69,031 research outputs found
Constraint-based reachability
Iterative imperative programs can be considered as infinite-state systems
computing over possibly unbounded domains. Studying reachability in these
systems is challenging as it requires to deal with an infinite number of states
with standard backward or forward exploration strategies. An approach that we
call Constraint-based reachability, is proposed to address reachability
problems by exploring program states using a constraint model of the whole
program. The keypoint of the approach is to interpret imperative constructions
such as conditionals, loops, array and memory manipulations with the
fundamental notion of constraint over a computational domain. By combining
constraint filtering and abstraction techniques, Constraint-based reachability
is able to solve reachability problems which are usually outside the scope of
backward or forward exploration strategies. This paper proposes an
interpretation of classical filtering consistencies used in Constraint
Programming as abstract domain computations, and shows how this approach can be
used to produce a constraint solver that efficiently generates solutions for
reachability problems that are unsolvable by other approaches.Comment: In Proceedings Infinity 2012, arXiv:1302.310
LSTM Neural Networks: Input to State Stability and Probabilistic Safety Verification
The goal of this paper is to analyze Long Short Term Memory (LSTM) neural
networks from a dynamical system perspective. The classical recursive equations
describing the evolution of LSTM can be recast in state space form, resulting
in a time-invariant nonlinear dynamical system. A sufficient condition
guaranteeing the Input-to-State (ISS) stability property of this class of
systems is provided. The ISS property entails the boundedness of the output
reachable set of the LSTM. In light of this result, a novel approach for the
safety verification of the network, based on the Scenario Approach, is devised.
The proposed method is eventually tested on a pH neutralization process.Comment: Accepted for Learning for dynamics & control (L4DC) 202
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