Search results for " minimization"
showing 10 items of 107 documents
Ab initiosimulations on rutile-based titania nanowires
2012
The rod symmetry groups for monoperiodic (1D) nanostructures have been applied for construction of models for bulk-like TiO2 nanowires (NWs) cut from a rutile-based 3D crystal along the chosen [001] and [110] directions of crystallographic axes. In this study, we have considered nanowires described by both the Ti-atom centered rotation axes as well as the hollow site centered axes passing through the interstitial positions between the Ti and O atoms closest to the axes. The most stable [001]-oriented TiO2 NWs with rhombic cross sections are found to display the energetically preferable {110} facets only while the nanowires with quasi-square sections across the [110] axis are formed by the a…
[MoO2(SCPh2CO2)2]2− and [MoO(SCPh2CO2)2]− anion complexes. A theoretical structure characterization
1995
Abstract Geometry optimization of [MoO 2 (SCH 2 CO 2 ) 2 ] 2− and [MoO(SCH 2 CO 2 ) 2 ] − systems as models of [MoO 2 (SCPh 2 CO 2 ) 2 ] 2− and [MoO(SCPh 2 CO 2 ) 2 ] − anion complexes have been carried out at STO-3G, 3-21G, LANL1MB and LANL2DZ basis set levels. A comparison of the theoretical results and X-ray experimental data has been performed. STO-3G minimal basis set produces the best geometrical agreement, in particular the distances and orientations of the different ligands linked to molybdenum transition metal. A large structural overlap with STO-3G optimized geometry and X-ray data has been found for the [MoO 2 (SCPh 2 CO 2 ) 2 ] 2− and [MoO(SCPh 2 CO 2 ) 2 ] − anion complexes.
Theoretical study on hydration of two particular diazanaphthalenes
2005
Abstract Cinnoline (1) and Phthalazine (2), diazanaphthalenes involved in certain biological reactions, have been studied computational with the purpose of comparing their protonation and covalent hydration mechanisms. Geometry optimizations of neutral, mono- and di-protonated cations and hydrated products were performed at HF, DFT/B3LYP levels of theory using 6-311G* basis set and single points energies were calculated at the MP2 level of theory using the same basis set. In agreement with experimental results, calculations predict a two-step mechanism resulting in a hydrated cation in which the OH of the water is located depending on the position of both nitrogen in the diazanaphthalene mo…
Epichristoffel Words and Minimization of Moore Automata
2014
This paper is focused on the connection between the combinatorics of words and minimization of automata. The three main ingredients are the epichristoffel words, Moore automata and a variant of Hopcroft's algorithm for their minimization. Epichristoffel words defined in [14] generalize some properties of circular sturmian words. Here we prove a factorization property and the existence of the reduction tree, that uniquely identifies the structure of the word. Furthermore, in the paper we investigate the problem of the minimization of Moore automata by defining a variant of Hopcroft's minimization algorithm. The use of this variant makes simpler the computation of the running time and consequ…
Transition Function Complexity of Finite Automata
2011
State complexity of finite automata in some cases gives the same complexity value for automata which intuitively seem to have completely different complexities. In this paper we consider a new measure of descriptional complexity of finite automata -- BC-complexity. Comparison of it with the state complexity is carried out here as well as some interesting minimization properties are discussed. It is shown that minimization of the number of states can lead to a superpolynomial increase of BC-complexity.
The Complexity of Probabilistic versus Quantum Finite Automata
2002
We present a language Ln which is recognizable by a probabilistic finite automaton (PFA) with probability 1 - ? for all ? > 0 with O(log2 n) states, with a deterministic finite automaton (DFA) with O(n) states, but a quantum finite automaton (QFA) needs at least 2?(n/log n) states.
Non-constructive Methods for Finite Probabilistic Automata
2007
Size (the number of states) of finite probabilistic automata with an isolated cut-point can be exponentially smaller than the size of any equivalent finite deterministic automaton. The result is presented in two versions. The first version depends on Artin's Conjecture (1927) in Number Theory. The second version does not depend on conjectures but the numerical estimates are worse. In both versions the method of the proof does not allow an explicit description of the languages used. Since our finite probabilistic automata are reversible, these results imply a similar result for quantum finite automata.
NON-CONSTRUCTIVE METHODS FOR FINITE PROBABILISTIC AUTOMATA
2008
Size (the number of states) of finite probabilistic automata with an isolated cut-point can be exponentially smaller than the size of any equivalent finite deterministic automaton. However, the proof is non-constructive. The result is presented in two versions. The first version depends on Artin's Conjecture (1927) in Number Theory. The second version does not depend on conjectures not proved but the numerical estimates are worse. In both versions the method of the proof does not allow an explicit description of the languages used. Since our finite probabilistic automata are reversible, these results imply a similar result for quantum finite automata.
On extremal cases of Hopcroft’s algorithm
2010
AbstractIn this paper we consider the problem of minimization of deterministic finite automata (DFA) with reference to Hopcroft’s algorithm. Hopcroft’s algorithm has several degrees of freedom, so there can exist different executions that can lead to different sequences of refinements of the set of the states up to the final partition. We find an infinite family of binary automata for which such a process is unique, whatever strategy is chosen. Some recent papers (cf. Berstel and Carton (2004) [3], Castiglione et al. (2008) [6] and Berstel et al. (2009) [1]) have been devoted to find families of automata for which Hopcroft’s algorithm has its worst execution time. They are unary automata as…
Artin’s Conjecture and Size of Finite Probabilistic Automata
2008
Size (the number of states) of finite probabilistic automata with an isolated cut-point can be exponentially smaller than the size of any equivalent finite deterministic automaton. The result is presented in two versions. The first version depends on Artin's Conjecture (1927) in Number Theory. The second version does not depend on conjectures but the numerical estimates are worse. In both versions the method of the proof does not allow an explicit description of the languages used. Since our finite probabilistic automata are reversible, these results imply a similar result for quantum finite automata.