the French language and the government's centralizing influence. The analysis focuses upon the erudite approach of the 16th century forerunner Jean de Nostredame, the pre-Romantic taste of Antoine Fabre d'Olivet (1767-1825), the Romantic demands of Frédéric Mistral (Nobel Prize for Literature, 1904), and the recent experiments by Max Rouquette (who died 2005). By examining these literary interpretations of the dream theme, it is therefore possible to highlight the common narrative and lyrical functions they fulfil synchronically and diachronically: the reverie appears to be a metadiegetic digression which brings poetic discourse to a halt and is conceived to express the poet's universalizing meditations on his historical, cultural and artistic mission