scholarly journals Bottom-Up derivatives of tree expressions

2021 ◽  
Vol 55 ◽  
pp. 4
Author(s):  
Samira Attou ◽  
Ludovic Mignot ◽  
Djelloul Ziadi
Keyword(s):  
Fixed Point ◽  
Tree Automaton ◽  
Bottom Up ◽  
Regular Tree ◽  
Partial Derivatives ◽  
New Family ◽  
Derivatives Of

In this paper, we extend the notion of (word) derivatives and partial derivatives due to (respectively) Brzozowski and Antimirov to tree derivatives using already known inductive formulae of quotients. We define a new family of extended regular tree expressions (using negation or intersection operators), and we show how to compute a Brzozowski-like inductive tree automaton; the fixed point of this construction, when it exists, is the derivative tree automaton. Such a deterministic tree automaton can be used to solve the membership test efficiently: the whole structure is not necessarily computed, and the derivative computations can be performed in parallel. We also show how to solve the membership test using our (Bottom-Up) partial derivatives, without computing an automaton.

Operational State Complexity of Subtree-Free Regular Tree Languages

2016 ◽  
Vol 27 (06) ◽  
pp. 705-724
Author(s):  
Sang-Ki Ko ◽  
Hae-Sung Eom ◽  
Yo-Sub Han
Keyword(s):  
The State ◽  
Tree Automaton ◽  
Top Down ◽  
Tree Language ◽  
Worst Case ◽  
Bottom Up ◽  
State Complexity ◽  
Regular Tree ◽  
Tree Languages

We introduce subtree-free regular tree languages that are closely related to XML schemas and investigate the state complexity of basic operations on subtree-free regular tree languages. The state complexity of an operation for regular tree languages is the number of states that are sufficient and necessary in the worst-case for the minimal deterministic ranked tree automaton that accepts the tree language obtained from the operation. We establish the precise state complexity of (sequential, parallel) concatenation, (bottom-up, top-down) star, intersection and union for subtree-free regular tree languages.

scholarly journals Solvability of fractional dynamic systems utilizing measure of noncompactness

2020 ◽  
Vol 25 (4) ◽  
Author(s):  
Hemant Kumar Nashine ◽  
Rabha W. Ibrahim ◽  
Reza Arab ◽  
Mohsen Rabbani
Keyword(s):  
Fixed Point ◽  
Dynamic Systems ◽  
Measure Of Noncompactness ◽  
Coupled Fixed Point ◽  
Sufficient Conditions ◽  
Time Interval ◽  
Fractional Dynamics ◽  
New Family ◽  
Growth System ◽  
Derivatives Of

Fractional dynamics is a scope of study in science considering the action of systems. These systems are designated by utilizing derivatives of arbitrary orders. In this effort, we discuss the sufficient conditions for the existence of the mild solution (m-solution) of a class of fractional dynamic systems (FDS). We deal with a new family of fractional m-solution in Rn for fractional dynamic systems. To accomplish it, we introduce first the concept of (F, ψ)-contraction based on the measure of noncompactness in some Banach spaces. Consequently, we establish requisite fixed point theorems (FPTs), which extend existing results following the Krasnoselskii FPT and coupled fixed point results as a outcomes of derived one. Finally, we give a numerical example to verify the considered FDS, and we solve it by iterative algorithm constructed by semianalytic method with high accuracy. The solution can be considered as bacterial growth system when the time interval is large. 

On Saint Venant’s Principle: Elastic Shells and Plates

1960 ◽  
Vol 27 (3) ◽  
pp. 417-422 ◽  
Author(s):  
P. M. Naghdi
Keyword(s):  
Fixed Point ◽  
Integral Formula ◽  
Middle Surface ◽  
The Other ◽  
Elastic Shells ◽  
Partial Derivatives ◽  
Other Hand ◽  
Derivatives Of ◽  
Surface Loads

This investigation is concerned with an examination of the validity of Saint Venant’s principle in the theory of thin elastic shells and plates. With the aid of an integral formula derived for the displacements and their relevant partial derivatives of all orders at a fixed point of the shell middle surface, the conclusions reached may be roughly stated as follows: If the loads acting on the shell maintained in equilibrium are purely edge loads, then the orders of magnitude of the displacements and stresses are in accord with the traditional statement of Saint Venant’s principle. On the other hand, if the loads on the shell are purely surface loads, then the conclusions concerning the orders of magnitude of the displacements and stresses are the same as those of the modified Saint Venant principle.

The Bottom-Up Position Tree Automaton and the Father Automaton

2020 ◽  
pp. 1-18
Author(s):  
Samira Attou ◽  
Ludovic Mignot ◽  
Djelloul Ziadi
Keyword(s):  
Tree Automaton ◽  
Tree Automata ◽  
Top Down ◽  
Bottom Up ◽  
Regular Tree ◽  
The One ◽  
Tree Expression

The conversion of a given regular tree expression into a tree automaton has been widely studied. However, classical interpretations are based upon a top-down interpretation of tree automata. In this paper, we propose new constructions based on Gluskov’s one and on the one by Ilie and Yu using a bottom-up interpretation. One of the main goals of this technique is to consider as a next step the links with deterministic recognizers, something which cannot be done with classical top-down approaches.

HYPER-MINIMIZATION FOR DETERMINISTIC TREE AUTOMATA

2013 ◽  
Vol 24 (06) ◽  
pp. 815-830 ◽  
Author(s):  
ARTUR JEŻ ◽  
ANDREAS MALETTI
Keyword(s):  
Finite Difference ◽  
Minimization Problem ◽  
Fast Algorithms ◽  
Input Tree ◽  
Tree Automaton ◽  
Tree Automata ◽  
Compression Technique ◽  
Bottom Up ◽  
Finite State ◽  
Transition Table

Hyper-minimization is a recent automaton compression technique that can reduce the size of an automaton beyond the limits imposed by classical minimization. The additional compression power is enabled by allowing a finite difference in the represented language. The necessary theory for hyper-minimization is developed for (bottom-up) deterministic tree automata. The hyper-minimization problem for deterministic tree automata is reduced to the hyper-minimization problem for deterministic finite-state string automata, for which fast algorithms exist. The fastest algorithm obtained in this way runs in time [Formula: see text], where m is the size of the transition table and n is the number of states of the input tree automaton.

Partial Derivatives of the Lambert Problem

2014 ◽  
Author(s):  
Nitin Arora ◽  
Ryan P. Russell ◽  
Nathan J. Strange
Keyword(s):  
Partial Derivatives ◽  
Lambert Problem ◽  
Derivatives Of

Perturbation theory and finite Markov chains

1968 ◽  
Vol 5 (2) ◽  
pp. 401-413 ◽  
Author(s):  
Paul J. Schweitzer
Keyword(s):  
Perturbation Theory ◽  
Markov Chain ◽  
Markov Chains ◽  
Stationary Distribution ◽  
Fundamental Matrix ◽  
Transition Probabilities ◽  
Semi Group ◽  
Partial Derivatives ◽  
Finite Markov Chains ◽  
Derivatives Of

A perturbation formalism is presented which shows how the stationary distribution and fundamental matrix of a Markov chain containing a single irreducible set of states change as the transition probabilities vary. Expressions are given for the partial derivatives of the stationary distribution and fundamental matrix with respect to the transition probabilities. Semi-group properties of the generators of transformations from one Markov chain to another are investigated. It is shown that a perturbation formalism exists in the multiple subchain case if and only if the change in the transition probabilities does not alter the number of, or intermix the various subchains. The formalism is presented when this condition is satisfied.

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