Related papers: Extraction of a computer-certified ODE solver
Solving algebraic word problems requires executing a series of arithmetic operations---a program---to obtain a final answer. However, since programs can be arbitrarily complicated, inducing them directly from question-answer pairs is a…
We study transformational program logics for correctness and incorrectness that we extend to explicitly handle both termination and nontermination. We show that the logics are abstract interpretations of the right image transformer for a…
We describe a method for the identification of models for dynamical systems from observational data. The method is based on the concept of symbolic regression and uses genetic programming to evolve a system of ordinary differential…
In order to give appropriate semantics to qualitative conditionals of the form "if A then normally B", ordinal conditional functions (OCFs) ranking the possible worlds according to their degree of plausibility can be used. An OCF accepting…
We consider the solution of initial value problems within the context of hybrid systems and emphasise the use of high precision approximations (in software for exact real arithmetic). We propose a novel algorithm for the computation of…
Formal verification techniques are widely used for detecting design flaws in software systems. Formal verification can be done by transforming an already implemented source code to a formal model and attempting to prove certain properties…
Problems in program analysis can be solved by developing novel program semantics and deriving abstractions conventionally. For over thirty years, higher-order program analysis has been sold as a hard problem. Its solutions have required…
Neural ordinary differential equations (NODE) have garnered significant attention for their design of continuous-depth neural networks and the ability to learn data/feature dynamics. However, for high-dimensional systems, estimating…
The present paper introduces a practical protocol for provably secure, outsourced computation. Our protocol minimizes overhead for verification by requiring solutions to withstand an interactive game between a prover and challenger. For…
This study focuses on the numerical discretization methods for the continuous-time discounted linear-quadratic optimal control problem (LQ-OCP) with time delays. By assuming piecewise constant inputs, we formulate the discrete system…
On the one hand, ordered completion is a fundamental technique in equational theorem proving that is employed by automated tools. On the other hand, their complexity makes such tools inherently error prone. As a remedy to this situation we…
As software systems increase in size and complexity dramatically, ensuring their correctness, security, and reliability becomes an increasingly formidable challenge. Despite significant advancements in verification techniques and tools,…
We present necessary and sufficient conditions for the termination of linear homogeneous programs. We also develop a complete method to check termination for this class of programs. Our complete characterization of termination for such…
We present exact mixed-integer linear programming formulations for verifying the performance of first-order methods for parametric quadratic optimization. We formulate the verification problem as a mixed-integer linear program where the…
Integer Linear Programming with $n$ binary variables and $m$ many $0/1$-constraints can be solved in time $2^{\tilde O(m^2)} \text{poly}(n)$ and it is open whether the dependence on $m$ is optimal. Several seemingly unrelated problems,…
We present an adaptation, based on program extraction in elementary linear logic, of Krivine & Leivant's system FA_2. This system allows to write higher-order equations in order to specify the computational content of extracted programs.…
Most automated program verifiers for separation logic use either symbolic execution or verification condition generation to extract proof obligations, which are then handed over to an SMT solver. Existing verification algorithms are…
One recurring problem in program development is that of understanding how to re-use code developed by a third party. In the context of (constraint) logic programming, part of this problem reduces to figuring out how to query a program. If…
How can complexity theory and algorithms benefit from practical advances in computing? We give a short overview of some prior work using practical computing to attack problems in computational complexity and algorithms, informally describe…
In this work, we show a methodology aimed to improve the quality of the assessment process for subjects related to basic programming. The method takes into account the relevance of the items and the students answers to follow different…