14 research outputs found
Pushing the envelope of Optimization Modulo Theories with Linear-Arithmetic Cost Functions
In the last decade we have witnessed an impressive progress in the
expressiveness and efficiency of Satisfiability Modulo Theories (SMT) solving
techniques. This has brought previously-intractable problems at the reach of
state-of-the-art SMT solvers, in particular in the domain of SW and HW
verification. Many SMT-encodable problems of interest, however, require also
the capability of finding models that are optimal wrt. some cost functions. In
previous work, namely "Optimization Modulo Theory with Linear Rational Cost
Functions -- OMT(LAR U T )", we have leveraged SMT solving to handle the
minimization of cost functions on linear arithmetic over the rationals, by
means of a combination of SMT and LP minimization techniques. In this paper we
push the envelope of our OMT approach along three directions: first, we extend
it to work also with linear arithmetic on the mixed integer/rational domain, by
means of a combination of SMT, LP and ILP minimization techniques; second, we
develop a multi-objective version of OMT, so that to handle many cost functions
simultaneously; third, we develop an incremental version of OMT, so that to
exploit the incrementality of some OMT-encodable problems. An empirical
evaluation performed on OMT-encoded verification problems demonstrates the
usefulness and efficiency of these extensions.Comment: A slightly-shorter version of this paper is published at TACAS 2015
conferenc
Abduction-Based Explanations for Machine Learning Models
The growing range of applications of Machine Learning (ML) in a multitude of
settings motivates the ability of computing small explanations for predictions
made. Small explanations are generally accepted as easier for human decision
makers to understand. Most earlier work on computing explanations is based on
heuristic approaches, providing no guarantees of quality, in terms of how close
such solutions are from cardinality- or subset-minimal explanations. This paper
develops a constraint-agnostic solution for computing explanations for any ML
model. The proposed solution exploits abductive reasoning, and imposes the
requirement that the ML model can be represented as sets of constraints using
some target constraint reasoning system for which the decision problem can be
answered with some oracle. The experimental results, obtained on well-known
datasets, validate the scalability of the proposed approach as well as the
quality of the computed solutions
A Generic Framework for Implicate Generation Modulo Theories
International audienceThe clausal logical consequences of a formula are called its implicates. The generation of these implicates has several applications, such as the identification of missing hypotheses in a logical specification. We present a procedure that generates the implicates of a quantifier-free formula modulo a theory. No assumption is made on the considered theory, other than the existence of a decision procedure. The algorithm has been implemented (using the solvers MiniSAT, CVC4 and Z3) and experimental results show evidence of the practical relevance of the proposed approach
Discovering, quantifying, and displaying attacks
In the design of software and cyber-physical systems, security is often
perceived as a qualitative need, but can only be attained quantitatively.
Especially when distributed components are involved, it is hard to predict and
confront all possible attacks. A main challenge in the development of complex
systems is therefore to discover attacks, quantify them to comprehend their
likelihood, and communicate them to non-experts for facilitating the decision
process. To address this three-sided challenge we propose a protection analysis
over the Quality Calculus that (i) computes all the sets of data required by an
attacker to reach a given location in a system, (ii) determines the cheapest
set of such attacks for a given notion of cost, and (iii) derives an attack
tree that displays the attacks graphically. The protection analysis is first
developed in a qualitative setting, and then extended to quantitative settings
following an approach applicable to a great many contexts. The quantitative
formulation is implemented as an optimisation problem encoded into
Satisfiability Modulo Theories, allowing us to deal with complex cost
structures. The usefulness of the framework is demonstrated on a national-scale
authentication system, studied through a Java implementation of the framework.Comment: LMCS SPECIAL ISSUE FORTE 201
Optimization Modulo Theories with Linear Rational Costs
In the contexts of automated reasoning (AR) and formal verification (FV),
important decision problems are effectively encoded into Satisfiability Modulo
Theories (SMT). In the last decade efficient SMT solvers have been developed
for several theories of practical interest (e.g., linear arithmetic, arrays,
bit-vectors). Surprisingly, little work has been done to extend SMT to deal
with optimization problems; in particular, we are not aware of any previous
work on SMT solvers able to produce solutions which minimize cost functions
over arithmetical variables. This is unfortunate, since some problems of
interest require this functionality.
In the work described in this paper we start filling this gap. We present and
discuss two general procedures for leveraging SMT to handle the minimization of
linear rational cost functions, combining SMT with standard minimization
techniques. We have implemented the procedures within the MathSAT SMT solver.
Due to the absence of competitors in the AR, FV and SMT domains, we have
experimentally evaluated our implementation against state-of-the-art tools for
the domain of linear generalized disjunctive programming (LGDP), which is
closest in spirit to our domain, on sets of problems which have been previously
proposed as benchmarks for the latter tools. The results show that our tool is
very competitive with, and often outperforms, these tools on these problems,
clearly demonstrating the potential of the approach.Comment: Submitted on january 2014 to ACM Transactions on Computational Logic,
currently under revision. arXiv admin note: text overlap with arXiv:1202.140
Synthesizing Adaptive Test Strategies from Temporal Logic Specifications
Constructing good test cases is difficult and time-consuming, especially if
the system under test is still under development and its exact behavior is not
yet fixed. We propose a new approach to compute test strategies for reactive
systems from a given temporal logic specification using formal methods. The
computed strategies are guaranteed to reveal certain simple faults in every
realization of the specification and for every behavior of the uncontrollable
part of the system's environment. The proposed approach supports different
assumptions on occurrences of faults (ranging from a single transient fault to
a persistent fault) and by default aims at unveiling the weakest one. Based on
well-established hypotheses from fault-based testing, we argue that such tests
are also sensitive for more complex bugs. Since the specification may not
define the system behavior completely, we use reactive synthesis algorithms
with partial information. The computed strategies are adaptive test strategies
that react to behavior at runtime. We work out the underlying theory of
adaptive test strategy synthesis and present experiments for a safety-critical
component of a real-world satellite system. We demonstrate that our approach
can be applied to industrial specifications and that the synthesized test
strategies are capable of detecting bugs that are hard to detect with random
testing