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Abstract separation systems are a new unifying framework in which separations of graph, matroids and other combinatorial structures can be expressed and studied. We characterize the abstract separation systems that have representations as…
The vertices of a finite state system are usually a subset of the natural numbers. Most algorithms relative to these systems only use this fact to select vertices. For infinite state systems, however, the situation is different: in…
Abstract separation systems provide a simple general framework in which both tree-shape and high cohesion of many combinatorial structures can be expressed, and their duality proved. Applications range from tangle-type duality and tree…
Refinement transforms an abstract system model into a concrete, executable program, such that properties established for the abstract model carry over to the concrete implementation. Refinement has been used successfully in the development…
Neural network controllers are currently being proposed for use in many safety-critical tasks. Most analysis methods for neural network control systems assume a fixed control period. In control theory, higher frequency usually improves…
We present abstraction techniques that transform a given non-linear dynamical system into a linear system or an algebraic system described by polynomials of bounded degree, such that, invariant properties of the resulting abstraction can be…
Chain-of-thought (CoT) significantly enhances the performance of large language models (LLMs) across a wide range of tasks, and prior research shows that CoT can theoretically increase expressiveness. However, there is limited mechanistic…
We introduce a new framework for verifying systems with a parametric number of concurrently running processes. The systems we consider are well-structured with respect to a specific well-quasi order. This allows us to decide a wide range of…
We investigate unitary and state $t$-designs from a computational complexity perspective. First, we address the problems of computing frame potentials that characterize (approximate) $t$-designs. We present a quantum algorithm for computing…
Automated Theorem Proving (ATP) is an established branch of Artificial Intelligence. The purpose of ATP is to design a system which can automatically figure out an algorithm either to prove or disprove a mathematical claim, on the basis of…
The growing size of graph-based modeling artifacts in model-driven engineering calls for techniques that enable efficient execution of graph queries. Incremental approaches based on the RETE algorithm provide an adequate solution in many…
GraphFlow is a visual workflow system designed to improve the reliability of agentic AI automation in multi-step, mission-critical processes. In these workflows, small errors compound rapidly: under an idealized model of independent steps,…
Linear Time Invariant (LTI) systems are ubiquitous in control applications. Unbounded-time reachability analysis that can cope with industrial-scale models with thousands of variables is needed. To tackle this problem, we use abstract…
One of the challenges facing artificial intelligence research today is designing systems capable of utilizing systematic reasoning to generalize to new tasks. The Abstraction and Reasoning Corpus (ARC) measures such a capability through a…
We build on a fine-grained analysis of session-based interaction as provided by the linear logic typing disciplines to introduce the SAM, an abstract machine for mechanically executing session-typed processes. A remarkable feature of the…
interpretation is a general methodology for building static analyses of programs. It was introduced by P. and R. Cousot in \cite{cc}. We present, in this paper, an application of a generic abstract interpretation to domain of…
State aggregation is a popular model reduction method rooted in optimal control. It reduces the complexity of engineering systems by mapping the system's states into a small number of meta-states. The choice of aggregation map often depends…
Mechanistic interpretability aims to reverse engineer neural networks by uncovering which high-level algorithms they implement. Causal abstraction provides a precise notion of when a network implements an algorithm, i.e., a causal model of…
Computing the probability of reaching a set of goal states G in a discrete-time Markov chain (DTMC) is a core task of probabilistic model checking. We can do so by directly computing the probability mass of the set of all finite paths from…
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…