Related papers: Tree Automata Acceptance up to Measurable Defect
We study the problem of how well a tree metric is able to preserve the sum of pairwise distances of an arbitrary metric. This problem is closely related to low-stretch metric embeddings and is interesting by its own flavor from the line of…
Given a tree $T=(V,E)$ on $n$ vertices, we consider the $(1 : q)$ Maker-Breaker tree embedding game ${\mathcal T}_n$. The board of this game is the edge set of the complete graph on $n$ vertices. Maker wins ${\mathcal T}_n$ if and only if…
We present relaxed notions of simulation and bisimulation on Probabilistic Automata (PA), that allow some error epsilon. When epsilon is zero we retrieve the usual notions of bisimulation and simulation on PAs. We give logical…
The probabilistic bisimilarity distance of Deng et al. has been proposed as a robust quantitative generalization of Segala and Lynch's probabilistic bisimilarity for probabilistic automata. In this paper, we present a characterization of…
Optimal transport provides a metric which quantifies the dissimilarity between probability measures. For measures supported in discrete metric spaces, finding the optimal transport distance has cubic time complexity in the size of the…
An automata network is a network of entities, each holding a state from a finite set and evolving according to a local update rule which depends only on its neighbors in the network's graph. It is freezing if there is an order on states…
We analyze the trade-off between model complexity and accuracy for random forests by breaking the trees up into individual classification rules and selecting a subset of them. We show experimentally that already a few rules are sufficient…
This work addresses the problem of computing measures of recognisable sets of infinite trees. An algorithm is provided to compute the probability measure of a tree language recognisable by a weak alternating automaton, or equivalently…
Recent advances in bandit tools and techniques for sequential learning are steadily enabling new applications and are promising the resolution of a range of challenging related problems. We study the game tree search problem, where the goal…
Recent advances in machine learning and artificial intelligence are now being considered in safety-critical autonomous systems where software defects may cause severe harm to humans and the environment. Design organizations in these domains…
This paper presents the first step of a wider research effort to apply tree automata completion to the static analysis of functional programs. Tree Automata Completion is a family of techniques for computing or approximating the set of…
An automaton is universal if it accepts every possible input. We study the notion of u-universality, which asserts that the automaton accepts every input starting with u. Universality and u-universality are both EXPTIME-hard for…
Decision trees are widely used for interpretable machine learning due to their clearly structured reasoning process. However, this structure belies a challenge we refer to as predictive equivalence: a given tree's decision boundary can be…
We consider simulation games played between Spoiler and Duplicator on two B\"uchi automata in which the choices made by Spoiler can be buffered by Duplicator in several buffers before she executes them on her structure. We show that the…
Automata admitting at most one accepting run per structure, known as unambiguous automata, find applications in verification of reactive systems as they extend the class of deterministic automata whilst maintaining some of their desirable…
We study a game for recognising formal languages, in which two players with imperfect information need to coordinate on a common decision, given private input words correlated by a finite graph. The players have a joint objective to avoid…
A tree $t$-spanner of a graph $G$ is a spanning tree of $G$ such that the distance between pairs of vertices in the tree is at most $t$ times their distance in $G$. Deciding tree $t$-spanner admissible graphs has been proved to be tractable…
The specification and validation of robotics applications require bridging the gap between formulating requirements and systematic testing. This often involves manual and error-prone tasks that become more complex as requirements, design,…
Algorithms for binary classification based on adaptive tree partitioning are formulated and analyzed for both their risk performance and their friendliness to numerical implementation. The algorithms can be viewed as generating a set…
Tree ensembles are non-parametric methods widely recognized for their accuracy and ability to capture complex interactions. While these models excel at prediction, they are difficult to interpret and may fail to uncover useful relationships…