Lipschitz Robustness of Finite-state Transducers

We investigate the problem of checking if a finite-state transducer is robust to uncertainty in its input. Our notion of robustness is based on the analytic notion of Lipschitz continuity --- a transducer is K-(Lipschitz) robust if the perturbation in its output is at most K times the perturbation in its input. We quantify input and output perturbation using similarity functions. We show that K-robustness is undecidable even for deterministic transducers. We identify a class of functional transducers, which admits a polynomial time automata-theoretic decision procedure for K-robustness. This class includes Mealy machines and functional letter-to-letter transducers. We also study K-robustness of nondeterministic transducers. Since a nondeterministic transducer generates a set of output words for each input word, we quantify output perturbation using set-similarity functions. We show that K-robustness of nondeterministic transducers is undecidable, even for letter-to-letter transducers. We identify a class of set-similarity functions which admit decidable K-robustness of letter-to-letter transducers.Comment: In FSTTCS 201

NAIS-Net: Stable Deep Networks from Non-Autonomous Differential Equations

This paper introduces Non-Autonomous Input-Output Stable Network (NAIS-Net), a very deep architecture where each stacked processing block is derived from a time-invariant non-autonomous dynamical system. Non-autonomy is implemented by skip connections from the block input to each of the unrolled processing stages and allows stability to be enforced so that blocks can be unrolled adaptively to a pattern-dependent processing depth. NAIS-Net induces non-trivial, Lipschitz input-output maps, even for an infinite unroll length. We prove that the network is globally asymptotically stable so that for every initial condition there is exactly one input-dependent equilibrium assuming tanh units, and multiple stable equilibria for ReL units. An efficient implementation that enforces the stability under derived conditions for both fully-connected and convolutional layers is also presented. Experimental results show how NAIS-Net exhibits stability in practice, yielding a significant reduction in generalization gap compared to ResNets.Comment: NIPS 201

Weighted Transducers for Robustness Verification

Automata theory provides us with fundamental notions such as languages, membership, emptiness and inclusion that in turn allow us to specify and verify properties of reactive systems in a useful manner. However, these notions all yield "yes"/"no" answers that sometimes fall short of being satisfactory answers when the models being analyzed are imperfect, and the observations made are prone to errors. To address this issue, a common engineering approach is not just to verify that a system satisfies a property, but whether it does so robustly. We present notions of robustness that place a metric on words, thus providing a natural notion of distance between words. Such a metric naturally leads to a topological neighborhood of words and languages, leading to quantitative and robust versions of the membership, emptiness and inclusion problems. More generally, we consider weighted transducers to model the cost of errors. Such a transducer models neighborhoods of words by providing the cost of rewriting a word into another. The main contribution of this work is to study robustness verification problems in the context of weighted transducers. We provide algorithms for solving the robust and quantitative versions of the membership and inclusion problems while providing useful motivating case studies including approximate pattern matching problems to detect clinically relevant events in a large type-1 diabetes dataset

The many facets of string transducers

Regular word transductions extend the robust notion of regular languages from a qualitative to a quantitative reasoning. They were already considered in early papers of formal language theory, but turned out to be much more challenging. The last decade brought considerable research around various transducer models, aiming to achieve similar robustness as for automata and languages. In this paper we survey some older and more recent results on string transducers. We present classical connections between automata, logic and algebra extended to transducers, some genuine definability questions, and review approaches to the equivalence problem

A Survey on Continuous Time Computations

We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models. We survey the existing models, summarizing results, and point to relevant references in the literature

The Triangular Observer-Based Integral Sliding-Mode Wind System Energy Control

We describe a fresh way to constructing a dependable controller utilizing a modified integrated sliding mode control technique in this research. Our proposed solution is intended to address the problem of attaining phase in systems with matching disturbances. As a starting point for demonstrating the usefulness of our technique, we propose replicating a wind turbine system. The inbuilt sliding mode control system is therefore used, which just requires the rotor speed as an accessible measurement. We use an asymptotic observer design that lowers observing errors over time to predict the unknown rotor acceleration required for the control law. The control law is based on Lyapunov stability analysis, which ensures the system's stability. We compare the performance of our proposed system to that of typical sliding mode control using simulation results in terms of settling time, tracking precision, energy usage, and input smoothness. Our findings show that the proposed technique outperforms classic sliding mode control across various performance parameters, showing its potential for developing a reliable controller in real applications