Related papers: A General Theory of Additive State Space Abstracti…
Distributed abstract programs are a novel class of distributed optimization problems where (i) the number of variables is much smaller than the number of constraints and (ii) each constraint is associated to a network node. Abstract…
Abstraction logic is a new logic, serving as a foundation of mathematics. It combines features of both predicate logic and higher-order logic: abstraction logic can be viewed both as higher-order logic minus static types as well as…
Finite abstractions (a.k.a. symbolic models) offer an effective scheme for approximating the complex continuous-space systems with simpler models in the discrete-space domain. A crucial aspect, however, is to establish a formal relation…
A symmetry of a dynamical system is a map that transforms one trajectory to another trajectory. We introduce a new type of abstraction for hybrid automata based on symmetries. The abstraction combines different modes in a concrete automaton…
In additive number theory, a finite set $A$ of integers is an $h$-basis for $n$ if every integer in $\{0,1,2,\ldots, n\}$ can be represented as the sum of exactly $h$ not necessarily distinct elements of $A$. This paper introduces a new…
This paper presents a novel set of algorithms for heap abstraction, identifying logically related regions of the heap. The targeted regions include objects that are part of the same component structure (recursive data structure). The result…
Strategy video games challenge AI agents with their combinatorial search space caused by complex game elements. State abstraction is a popular technique that reduces the state space complexity. However, current state abstraction methods for…
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…
In a model-based testing approach as well as for the verification of properties, B models provide an interesting solution. However, for industrial applications, the size of their state space often makes them hard to handle. To reduce the…
We introduce the notion of additive units, or `addits', of a pointed Arveson system, and demonstrate their usefulness through several applications. By a pointed Arveson system we mean a spatial Arveson system with a fixed normalised…
We study generalised additive models, with shape restrictions (e.g. monotonicity, convexity, concavity) imposed on each component of the additive prediction function. We show that this framework facilitates a nonparametric estimator of each…
We consider the problem of learning a $d$-variate function $f$ defined on the cube $[-1,1]^d\subset {\mathbb R}^d$, where the algorithm is assumed to have black box access to samples of $f$ within this domain. Denote ${\mathcal S}_r \subset…
Multi-valued networks provide a simple yet expressive qualitative state based modelling approach for biological systems. In this paper we develop an abstraction theory for asynchronous multi-valued network models that allows the state space…
The well-known problem of state space explosion in model checking is even more critical when applying this technique to programming languages, mainly due to the presence of complex data structures. One recent and promising approach to deal…
We present a methodology for formulating simplifying abstractions in machine learning systems by identifying and harnessing the utility structure of decisions. Machine learning tasks commonly involve high-dimensional output spaces (e.g.,…
Reasoning requires going beyond pattern matching or memorization of solutions to identify and implement "algorithmic procedures" that can be used to deduce answers to hard problems. Doing so requires realizing the most relevant primitives,…
Predicate abstraction is a key enabling technology for applying finite-state model checkers to programs written in mainstream languages. It has been used very successfully for debugging sequential system-level C code. Although model…
Multi-head finite-state dimensions and predimensions quantify the predictability of a sequence by a gambler with trailing heads acting as "probes to the past." These additional heads allow the gambler to exploit patterns that are simple but…
We construct compositional continuous approximations for an interconnection of infinitely many discrete-time switched systems. An approximation (known as abstraction) is itself a continuous-space system, which can be used as a replacement…
In this paper, we develop a framework for path-planning on abstractions that are not provided to the agent a priori but instead emerge as a function of the available computational resources. We show how a path-planning problem in an…