Related papers: Divide-and-Conquer Determinization of B\"uchi Auto…
We observe that the classical Cartesian product construction for the intersection of (languages of) nondeterministic finite automata (NFA) is non-optimal in the worst case, if the automata have many transitions. For a fixed alphabet, the…
Uncertainties arising from localization error, trajectory prediction errors of the moving obstacles and environmental disturbances pose significant challenges to robot's safe navigation. Existing uncertainty-aware planners often approximate…
This paper gives a concise introduction into the basic theory of {\omega}-automata (as of March 2014). The starting point are the different types of recurrence conditions, modes of operation (deterministic, nondeterministic, alternating…
Given a matrix U, using a deterministic method, we extract a "large" submatrix of U'(whose columns are obtained by normalizing those of U) and estimate its smallest and largest singular value. We apply this result to the study of contact…
An automaton is history-deterministic if its nondeterminism can be resolved on the fly, only using the prefix of the word read so far. This mild form of nondeterminism has attracted particular attention for its applications in synthesis…
We introduce improvements in the algorithm by Gastin and Oddoux translating LTL formulae into B\"uchi automata via very weak alternating co-B\"uchi automata and generalized B\"uchi automata. Several improvements are based on specific…
We study the accuracy of the divide-and-conquer method for electronic structure calculations. The analysis is conducted for a prototypical subdomain problem in the method. We prove that the pointwise difference between electron densities of…
The RPNI algorithm (Oncina, Garcia 1992) constructs deterministic finite automata from finite sets of negative and positive example words. We propose and analyze an extension of this algorithm to deterministic $\omega$-automata with…
Distributed algorithms and theories are called for in this era of big data. Under weaker local signal-to-noise ratios, we improve upon the celebrated one-round distributed principal component analysis (PCA) algorithm designed in the spirit…
Br\"uggemann-Klein and Wood define a one-unambiguous regular language as a language that can be recognized by a deterministic Glushkov automaton. They give a procedure performed on the minimal DFA, the BW-test, to decide whether a language…
While the surjectivity of the global map in two-dimensional cellular automata (2D CA) is undecidable in general, in specific cases one can often decide if the rule is surjective or not. We attempt to classify as many 2D CA as possible by…
Conformal prediction offers a distribution-free framework for constructing prediction sets with finite-sample coverage. Yet, efficiently leveraging multiple conformity scores to reduce prediction set size remains a major open challenge.…
We introduce deterministic suffix-reading automata (DSA), a new automaton model over finite words. Transitions in a DSA are labeled with words. From a state, a DSA triggers an outgoing transition on seeing a word ending with the…
Large-scale optimization problems that involve thousands of decision variables have extensively arisen from various industrial areas. As a powerful optimization tool for many real-world applications, evolutionary algorithms (EAs) fail to…
We propose $\omega$MSO$\Join$BAPA, an expressive logic for describing countable structures, which subsumes and transcends both Counting Monadic Second-Order Logic (CMSO) and Boolean Algebra with Presburger Arithmetic (BAPA). We show that…
Methods for split conformal prediction leverage calibration samples to transform any prediction rule into a set-prediction rule that complies with a target coverage probability. Existing methods provide remarkably strong performance…
We show that it is decidable whether two regular languages of infinite trees are separable by a deterministic language, resp., a game language. We consider two variants of separability, depending on whether the set of priorities of the…
Uncertainty quantification is crucial for building reliable and trustable machine learning systems. We propose to estimate uncertainty in recurrent neural networks (RNNs) via stochastic discrete state transitions over recurrent timesteps.…
In this paper, we present several new results on minimizing a nonsmooth and nonconvex function under a Lipschitz condition. Recent work shows that while the classical notion of Clarke stationarity is computationally intractable up to some…
Low-rank tensor decompositions (TDs) provide an effective framework for multiway data analysis. Traditional TD methods rely on predefined structural assumptions, such as CP or Tucker decompositions. From a probabilistic perspective, these…