Concept

Primitive recursive function

Related publications (51)

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This paper reports on the computation of a discrete logarithm in the finite field F-230750, breaking by a large margin the previous record, which was set in January 2014 by a computation in F-29234. The present computation made essential use of the elimina ...

AMER MATHEMATICAL SOC2021

Multi-memristive synaptic architectures for training neural networks

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Highly data-centric AI workloads require that new computing paradigms be adopted because the performance of traditional CPU- and GPU-based systems are limited by data access and transfer. Training deep neural networks with millions of tunable parameters ta ...

EPFL2020

Algorithmic Resource Verification

Ravichandhran Kandhadai Madhavan

Static estimation of resource utilisation of programs is a challenging and important problem with numerous applications. In this thesis, I present new algorithms that enable users to specify and verify their desired bounds on resource usage of functional p ...

EPFL2017

Termination of Open Higher-Order Programs

Viktor Kuncak, Nicolas Charles Yves Voirol, Ravichandhran Kandhadai Madhavan

We study the problem of proving termination of open, higher-order programs with recursive functions and datatypes. We identify a new point in the design space of solutions, with an appealing trade-off between simplicity of specification, modularity, and am ...

2017

Proactive Synthesis of Recursive Tree-to-String Functions from Examples

Viktor Kuncak, Mikaël Mayer, Jad Hamza

Synthesis from examples enables non-expert users to generate programs by specifying examples of their behavior. A domain-specific form of such synthesis has been recently deployed in a widely used spreadsheet software product. In this paper we contribute t ...

2017

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In this thesis, we explore techniques for the development of recursive functional programs over unbounded domains that are proved correct according to their high-level specifications. We present algorithms for automatically synthesizing executable code, st ...

EPFL2016

Automating Verification of Functional Programs with Quantified Invariants

Viktor Kuncak, Nicolas Charles Yves Voirol

We present the foundations of a verifier for higher-order functional programs with generics and recursive algebraic data types. Our ver- ifier supports finding sound proofs and counterexamples even in the presence of certain quantified invariants and recur ...

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Undecidability through Fourier series

In computability theory a variety of combinatorial systems are encountered (word problems, production systems) that exhibit undecidability properties. Here we seek such structures in the realm of Analysis, more specifically in the area of Fourier Analysis. ...

Elsevier Science Bv2016

Tensor train approximation of moment equations for elliptic equations with lognormal coefficient

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We study an elliptic equation with stochastic coefficient modeled as a lognormal random field. A perturbation approach is adopted, expanding the solution in Taylor series around the nominal value of the coefficient. The resulting recursive deterministic pr ...

Elsevier2016

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We propose two different improvements of reduced basis (RB) methods to enable the efficient and accurate evaluation of an output functional based on the numerical solution of parametrized partial differential equations with a possibly high-dimensional para ...

Springer Verlag2016

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