3,244 research outputs found
Abstraction of Elementary Hybrid Systems by Variable Transformation
Elementary hybrid systems (EHSs) are those hybrid systems (HSs) containing
elementary functions such as exp, ln, sin, cos, etc. EHSs are very common in
practice, especially in safety-critical domains. Due to the non-polynomial
expressions which lead to undecidable arithmetic, verification of EHSs is very
hard. Existing approaches based on partition of state space or
over-approximation of reachable sets suffer from state explosion or inflation
of numerical errors. In this paper, we propose a symbolic abstraction approach
that reduces EHSs to polynomial hybrid systems (PHSs), by replacing all
non-polynomial terms with newly introduced variables. Thus the verification of
EHSs is reduced to the one of PHSs, enabling us to apply all the
well-established verification techniques and tools for PHSs to EHSs. In this
way, it is possible to avoid the limitations of many existing methods. We
illustrate the abstraction approach and its application in safety verification
of EHSs by several real world examples
Abstract State Machines 1988-1998: Commented ASM Bibliography
An annotated bibliography of papers which deal with or use Abstract State
Machines (ASMs), as of January 1998.Comment: Also maintained as a BibTeX file at http://www.eecs.umich.edu/gasm
Interpolant-Based Transition Relation Approximation
In predicate abstraction, exact image computation is problematic, requiring
in the worst case an exponential number of calls to a decision procedure. For
this reason, software model checkers typically use a weak approximation of the
image. This can result in a failure to prove a property, even given an adequate
set of predicates. We present an interpolant-based method for strengthening the
abstract transition relation in case of such failures. This approach guarantees
convergence given an adequate set of predicates, without requiring an exact
image computation. We show empirically that the method converges more rapidly
than an earlier method based on counterexample analysis.Comment: Conference Version at CAV 2005. 17 Pages, 9 Figure
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Using formal methods to support testing
Formal methods and testing are two important approaches that assist in the development of high quality software. While traditionally these approaches have been seen as rivals, in recent
years a new consensus has developed in which they are seen as complementary. This article reviews the state of the art regarding ways in which the presence of a formal specification can be used to assist testing
PrIC3: Property Directed Reachability for MDPs
IC3 has been a leap forward in symbolic model checking. This paper proposes
PrIC3 (pronounced pricy-three), a conservative extension of IC3 to symbolic
model checking of MDPs. Our main focus is to develop the theory underlying
PrIC3. Alongside, we present a first implementation of PrIC3 including the key
ingredients from IC3 such as generalization, repushing, and propagation
Integrating Abstraction Techniques for Formal Verification of Analog Designs
The verification of analog designs is a challenging and exhaustive task that requires deep understanding of physical
behaviours. In this paper, we propose a qualitative based predicate abstraction method for the verification of a class
of non-linear analog circuits. In the proposed method, system equations are automatically extracted from a circuit
diagram by means of a bond graph. Verification is applied based on combining techniques from constraint solving and
computer algebra along with symbolic model checking. Our methodology has the advantage of avoiding exhaustive
simulation normally encountered in the verification of analog designs. To this end, we have used Dymola, Hsolver,
SMV and Mathematica to implement the verification flow. We illustrate the methodology on several analog examples
including Colpitts and tunnel diode oscillators
BDD for Complete Characterization of a Safety Violation in Linear Systems with Inputs
The control design tools for linear systems typically involves pole placement
and computing Lyapunov functions which are useful for ensuring stability. But
given higher requirements on control design, a designer is expected to satisfy
other specification such as safety or temporal logic specification as well, and
a naive control design might not satisfy such specification. A control designer
can employ model checking as a tool for checking safety and obtain a
counterexample in case of a safety violation. While several scalable techniques
for verification have been developed for safety verification of linear
dynamical systems, such tools merely act as decision procedures to evaluate
system safety and, consequently, yield a counterexample as an evidence to
safety violation. However these model checking methods are not geared towards
discovering corner cases or re-using verification artifacts for another
sub-optimal safety specification. In this paper, we describe a technique for
obtaining complete characterization of counterexamples for a safety violation
in linear systems. The proposed technique uses the reachable set computed
during safety verification for a given temporal logic formula, performs
constraint propagation, and represents all modalities of counterexamples using
a binary decision diagram (BDD). We introduce an approach to dynamically
determine isomorphic nodes for obtaining a considerably reduced (in size)
decision diagram. A thorough experimental evaluation on various benchmarks
exhibits that the reduction technique achieves up to reduction in the
number of nodes and reduction in the width of the decision diagram.Comment: 16 pages, 5 figures, 2 table
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