相关论文: Pushdown dimension

In this paper we develop a method for investigating semi-device-independent randomness expansion protocols that was introduced in [Li et al., Phys. Rev. A $\mathbf{87}$, 020302(R) (2013)]. This method allows to lower-bound, with…

Automata operating on strings of nested brackets, known as input-driven pushdown automata, and as visibly pushdown automata, have been studied since the 1980s. They were extended to the case of infinite strings by Alur and Madhusudan…

In this paper we introduce a new formulation of Bennett's logical depth based on pebble transducers. This notion is defined based on the difference between the minimal length descriptional complexity of prefixes of infinite sequences from…

In this paper we prove some lower bounds on the Hausdorff dimension of sets of Furstenberg type. Moreover, we extend these results to sets of generalized Furstenberg type, associated to doubling dimension functions. With some additional…

Input-driven pushdown automata (also known as visibly pushdown automata and as nested word automata) are a subclass of deterministic pushdown automata and a superclass of the parenthesis languages. Nguyen and Ogawa ("Event-clock visibly…

The Turing machine models an old-fashioned computer, that does not interact with the user or with other computers, and only does batch processing. Therefore, we came up with a Reactive Turing Machine that does not have these shortcomings.…

We consider the question of how large a subspace of a given bipartite quantum system can be when the subspace contains only highly entangled states. This is motivated in part by results of Hayden et al., which show that in large d x…

This paper introduces two mechanisms for computing over-approximations of sets of reachable states, with the aim of ensuring termination of state-space exploration. The first mechanism consists in over-approximating the automata…

We provide a formal, simple and intuitive theory of rational decision making including sequential decisions that affect the environment. The theory has a geometric flavor, which makes the arguments easy to visualize and understand. Our…

Dynamical systems on networks are inherently high-dimensional unless the number of nodes is extremely small. Dimension reduction methods for dynamical systems on networks aim to find a substantially lower-dimensional system that preserves…

We show that the minimization of visibly pushdown automata is NP-complete. This result is obtained by introducing immersions, that recognize multiple languages (over a usual, non-visible alphabet) using a common deterministic transition…

Hyper-minimization is a state reduction technique that allows a finite change in the semantics. The theory for hyper-minimization of deterministic weighted tree automata is provided. The presence of weights slightly complicates the…

Finite version of Random Domino Automaton (FRDA) - recently proposed a toy model of earthquakes - is investigated. Respective set of equations describing stationary state of the FRDA is derived and compared with infinite case. It is shown…

We consider a linear runs and tumbles equation in dimension d $\ge$ 1 for which we establish the existence of a unique positive and normalized steady state as well as its asymptotic stability, improving similar results obtained by Calvez et…

Notions of (pointwise) tangential dimension are considered, for measures of R^n. Under regularity conditions (volume doubling), the upper resp. lower dimension at a point x of a measure can be defined as the supremum, resp. infimum, of…

We study approachability theory in the presence of constraints. Given a repeated game with vector payoffs, we characterize the pairs of sets (A,D) in the payoff space such that Player 1 can guarantee that the long-run average payoff…

We use branes to generalize the Distance Conjecture. We conjecture that in any infinite-distance limit in the moduli space of a $d$-dimensional quantum gravity theory, among the set of particle towers and fundamental branes with at most…

The notion of a normal bit sequence was introduced by Borel in 1909; it was the first definition of an individual random object. Normality is a weak notion of randomness requiring only that all $2^n$ factors (substrings) of arbitrary…

We ask how quantum theory compares to more general physical theories from the point of view of dimension. To do so, we first give two model independent definition of the dimension of physical systems, based on measurements and on the…

We construct a hierarchy of regular languages such that the current language in the hierarchy can be accepted by 1-way quantum finite automata with a probability smaller than the corresponding probability for the preceding language in the…