Related papers: Abstractions of Sequences, Functions and Operators
The intention of the present study is to establish the mathematical fundamentals for automated problem solving essentially targeted for robotics by approaching the task universal algebraically introducing knowledge as realizations of…
Automated synthesis of reactive control protocols from temporal logic specifications has recently attracted considerable attention in various applications in, for example, robotic motion planning, network management, and hardware design. An…
ion is one of the most promising approaches to improve the performance of problem solvers. In several domains abstraction by dropping sentences of a domain description -- as used in most hierarchical planners -- has proven useful. In this…
The complexity of large-scale distributed systems, particularly when deployed in physical space, calls for new mechanisms to address composability and reusability of collective adaptive behaviour. Computational fields have been proposed as…
In David Schmidt's PhD work he explored the use of denotational semantics as a programming language. It was part of an effort to not only treat formal semantics as specifications but also as interpreters and input to compiler generators.…
The inference and the verification of numerical relationships among variables of a program is one of the main goals of static analysis. In this paper, we propose an Abstract Interpretation framework based on higher-dimensional ellipsoids to…
Concept lattices are well-known conceptual structures that organise interesting patterns-the concepts-extracted from data. In some applications, such as software engineering or data mining, the size of the lattice can be a problem, as it is…
This paper describes a new abstract interpretation-based approach to verify temporal safety properties of recursive, higher-order programs. While prior works have provided theoretical impact and some automation, they have had limited…
Multiple types can represent the same concept. For example, lists and trees can both represent sets. Unfortunately, this easily leads to incomplete libraries: some set-operations may only be available on lists, others only on trees.…
This article presents the systematic design of a class of relational numerical abstract domains from non-relational ones. Constructed domains represent sets of invariants of the form (vj - vi in C), where vj and vi are two variables, and C…
The modelling of discrete regulatory networks combines a graph specifying the pairwise influences between the variables of the system, and a parametrisation from which can be derived a discrete transition system. Given the influence graph…
Many example-guided program synthesis techniques use abstractions to prune the search space. While abstraction-based synthesis has proven to be very powerful, a domain expert needs to provide a suitable abstract domain, together with the…
Recent work by Hermanns et al. and Kattenbelt et al. has extended counterexample-guided abstraction refinement (CEGAR) to probabilistic programs. These approaches are limited to predicate abstraction. We present a novel technique, based on…
In this article we discuss how abstraction boundaries can help tame complexity in mathematical research, with the help of an interactive theorem prover. While many of the ideas we present here have been used implicitly by mathematicians for…
Designing controllers to satisfy temporal requirements has proven to be challenging for dynamical systems that are affected by uncertainty. This is mainly due to the states evolving in a continuous uncountable space, the stochastic…
Limit computable functions can be characterized by Turing jumps on the input side or limits on the output side. As a monad of this pair of adjoint operations we obtain a problem that characterizes the low functions and dually to this…
The theory of fractional calculus in the complex plane was not built with a specific application in mind. The main obstacle to application was the difficulty with obtaining analytic continuations of fractional derivatives and integrals. It…
The practical impact of abstraction-based controller synthesis methods is currently limited by the immense computational effort for obtaining abstractions. In this note we focus on a recently proposed method to compute abstractions whose…
Finite-state abstractions (a.k.a. symbolic models) present a promising avenue for the formal verification and synthesis of controllers in continuous-space control systems. These abstractions provide simplified models that capture the…
With the increasing ubiquity of safety-critical autonomous systems operating in uncertain environments, there is a need for mathematical methods for formal verification of stochastic models. Towards formally verifying properties of…