Related papers: Reachability analysis of first-order definable pus…
We propose a scalable method for forward stochastic reachability analysis for uncontrolled linear systems with affine disturbance. Our method uses Fourier transforms to efficiently compute the forward stochastic reach probability measure…
A shortcoming of existing reachability approaches for nonlinear systems is the poor scalability with the number of continuous state variables. To mitigate this problem we present a simulation-based approach where we first sample a number of…
Shape analysis concerns the problem of determining "shape invariants" for programs that perform destructive updating on dynamically allocated storage. In recent work, we have shown how shape analysis can be performed, using an abstract…
We develop a tractable identification approach for strategic network formation models with both strategic link interdependence and individual unobserved heterogeneity (fixed effects). The key challenge is that endogenous network statistics…
A deterministic finite automaton in which every non-empty set of states occurs as the image of the whole state set under the action of a suitable input word is called completely reachable. We characterize such automata in terms of graphs…
In this article we construct uncountably many new homogeneous locally finite Steiner triple systems of countably infinite order as Fra\"{\i}ss\'{e} limits of classes of finite Steiner triple systems avoiding certain subsystems. The…
There has been an increasing interest in using neural networks in closed-loop control systems to improve performance and reduce computational costs for on-line implementation. However, providing safety and stability guarantees for these…
Complex systems are difficult to study not only because they are nonlinear, multiscale, and often nonstationary, but because their scientifically relevant organization is often invisible at the level of individual components, pairwise…
We address the verification problem of ordered multi-pushdown automata: A multi-stack extension of pushdown automata that comes with a constraint on stack transitions such that a pop can only be performed on the first non-empty stack.…
We introduce structural heterogeneity, a new topological characteristic for semi-ordered materials that captures their degree of organisation at a mesoscopic level and tracks their time-evolution, ultimately detecting the order-disorder…
Although there is a somewhat standard formalization of computability on countable sets given by Turing machines, the same cannot be said about uncountable sets. Among the approaches to define computability in these sets, order-theoretic…
Vector Addition Systems with States (VASS), equivalent to Petri nets, are a well-established model of concurrency. The central algorithmic challenge in VASS is the reachability problem: is there a run from a given starting state and counter…
Suppose L = {<, . . .} is any countable first order language in which < is interpreted as a linear order. Let T be any complete first order theory in the language L such that T has a kappa-like model where kappa is an inaccessible cardinal.…
We deal with first-order definability in the embeddability ordering $( \mathcal{D}; \leq)$ of finite directed graphs. A directed graph $G\in \mathcal{D}$ is said to be embeddable into $G' \in \mathcal{D}$ if there exists an injective graph…
Time-invariant finite-dimensional systems, under reasonable continuity assumptions, exhibit the property that if solutions exist for all future times, the set of vectors reachable from a bounded set of initial conditions over bounded time…
Automatic structures are first-order structures whose universe and relations can be represented as regular languages. It follows from the standard closure properties of regular languages that the first-order theory of an automatic structure…
Efficient implementations of atomic objects such as concurrent stacks and queues are especially susceptible to programming errors, and necessitate automatic verification. Unfortunately their correctness criteria - linearizability with…
In a dynamic parametric process every subprocess may spawn arbitrarily many, identical child processes, that may communicate either over global variables, or over local variables that are shared with their parent. We show that reachability…
Sharpness is an almost generic assumption in continuous optimization that bounds the distance from minima by objective function suboptimality. It facilitates the acceleration of first-order methods through restarts. However, sharpness…
Temporal networks are a class of time-varying networks, which change their topology according to a given time-ordered sequence of static networks (known as subsystems). This paper investigates the reachability and controllability of…