657 research outputs found
k-Step Relative Inductive Generalization
We introduce a new form of SAT-based symbolic model checking. One common idea
in SAT-based symbolic model checking is to generate new clauses from states
that can lead to property violations. Our previous work suggests applying
induction to generalize from such states. While effective on some benchmarks,
the main problem with inductive generalization is that not all such states can
be inductively generalized at a given time in the analysis, resulting in long
searches for generalizable states on some benchmarks. This paper introduces the
idea of inductively generalizing states relative to -step
over-approximations: a given state is inductively generalized relative to the
latest -step over-approximation relative to which the negation of the state
is itself inductive. This idea motivates an algorithm that inductively
generalizes a given state at the highest level so far examined, possibly by
generating more than one mutually -step relative inductive clause. We
present experimental evidence that the algorithm is effective in practice.Comment: 14 page
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
Sciduction: Combining Induction, Deduction, and Structure for Verification and Synthesis
Even with impressive advances in automated formal methods, certain problems
in system verification and synthesis remain challenging. Examples include the
verification of quantitative properties of software involving constraints on
timing and energy consumption, and the automatic synthesis of systems from
specifications. The major challenges include environment modeling,
incompleteness in specifications, and the complexity of underlying decision
problems.
This position paper proposes sciduction, an approach to tackle these
challenges by integrating inductive inference, deductive reasoning, and
structure hypotheses. Deductive reasoning, which leads from general rules or
concepts to conclusions about specific problem instances, includes techniques
such as logical inference and constraint solving. Inductive inference, which
generalizes from specific instances to yield a concept, includes algorithmic
learning from examples. Structure hypotheses are used to define the class of
artifacts, such as invariants or program fragments, generated during
verification or synthesis. Sciduction constrains inductive and deductive
reasoning using structure hypotheses, and actively combines inductive and
deductive reasoning: for instance, deductive techniques generate examples for
learning, and inductive reasoning is used to guide the deductive engines.
We illustrate this approach with three applications: (i) timing analysis of
software; (ii) synthesis of loop-free programs, and (iii) controller synthesis
for hybrid systems. Some future applications are also discussed
Counterexample Guided Inductive Optimization Applied to Mobile Robots Path Planning (Extended Version)
We describe and evaluate a novel optimization-based off-line path planning
algorithm for mobile robots based on the Counterexample-Guided Inductive
Optimization (CEGIO) technique. CEGIO iteratively employs counterexamples
generated from Boolean Satisfiability (SAT) and Satisfiability Modulo Theories
(SMT) solvers, in order to guide the optimization process and to ensure global
optimization. This paper marks the first application of CEGIO for planning
mobile robot path. In particular, CEGIO has been successfully applied to obtain
optimal two-dimensional paths for autonomous mobile robots using off-the-shelf
SAT and SMT solvers.Comment: 7 pages, 14rd Latin American Robotics Symposium (LARS'2017
Global Guidance for Local Generalization in Model Checking
SMT-based model checkers, especially IC3-style ones, are currently the most
effective techniques for verification of infinite state systems. They infer
global inductive invariants via local reasoning about a single step of the
transition relation of a system, while employing SMT-based procedures, such as
interpolation, to mitigate the limitations of local reasoning and allow for
better generalization. Unfortunately, these mitigations intertwine model
checking with heuristics of the underlying SMT-solver, negatively affecting
stability of model checking. In this paper, we propose to tackle the
limitations of locality in a systematic manner. We introduce explicit global
guidance into the local reasoning performed by IC3-style algorithms. To this
end, we extend the SMT-IC3 paradigm with three novel rules, designed to
mitigate fundamental sources of failure that stem from locality. We instantiate
these rules for the theory of Linear Integer Arithmetic and implement them on
top of SPACER solver in Z3. Our empirical results show that GSPACER, SPACER
extended with global guidance, is significantly more effective than both SPACER
and sole global reasoning, and, furthermore, is insensitive to interpolation.Comment: Published in CAV 202
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