Search results for "deterministic"

Causal Inference in Geoscience and Remote Sensing From Observational Data

2020

Establishing causal relations between random variables from observational data is perhaps the most important challenge in today’s science. In remote sensing and geosciences, this is of special relevance to better understand the earth’s system and the complex interactions between the governing processes. In this paper, we focus on an observational causal inference, and thus, we try to estimate the correct direction of causation using a finite set of empirical data. In addition, we focus on the more complex bivariate scenario that requires strong assumptions and no conditional independence tests can be used. In particular, we explore the framework of (nondeterministic) additive noise models, …

Special factors and the combinatorics of suffix and factor automata

2011

AbstractThe suffix automaton (resp. factor automaton) of a finite word w is the minimal deterministic automaton recognizing the set of suffixes (resp. factors) of w. We study the relationships between the structure of the suffix and factor automata and classical combinatorial parameters related to the special factors of w. We derive formulae for the number of states of these automata. We also characterize the languages LSA and LFA of words having respectively suffix automaton and factor automaton with the minimal possible number of states.

Unary Probabilistic and Quantum Automata on Promise Problems

2015

We continue the systematic investigation of probabilistic and quantum finite automata (PFAs and QFAs) on promise problems by focusing on unary languages. We show that bounded-error QFAs are more powerful than PFAs. But, in contrary to the binary problems, the computational powers of Las-Vegas QFAs and bounded-error PFAs are equivalent to deterministic finite automata (DFAs). Lastly, we present a new family of unary promise problems with two parameters such that when fixing one parameter QFAs can be exponentially more succinct than PFAs and when fixing the other parameter PFAs can be exponentially more succinct than DFAs.

Rough linear PDE's with discontinuous coefficients - existence of solutions via regularization by fractional Brownian motion

2020

We consider two related linear PDE's perturbed by a fractional Brownian motion. We allow the drift to be discontinuous, in which case the corresponding deterministic equation is ill-posed. However, the noise will be shown to have a regularizing effect on the equations in the sense that we can prove existence of solutions for almost all paths of the fractional Brownian motion.

Quantitative ergodicity for some switched dynamical systems

2012

International audience; We provide quantitative bounds for the long time behavior of a class of Piecewise Deterministic Markov Processes with state space Rd × E where E is a finite set. The continuous component evolves according to a smooth vector field that switches at the jump times of the discrete coordinate. The jump rates may depend on the whole position of the process. Under regularity assumptions on the jump rates and stability conditions for the vector fields we provide explicit exponential upper bounds for the convergence to equilibrium in terms of Wasserstein distances. As an example, we obtain convergence results for a stochastic version of the Morris-Lecar model of neurobiology.

Probabilistic versus deterministic memory limited learning

1995

Quantum Computers and Quantum Automata

2000

Quantum computation is a most challenging project involving research both by physicists and computer scientists. The principles of quantum computation differ from the principles of classical computation very much. When quantum computers become available, the public-key cryptography will change radically. It is no exaggeration to assert that building a quantum computer means building a universal code-breaking machine. Quantum finite automata are expected to appear much sooner. They do not generalize deterministic finite automata. Their capabilities are incomparable.

Descriptional and Computational Complexity of the Circuit Representation of Finite Automata

2018

In this paper we continue to investigate the complexity of the circuit representation of DFA—BC-complexity. We compare it with nondeterministic state complexity, obtain upper and lower bounds which differ only by a factor of 4 for a Binary input alphabet. Also we prove that many simple operations (determining if a state is reachable or if an automaton is minimal) are PSPACE-complete for DFA given in circuit representation.

An Approximate Determinization Algorithm for Weighted Finite-State Automata

2001

Nondeterministic weighted finite-state automata are a key abstraction in automatic speech recognition systems. The efficiency of automatic speech recognition depends directly on the sizes of these automata and the degree of nondeterminism present, so recent research has studied ways to determinize and minimize them, using analogues of classical automata determinization and minimization. Although, as we describe here, determinization can in the worst case cause poly-exponential blowup in the number of states of a weighted finite-state automaton, in practice it is remarkably successful. In extensive experiments in automatic speech recognition systems, deterministic weighted finite-state autom…

Quantum versus Probabilistic One-Way Finite Automata with Counter

2001

The paper adds the one-counter one-way finite automaton [6] to the list of classical computing devices having quantum counterparts more powerful in some cases. Specifically, two languages are considered, the first is not recognizable by deterministic one-counter one-way finite automata, the second is not recognizable with bounded error by probabilistic one-counter one-way finite automata, but each recognizable with bounded error by a quantum one-counter one-way finite automaton. This result contrasts the case of one-way finite automata without counter, where it is known [5] that the quantum device is actually less powerful than its classical counterpart.