Related papers: Sapo: Reachability Computation and Parameter Synth…
Modal synthesis is an important area of physical modeling whose exploration in the past has been held back by a large number of control parameters, the scarcity of general-purpose design tools and the difficulty of obtaining the…
State-Space Models (SSMs) have re-emerged as a powerful tool for online function approximation, and as the backbone of machine learning models for long-range dependent data. However, to date, only a few polynomial bases have been explored…
We address the safety verification and synthesis problems for real-time systems. We introduce real-time programs that are made of instructions that can perform assignments to discrete and real-valued variables. They are general enough to…
We consider the problem of symbolic reachability analysis of higher-order context-free processes. These models are generalizations of the context-free processes (also called BPA processes) where each process manipulates a data structure…
A robust-to-dynamics optimization (RDO) problem is an optimization problem specified by two pieces of input: (i) a mathematical program (an objective function $f:\mathbb{R}^n\rightarrow\mathbb{R}$ and a feasible set…
To verify the correct operation of systems, engineers need to determine the set of configurations of a dynamical model that are able to safely reach a specified configuration under a control law. Unfortunately, constructing models for…
Computing tight over-approximation of reach sets of a controlled uncertain dynamical system is a common practice in verification of safety-critical cyber-physical systems (CPS). While several algorithms are available for this purpose, they…
An important mathematical tool in the analysis of dynamical systems is the approximation of the reach set, i.e., the set of states reachable after a given time from a given initial state. This set is difficult to compute for complex systems…
Sofic shifts are symbolic dynamical systems defined by the set of bi-infinite sequences on an edge-labeled directed graph, called a presentation. We study the computational complexity of an array of natural decision problems about…
Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct randomized algorithm for solving large, weakly constrained SDP…
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…
The current landscape of scientific research is widely based on modeling and simulation, typically with complexity in the simulation's flow of execution and parameterization properties. Execution flows are not necessarily straightforward…
We study the convex hulls of reachable sets of nonlinear systems with bounded disturbances and uncertain initial conditions. Reachable sets play a critical role in control, but remain notoriously challenging to compute, and existing…
The problem of computing the reachable set for a given system is a quintessential question in nonlinear control theory. While previous work has yielded a plethora of approximate and analytical methods for determining such a set, these…
PAWS is a tool to analyse the behaviour of weighted automata and conditional transition systems. At its core PAWS is based on a generic implementation of algorithms for checking language equivalence in weighted automata and bisimulation in…
Sum-of-squares (SOS) methods have been shown to be very useful in computing polynomial Lyapunov functions for systems of reasonably small size. However for large scale systems it is necessary to use a scalable alternative using vector…
In this paper, we present a new, graph-based modeling approach and a polynomial-sized linear programming (LP) formulation of the Boolean satisfiability problem (SAT). The approach is illustrated with a numerical example.
This paper presents a method to determine the reachable set (RS) of spacecraft after a single velocity impulse with an arbitrary direction, which is appropriate for the RS in both the state and observation spaces under arbitrary dynamics,…
Constraint satisfaction problem (CSP) has been actively used for modeling and solving a wide range of complex real-world problems. However, it has been proven that developing efficient methods for solving CSP, especially for large problems,…
A constraint satisfaction problem (CSP) is a computational problem where the input consists of a finite set of variables and a finite set of constraints, and where the task is to decide whether there exists a satisfying assignment of values…