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Weighted Model Integration (WMI) is a popular technique for probabilistic inference that extends Weighted Model Counting (WMC) -- the standard inference technique for inference in discrete domains -- to domains with both discrete and... more
Weighted Model Integration (WMI) is a popular technique for probabilistic inference that extends Weighted Model Counting (WMC) -- the standard inference technique for inference in discrete domains -- to domains with both discrete and continuous variables. However, existing WMI solvers each have different interfaces and use different formats for representing WMI problems. Therefore, we introduce pywmi (http://pywmi.org), an open source framework and toolbox for probabilistic inference using WMI, to address these shortcomings. Crucially, pywmi fixes a common internal format for WMI problems and introduces a common interface for WMI solvers. To assist users in modeling WMI problems, pywmi introduces modeling languages based on SMT-LIB.v2 or MiniZinc and parsers for both. To assist users in comparing WMI solvers, pywmi includes implementations of several state-of-the-art solvers, a fast approximate WMI solver, and a command-line interface to solve WMI problems. Finally, to assist ...
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The recent emergence of heavily-optimized modal decision procedures has highlighted the key role of empirical testing in this domain. Unfortunately, the introduction of extensive empirical tests for modal logics is recent, and so far none... more
The recent emergence of heavily-optimized modal decision procedures has highlighted the key role of empirical testing in this domain. Unfortunately, the introduction of extensive empirical tests for modal logics is recent, and so far none of the proposed test generators is very satisfactory. To cope with this fact, we present a new random generation method that provides benefits over previous methods for generating empirical tests. It fixes and much generalizes one of the best-known methods, the random CNF_[]m test, allowing for generating a much wider variety of problems, covering in principle the whole input space. Our new method produces much more suitable test sets for the current generation of modal decision procedures. We analyze the features of the new method by means of an extensive collection of empirical tests.
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Optimization Modulo Theories (OMT) is an extension of SMT, which combines SMT with optimization, finding models that make given objectives optimal. OMT has been extended to be incremental and to handle multiple objective functions either... more
Optimization Modulo Theories (OMT) is an extension of SMT, which combines SMT with optimization, finding models that make given objectives optimal. OMT has been extended to be incremental and to handle multiple objective functions either independently or with their linear, lexicographic, Pareto, min-max/max-min combinations. OMT applications can be found not only in the domains of Formal Verification, Automated Reasoning and Planning with Resources, but also Machine Learning and Requirement Engineering. (Partial weighted) MAXSMT–or, alternatively, OMT with Pseudo-Boolean objective functions– is a very-relevant subcase of OMT. Unfortunately, using general OMT algorithm for MAXSMT suffers from some intrinsic inefficiencies in some cases. In this paper we identify the sources of such inefficiencies and address them by enhancing general OMT by means of sorting networks. We implemented this idea on top of the OPTIMATHSAT OMT solver and evaluated them empirically on problems coming from M...
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Optimization modulo theories (OMT) is an important extension of SMT which allows for finding models that optimize given objective functions, typically consisting in linear-arithmetic or Pseudo-Boolean terms. However, many SMT and OMT... more
Optimization modulo theories (OMT) is an important extension of SMT which allows for finding models that optimize given objective functions, typically consisting in linear-arithmetic or Pseudo-Boolean terms. However, many SMT and OMT applications, in particular from SW and HW verification, require handling bit-precise representations of numbers, which in SMT are handled by means of the theory of bit-vectors ($${{\mathcal {B}}}{{\mathcal {V}}}$$ B V ) for the integers and that of floating-point numbers ($$\mathcal {FP}$$ FP ) for the reals respectively. Whereas an approach for OMT with (unsigned) $${{\mathcal {B}}}{{\mathcal {V}}}$$ B V objectives has been proposed by Nadel & Ryvchin, unfortunately we are not aware of any existing approach for OMT with $$\mathcal {FP}$$ FP objectives. In this paper we fill this gap, and we address for the first time $$\text {OMT}$$ OMT with $$\mathcal {FP}$$ FP objectives. We present a novel OMT approach, based on the novel concept of attractor and d...
