Efficient Generation of Craig Interpolants in Satisfiability Modulo Theories

The problem of computing Craig Interpolants has recently received a lot of interest. In this paper, we address the problem of efficient generation of interpolants for some important fragments of first order logic, which are amenable for effective decision procedures, called Satisfiability Modulo Theory solvers. We make the following contributions. First, we provide interpolation procedures for several basic theories of interest: the theories of linear arithmetic over the rationals, difference logic over rationals and integers, and UTVPI over rationals and integers. Second, we define a novel approach to interpolate combinations of theories, that applies to the Delayed Theory Combination approach. Efficiency is ensured by the fact that the proposed interpolation algorithms extend state of the art algorithms for Satisfiability Modulo Theories. Our experimental evaluation shows that the MathSAT SMT solver can produce interpolants with minor overhead in search, and much more efficiently than other competitor solvers.Comment: submitted to ACM Transactions on Computational Logic (TOCL

Efficient Interpolant Generation in Satisfiability Modulo Theories

The problem of computing Craig Interpolants for propositional (SAT) formulas has recently received a lot of interest, mainly for its applications in formal verification. However, propositional logic is often not expressive enough for representing many interesting verification problems, which can be more naturally addressed in the framework of Satisfiability Modulo Theories, SMT. Although {some} works have addressed the topic of generating interpolants in SMT, the techniques and tools that are currently available have some limitations, and their performance still does not exploit the full power of current state-of-the-art SMT solvers. In this paper we try to close this gap. We present several techniques for interpolant generation in SMT which overcome the limitations of the current generators mentioned above, and which take full advantage of state-of-the-art SMT technology. These novel techniques can lead to substantial performance improvements wrt. the currently available tools. We support our claims with an extensive experimental evaluation of our implementation of the proposed techniques in the MathSAT SMT solver

A Simple and Flexible Way of Computing Small Unsatisfiable Cores in SAT Modulo Theories

Finding small unsatisfiable cores for SAT problems has recently received a lot of interest, mostly for its applications in formal verification. However, propositional logic is often not expressive enough for representing many interesting verification problems, which can be more naturally addressed in the framework of Satisfiability Modulo Theories, SMT. Surprisingly, the problem of finding unsatisfiable cores in SMT has received very little attention in the literature; in particular, we are not aware of any work aiming at producing small unsatisfiable cores in SMT. In this paper we present a novel approach to this problem. The main idea is to combine an SMT solver with an external propositional core extractor: the SMT solver produces the theory lemmas found during the search; the core extractor is then called on the boolean abstraction of the original SMT problem and of the theory lemmas. This results in an unsatisfiable core for the original SMT problem, once the remaining theory lemmas have been removed. The approach is conceptually interesting, since the SMT solver is used to dynamically lift the suitable amount of theory information to the boolean level, and it also has several advantages in practice. In fact, it is extremely simple to implement and to update, and it can be interfaced with every propositional core extractor in a plug-and-play manner, so that to benefit for free of all unsat-core reduction techniques which have been or will be made available. We have evaluated our approach by an extensive empirical test on SMT-LIB benchmarks, which confirms the validity and potential of this approach

Software Model Checking via Large-Block Encoding

The construction and analysis of an abstract reachability tree (ART) are the basis for a successful method for software verification. The ART represents unwindings of the control-flow graph of the program. Traditionally, a transition of the ART represents a single block of the program, and therefore, we call this approach single-block encoding (SBE). SBE may result in a huge number of program paths to be explored, which constitutes a fundamental source of inefficiency. We propose a generalization of the approach, in which transitions of the ART represent larger portions of the program; we call this approach large-block encoding (LBE). LBE may reduce the number of paths to be explored up to exponentially. Within this framework, we also investigate symbolic representations: for representing abstract states, in addition to conjunctions as used in SBE, we investigate the use of arbitrary Boolean formulas; for computing abstract-successor states, in addition to Cartesian predicate abstraction as used in SBE, we investigate the use of Boolean predicate abstraction. The new encoding leverages the efficiency of state-of-the-art SMT solvers, which can symbolically compute abstract large-block successors. Our experiments on benchmark C programs show that the large-block encoding outperforms the single-block encoding.Comment: 13 pages (11 without cover), 4 figures, 5 table

Punk is dad. Parole e retorica negli articoli di Valerio Evangelisti

Analisi di stilemi di Valerio Evangelisti nella sua scrittura saggistica e pubblicistica, in particolare della sua produzione per la rivista musicale "Rolling Stone", consistente in una rubrica tenuta dal 2005 al 2007 sulla musica heavy metal, per la prima volta recensita e studiata in prospettiva linguistica e stilistica e in relazione alla poetica dell'autore

Viaggi nella polifonia: la scrittura di Gipi

Lo studio presenta un'analisi linguistica e stilistica della produzione a fumetti di Gipi, anche come sceneggiatore, individuando dove la lingua è ubicata nelle sue tavole, rilevando l'importanza della scrittura da un punto di vista grafica, delineando come ottiene quella particolare polifonia che è la sua cifra stilistica, tra letterarietà, registri informali, dialetto, creatività lessicale. In particolare in Aldobrando (2020), disegnato da Luigi Critone, Gipi mostra di saper dare vita anche a un italiano "anticato", alla Armata Brancaleone di Monicelli, dall'effetto comico

La penna e lo spartito. Scrittori, musica e scrittura

Introduzione al volume monografico omonimo della rivista "Tratti" (n. 70, ottobre 2005), in cui sono pubblicate interviste di Alberto Sebastiani a 7 scrittori contemporanei (Aldo Gianolio, Paolo Nori, Enrico Brizzi, Gianluca Morozzi, Grazia Verasani, Guido Leotta, Emidio Clementi) sul loro lavoro in relazione alla musica, intesa come oggetto di scrittura, come realtà e panorama culturale del mondo descritto nei loro testi, come complice nella creazione di un ritmo nella scrittur

Silvio D’Arzo su “Gerarchia”. Lingua e stile tra regime e ricerca di “umanità”

Analisi linguistica e stilistica dell'intervento "Saggio sulle rivoluzioni" di Silvio D'Arzo, finora ignoto alle bibliografie, ma uscito nel 1939 nella sezione “Arengo”, che ospita le «(Collaborazione dei lettori)», come recita il sottotitolo della rubrica, di “Gerarchia. Rassegna mensile della rivoluzione fascista” (settembre 1939-XVII, anno XIX n. 9, pp. 644-645). Il testo presenta fenomeni linguistici, stilisti e retorici che D'Arzo poi svilupperà all'interno della successiva produzione saggistica e letteraria, in particolare in relazione al concetto di "umanità"