4,061 research outputs found
Adapting Real Quantifier Elimination Methods for Conflict Set Computation
The satisfiability problem in real closed fields is decidable. In the context
of satisfiability modulo theories, the problem restricted to conjunctive sets
of literals, that is, sets of polynomial constraints, is of particular
importance. One of the central problems is the computation of good explanations
of the unsatisfiability of such sets, i.e.\ obtaining a small subset of the
input constraints whose conjunction is already unsatisfiable. We adapt two
commonly used real quantifier elimination methods, cylindrical algebraic
decomposition and virtual substitution, to provide such conflict sets and
demonstrate the performance of our method in practice
Verification of Magnitude and Phase Responses in Fixed-Point Digital Filters
In the digital signal processing (DSP) area, one of the most important tasks
is digital filter design. Currently, this procedure is performed with the aid
of computational tools, which generally assume filter coefficients represented
with floating-point arithmetic. Nonetheless, during the implementation phase,
which is often done in digital signal processors or field programmable gate
arrays, the representation of the obtained coefficients can be carried out
through integer or fixed-point arithmetic, which often results in unexpected
behavior or even unstable filters. The present work addresses this issue and
proposes a verification methodology based on the digital-system verifier
(DSVerifier), with the goal of checking fixed-point digital filters w.r.t.
implementation aspects. In particular, DSVerifier checks whether the number of
bits used in coefficient representation will result in a filter with the same
features specified during the design phase. Experimental results show that
errors regarding frequency response and overflow are likely to be identified
with the proposed methodology, which thus improves overall system's
reliability
Encoding TLA+ set theory into many-sorted first-order logic
We present an encoding of Zermelo-Fraenkel set theory into many-sorted
first-order logic, the input language of state-of-the-art SMT solvers. This
translation is the main component of a back-end prover based on SMT solvers in
the TLA+ Proof System
SMT-Based Bounded Model Checking of Fixed-Point Digital Controllers
Digital controllers have several advantages with respect to their flexibility
and design's simplicity. However, they are subject to problems that are not
faced by analog controllers. In particular, these problems are related to the
finite word-length implementation that might lead to overflows, limit cycles,
and time constraints in fixed-point processors. This paper proposes a new
method to detect design's errors in digital controllers using a state-of-the
art bounded model checker based on satisfiability modulo theories. The
experiments with digital controllers for a ball and beam plant demonstrate that
the proposed method can be very effective in finding errors in digital
controllers than other existing approaches based on traditional simulations
tools
Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks
Deep neural networks have emerged as a widely used and effective means for
tackling complex, real-world problems. However, a major obstacle in applying
them to safety-critical systems is the great difficulty in providing formal
guarantees about their behavior. We present a novel, scalable, and efficient
technique for verifying properties of deep neural networks (or providing
counter-examples). The technique is based on the simplex method, extended to
handle the non-convex Rectified Linear Unit (ReLU) activation function, which
is a crucial ingredient in many modern neural networks. The verification
procedure tackles neural networks as a whole, without making any simplifying
assumptions. We evaluated our technique on a prototype deep neural network
implementation of the next-generation airborne collision avoidance system for
unmanned aircraft (ACAS Xu). Results show that our technique can successfully
prove properties of networks that are an order of magnitude larger than the
largest networks verified using existing methods.Comment: This is the extended version of a paper with the same title that
appeared at CAV 201
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