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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 ...
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 ...
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 ...
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 ...
This paper reports on the number field sieve computation of a 768-bit prime field discrete logarithm, describes the different parameter optimizations and resulting algorithmic changes compared to the factorization of a 768-bit RSA modulus, and briefly disc ...
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. ...
The objective of this thesis is to develop efficient numerical schemes to successfully tackle problems arising from the study of groundwater flows in a porous saturated medium; we deal therefore with partial differential equations(PDE) having random coeffi ...
Determining the size of a maximum independent set of a graph G, denoted by alpha(G), is an NP-hard problem. Therefore many attempts are made to find upper and lower bounds, or exact values of alpha(G) for special classes of graphs. This paper is aimed towa ...
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 ...
We prove that the quantifier-free fragment of the theory of character strings with regular language membership constraints and linear integer constraints over string lengths is decidable. We do that by describing a sound, complete and terminating tableaux ...
