Related papers: Intersection Types and (Positive) Almost-Sure Term…
The termination method of weakly monotonic algebras, which has been defined for higher-order rewriting in the HRS formalism, offers a lot of power, but has seen little use in recent years. We adapt and extend this method to the alternative…
Intersection types are a standard tool in operational and semantical studies of the lambda calculus. De Carvalho showed how multi types, a quantitative variant of intersection types providing a handy presentation of the relational…
We consider minimization of a smooth nonconvex function with inexact oracle access to gradient and Hessian (without assuming access to the function value) to achieve approximate second-order optimality. A novel feature of our method is that…
Probabilistic argumentation allows reasoning about argumentation problems in a way that is well-founded by probability theory. However, in practice, this approach can be severely limited by the fact that probabilities are defined by adding…
Type systems certify program properties in a compositional way. From a bigger program one can abstract out a part and certify the properties of the resulting abstract program by just using the type of the part that was abstracted away.…
Markov decision processes model systems subject to nondeterministic and probabilistic uncertainty. A plethora of verification techniques addresses variations of reachability properties, such as: Is there a scheduler resolving the…
We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…
In many iterative optimization methods, fixed-point theory enables the analysis of the convergence rate via the contraction factor associated with the linear approximation of the fixed-point operator. While this factor characterizes the…
Reachability analysis is an important method in providing safety guarantees for systems with unknown or uncertain dynamics. Due to the computational intractability of exact reachability analysis for general nonlinear, high-dimensional…
Contrary to the sequential world, the processes involved in a distributed system do not necessarily know when a computation is globally finished. This paper investigates the problem of the detection of the termination of local computations.…
We consider the two categories of termination problems of quantum programs with nondeterminism: 1) Is an input of a program terminating with probability one under all schedulers? If not, how can a scheduler be synthesized to evidence the…
We develop a practical and novel method for inference on intersection bounds, namely bounds defined by either the infimum or supremum of a parametric or nonparametric function, or equivalently, the value of a linear programming problem with…
We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive…
We analyze a simple randomized subgradient method for approximating solutions to stochastic systems of convex functional constraints, the only input to the algorithm being the size of minibatches. By introducing a new notion of what is…
Since many real-world problems arising in the fields of compiler optimisation, automated software engineering, formal proof systems, and so forth are equivalent to the Halting Problem--the most notorious undecidable problem--there is a…
While any infimum in a poset can also be computed as a supremum, and vice versa, categorical limits and colimits do not always approximate each other. If I approach a point from below, and you approach it from above, then we will surely…
Decentralized optimization is well studied for smooth unconstrained problems. However, constrained problems or problems with composite terms are an open direction for research. We study structured (or composite) optimization problems, where…
We describe an approximate rational arithmetic with round-off errors (both absolute and relative) controlled by the user. The rounding procedure is based on the continued fraction expansion of real numbers. Results of computer experiments…
Typing of lambda-terms in Elementary and Light Affine Logic (EAL, LAL, resp.) has been studied for two different reasons: on the one hand the evaluation of typed terms using LAL (EAL, resp.) proof-nets admits a guaranteed polynomial…
Two information structures are said to be close if, with high probability, there is approximate common knowledge that interim beliefs are close under the two information structures. We define an "almost common knowledge topology" reflecting…