Related papers: Tropical Abstractions of Max-Plus-Linear Systems

In this paper we develop a combinatorial abstraction of tropical linear programming. This generalizes the search for a feasible point of a system of min-plus-inequalities. It is based on the polyhedral properties of triangulations of the…

This paper introduces the abstraction of max-plus linear (MPL) systems via predicates. Predicates are automatically selected from system matrix, as well as from the specifications under consideration. We focus on verifying time-difference…

Max-Plus Linear (MPL) systems are an algebraic formalism with practical applications in transportation networks, manufacturing and biological systems. In this paper, we investigate the problem of automatically analyzing the properties of…

This paper proposes a transition system abstraction framework for neural network dynamical system models to enhance the model interpretability, with applications to complex dynamical systems such as human behavior learning and verification.…

This paper proposes a new approach, grounded in Satisfiability Modulo Theories (SMT), to study the transient of a Max-Plus Linear (MPL) system, that is the number of steps leading to its periodic regime. Differently from state-of-the-art…

This paper investigates reachability analysis for max-plus linear systems (MPLS), an important class of dynamical systems that model synchronization and delay phenomena in timed discrete-event systems. We specifically focus on backward…

A generalization of the max-plus transformation, which is known as a method to derive cellular automata from integrable equations, is proposed for complex numbers. Operation rules for this transformation is also studied for general number…

In this paper, we propose an incremental abstraction method for dynamically over-approximating nonlinear systems in a bounded domain by solving a sequence of linear programs, resulting in a sequence of affine upper and lower hyperplanes…

This work discusses the reachability analysis (RA) of Max-Plus Linear (MPL) systems, a class of continuous-space, discrete-event models defined over the max-plus algebra. Given the initial and target sets, we develop algorithms to verify…

Abstraction is a powerful idea widely used in science, to model, reason and explain the behavior of systems in a more tractable search space, by omitting irrelevant details. While notions of abstraction have matured for deterministic…

This article introduces the novel framework of max-algebraic hybrid automata as a hybrid modelling language in the max-plus algebra. We show that the modelling framework unifies and extends the switching max-plus linear systems framework…

We define a formal framework for the study of algebras of type Max-plus, Min-Plus, tropical algebras, and more generally algebras over a commutative idempotent semi-field. This work is motivated by the increasingly diversified use of these…

Iterative abstraction refinement techniques are one of the most prominent paradigms for the analysis and verification of systems with large or infinite state spaces. This paper investigates the changes of truth values of system properties…

This paper introduces a new structure of commutative semiring, generalizing the tropical semiring, and having an arithmetic that modifies the standard tropical operations, i.e. summation and maximum. Although our framework is combinatorial,…

This paper proposes a method to compute finite abstractions that can be used for synthesizing robust hybrid control strategies for nonlinear systems. Most existing methods for computing finite abstractions utilize some global, analytical…

A common technique to verify complex logic specifications for dynamical systems is the construction of symbolic abstractions: simpler, finite-state models whose behaviour mimics the one of the systems of interest. Typically, abstractions…

Many methods for Model-based Reinforcement learning (MBRL) in Markov decision processes (MDPs) provide guarantees for both the accuracy of the model they can deliver and the learning efficiency. At the same time, state abstraction…

Partially Observable Markov Decision Process (POMDP) is widely used to model probabilistic behavior for complex systems. Compared with MDPs, POMDP models a system more accurate but solving a POMDP generally takes exponential time in the…

Analysis of Markov Decision Processes (MDP) is often hindered by state space explosion. Abstraction is a well-established technique in model checking to mitigate this issue. This paper presents a novel lazy abstraction method for MDP…

This paper proposes a tropical geometry-based edge detection framework that reformulates convolution and gradient computations using min-plus and max-plus algebra. The tropical formulation emphasizes dominant intensity variations,…