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In the last two decades, modal and description logics have been applied to numerous areas of computer science, including knowledge representation, formal verification, database theory, distributed computing and, more recently, semantic... more
In the last two decades, modal and description logics have been applied to numerous areas of computer science, including knowledge representation, formal verification, database theory, distributed computing and, more recently, semantic web and ontologies. For this reason, the problem of automated reasoning in modal and description logics has been thoroughly investigated. In particular, many approaches have been proposed for efficiently handling the satisfiability of the core normal modal logic K(m), and of its notational variant, the description logic ALC. Although simple in structure, K(m)/ALC is computationally very hard to reason on, its satisfiability being PSPACE-complete. In this paper we start exploring the idea of performing automated reasoning tasks in modal and description logics by encoding them into SAT, so that to be handled by state-of-the-art SAT tools; as with most previous approaches, we begin our investigation from the satisfiability in K(m). We propose an efficien...
Research Interests: Cognitive Science, Applied Mathematics, Modal Logic, Computer Science, Distributed Computing, and 11 moreArtificial Intelligence, Theoretical Computer Science, Semantic Web, Knowledge Representation, Automated reasoning, Case Study, computer science Artificial intelligence, Modal, JAIR, Description Logic, and Boolean Satisfiability
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The problem of computing Craig interpolants has recently received a lot of interest. In this article, we address the problem of efficient generation of interpolants for some important fragments of first-order logic, which are amenable for... more
The problem of computing Craig interpolants has recently received a lot of interest. In this article, 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 (SMT) 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 effic...
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Abstract. Rarely verification problems originate from bit-level descriptions. Yet, most of the verification technologies are based on bit blasting, ie, reduction to boolean reasoning. In this paper we advocate reasoning at higher level of... more
Abstract. Rarely verification problems originate from bit-level descriptions. Yet, most of the verification technologies are based on bit blasting, ie, reduction to boolean reasoning. In this paper we advocate reasoning at higher level of abstraction, within the theory of bit vectors (BV), where ...
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Satisfiability Modulo Theories (SMT) is the problem of deciding the satisfiability of a first-order formula with respect to some theory or combination of theories; Verification Modulo Theories (VMT) is the problem of analyzing the... more
Satisfiability Modulo Theories (SMT) is the problem of deciding the satisfiability of a first-order formula with respect to some theory or combination of theories; Verification Modulo Theories (VMT) is the problem of analyzing the reachability for transition systems represented in terms of SMT formulae. In this article, we tackle the problems of SMT and VMT over the theories of nonlinear arithmetic over the reals (NRA) and of NRA augmented with transcendental (exponential and trigonometric) functions (NTA). We propose a new abstraction-refinement approach for SMT and VMT on NRA or NTA, called Incremental Linearization . The idea is to abstract nonlinear multiplication and transcendental functions as uninterpreted functions in an abstract space limited to linear arithmetic on the rationals with uninterpreted functions. The uninterpreted functions are incrementally axiomatized by means of upper- and lower-bounding piecewise-linear constraints. In the case of transcendental functions, ...
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Microcode is a critical component in modern microprocessors, and substantial effort has been devoted in the past to verify its correctness. A prominent approach, based on symbolic execution, traditionally relies on the use of boolean SAT... more
Microcode is a critical component in modern microprocessors, and substantial effort has been devoted in the past to verify its correctness. A prominent approach, based on symbolic execution, traditionally relies on the use of boolean SAT solvers as a backend engine. In this paper, we investigate the application of Satisfiability Modulo Theories (SMT) to the problem of microcode verification. We integrate MathSAT, an SMT solver for the theory of Bit Vectors, within the flow of microcode verification, and experimentally evaluate the effectiveness of some optimizations. The results demonstrate the potential of SMT technologies over pure boolean SAT.