Search results for "Computer Science::Artificial Intelligence"
showing 10 items of 15 documents
Vagueness and Roughness
2008
The paper proposes a new formal approach to vagueness and vague sets taking inspirations from Pawlak's rough set theory. Following a brief introduction to the problem of vagueness, an approach to conceptualization and representation of vague knowledge is presented from a number of different perspectives: those of logic, set theory, algebra, and computer science. The central notion of the vague set, in relation to the rough set, is defined as a family of sets approximated by the so called lower and upper limits. The family is simultaneously considered as a family of all denotations of sharp terms representing a suitable vague term, from the agent's point of view. Some algebraic operations on…
Modeling Snow Dynamics Using a Bayesian Network
2015
In this paper we propose a novel snow accumulation and melt model, formulated as a Dynamic Bayesian Network DBN. We encode uncertainty explicitly and train the DBN using Monte Carlo analysis, carried out with a deterministic hydrology model under a wide range of plausible parameter configurations. The trained DBN was tested against field observations of snow water equivalents SWE. The results indicate that our DBN can be used to reason about uncertainty, without doing resampling from the deterministic model. In all brevity, the DBN's ability to reproduce the mean of the observations was similar to what could be obtained with the deterministic hydrology model, but with a more realistic repre…
Reordering Method and Hierarchies for Quantum and Classical Ordered Binary Decision Diagrams
2017
We consider Quantum OBDD model. It is restricted version of read-once Quantum Branching Programs, with respect to “width” complexity. It is known that maximal complexity gap between deterministic and quantum model is exponential. But there are few examples of such functions. We present method (called “reordering”), which allows to build Boolean function g from Boolean Function f, such that if for f we have gap between quantum and deterministic OBDD complexity for natural order of variables, then we have almost the same gap for function g, but for any order. Using it we construct the total function REQ which deterministic OBDD complexity is \(2^{\varOmega (n/log n)}\) and present quantum OBD…
Very Narrow Quantum OBDDs and Width Hierarchies for Classical OBDDs
2014
In the paper we investigate a model for computing of Boolean functions – Ordered Binary Decision Diagrams (OBDDs), which is a restricted version of Branching Programs. We present several results on the comparative complexity for several variants of OBDD models. We present some results on the comparative complexity of classical and quantum OBDDs. We consider a partial function depending on a parameter k such that for any k > 0 this function is computed by an exact quantum OBDD of width 2, but any classical OBDD (deterministic or stable bounded-error probabilistic) needs width 2 k + 1. We consider quantum and classical nondeterminism. We show that quantum nondeterminism can be more efficient …
Error-Free Affine, Unitary, and Probabilistic OBDDs
2018
We introduce the affine OBDD model and show that zero-error affine OBDDs can be exponentially narrower than bounded-error unitary and probabilistic OBDDs on certain problems. Moreover, we show that Las Vegas unitary and probabilistic OBDDs can be quadratically narrower than deterministic OBDDs. We also obtain the same results for the automata versions of these models.
Error-Free Affine, Unitary, and Probabilistic OBDDs
2021
We introduce the affine OBDD model and show that zero-error affine OBDDs can be exponentially narrower than bounded-error unitary and probabilistic OBDDs on certain problems. Moreover, we show that Las-Vegas unitary and probabilistic OBDDs can be quadratically narrower than deterministic OBDDs. We also obtain the same results for the automata counterparts of these models.
Transitive Reasoning with Imprecise Probabilities
2015
We study probabilistically informative (weak) versions of transitivity by using suitable definitions of defaults and negated defaults in the setting of coherence and imprecise probabilities. We represent \(\text{ p-consistent }\) sequences of defaults and/or negated defaults by g-coherent imprecise probability assessments on the respective sequences of conditional events. Finally, we present the coherent probability propagation rules for Weak Transitivity and the validity of selected inference patterns by proving p-entailment of the associated knowledge bases.
Zero-Error Affine, Unitary, and Probabilistic OBDDs
2017
We introduce the affine OBDD model and show that zero-error affine OBDDs can be exponentially narrower than bounded-error unitary and probabilistic OBDDs on certain problems. Moreover, we show that Las Vegas unitary and probabilistic OBDDs can be quadratically narrower than deterministic OBDDs. We also obtain the same results by considering the automata versions of these models.
Reordering Method and Hierarchies for Quantum and Classical Ordered Binary Decision Diagrams
2017
We consider Quantum OBDD model. It is restricted version of read-once Quantum Branching Programs, with respect to "width" complexity. It is known that maximal complexity gap between deterministic and quantum model is exponential. But there are few examples of such functions. We present method (called "reordering"), which allows to build Boolean function $g$ from Boolean Function $f$, such that if for $f$ we have gap between quantum and deterministic OBDD complexity for natural order of variables, then we have almost the same gap for function $g$, but for any order. Using it we construct the total function $REQ$ which deterministic OBDD complexity is $2^{\Omega(n/\log n)}$ and present quantu…
Transitive reasoning with imprecise probabilities
2015
We study probabilistically informative (weak) versions of transitivity, by using suitable definitions of defaults and negated defaults, in the setting of coherence and imprecise probabilities. We represent p-consistent sequences of defaults and/or negated defaults by g-coherent imprecise probability assessments on the respective sequences of conditional events. Finally, we prove the coherent probability propagation rules for Weak Transitivity and the validity of selected inference patterns by proving the p-entailment for the associated knowledge bases.