EXACT GENERATION OF MINIMAL ACYCLIC DETERMINISTIC FINITE AUTOMATA

2008 ◽  
Vol 19 (04) ◽  
pp. 751-765 ◽  
Author(s):  
MARCO ALMEIDA ◽  
NELMA MOREIRA ◽  
ROGÉRIO REIS
Keyword(s):  
Normal Form ◽  
Lower Bounds ◽  
Finite Automata ◽  
Canonical Representation ◽  
Upper And Lower Bounds ◽  
Generation Algorithm ◽  
Deterministic Finite Automata

We give a canonical representation for minimal acyclic deterministic finite automata (MADFA) with n states over an alphabet of k symbols. Using this normal form, we present a method for the exact generation of MADFAs. This method avoids a rejection phase that would be needed if a generation algorithm for a larger class of objects that contains the MADFAs were used. We give upper and lower bounds for MADFAs enumeration and some exact formulas for small values of n.

Minimal Reversible Deterministic Finite Automata

2018 ◽  
Vol 29 (02) ◽  
pp. 251-270 ◽  
Author(s):  
Markus Holzer ◽  
Sebastian Jakobi ◽  
Martin Kutrib
Keyword(s):  
Lower Bounds ◽  
Finite Automata ◽  
Transition Function ◽  
Upper And Lower Bounds ◽  
State Graph ◽  
Deterministic Finite Automata ◽  
Injective Mapping ◽  
Pattern Approach ◽  
Almost All

We study reversible deterministic finite automata (REV-DFAs), that are partial deterministic finite automata whose transition function induces an injective mapping on the state set for every letter of the input alphabet. We give a structural characterization of regular languages that can be accepted by REV-DFAs. This characterization is based on the absence of a forbidden pattern in the (minimal) deterministic state graph. Again with a forbidden pattern approach, we also show that the minimality of REV-DFAs among all equivalent REV-DFAs can be decided. Both forbidden pattern characterizations give rise to [Formula: see text]-complete decision algorithms. In fact, our techniques allow us to construct the minimal REV-DFA for a given minimal DFA. These considerations lead to asymptotic upper and lower bounds on the conversion from DFAs to REV-DFAs. Thus, almost all problems that concern uniqueness and the size of minimal REV-DFAs are solved.

SIMULATIONS OF UNARY ONE-WAY MULTI-HEAD FINITE AUTOMATA

2014 ◽  
Vol 25 (07) ◽  
pp. 877-896 ◽  
Author(s):  
MARTIN KUTRIB ◽  
ANDREAS MALCHER ◽  
MATTHIAS WENDLANDT
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Finite Automaton ◽  
Finite Automata ◽  
Upper And Lower Bounds ◽  
Unary Languages ◽  
Order Of Magnitude ◽  
Simulation Results ◽  
Special Case ◽  
Nondeterministic Finite Automaton

We investigate the descriptional complexity of deterministic one-way multi-head finite automata accepting unary languages. It is known that in this case the languages accepted are regular. Thus, we study the increase of the number of states when an n-state k-head finite automaton is simulated by a classical (one-head) deterministic or nondeterministic finite automaton. In the former case upper and lower bounds that are tight in the order of magnitude are shown. For the latter case we obtain an upper bound of O(n2k) and a lower bound of Ω(nk) states. We investigate also the costs for the conversion of one-head nondeterministic finite automata to deterministic k-head finite automata, that is, we trade nondeterminism for heads. In addition, we study how the conversion costs vary in the special case of finite and, in particular, of singleton unary lanuages. Finally, as an application of the simulation results, we show that decidability problems for unary deterministic k-head finite automata such as emptiness or equivalence are LOGSPACE-complete.

Exponentially Small Splitting and Arnold Diffusion for Multiple Time Scale Systems

2003 ◽  
Vol 15 (04) ◽  
pp. 339-386 ◽  
Author(s):  
Michela Procesi
Keyword(s):  
Phase Space ◽  
Normal Form ◽  
Lower Bounds ◽  
Time Scale ◽  
Upper And Lower Bounds ◽  
Multiple Time ◽  
Multiple Time Scale ◽  
Arnold Diffusion ◽  
Normal Form Theorem ◽  
Exponentially Small Splitting

We consider the class of Hamiltonians: [Formula: see text] where [Formula: see text], and the perturbing function f(q) is a rational function of eiq. We prove upper and lower bounds on the splitting for such class of systems, in regions of the phase space characterized by one fast frequency. Finally using an appropriate Normal Form theorem we prove the existence of chains of heteroclinic intersections.

On a Conjecture by Christian Choffrut

2017 ◽  
Vol 28 (05) ◽  
pp. 483-501 ◽  
Author(s):  
Aleksandrs Belovs ◽  
J. Andres Montoya ◽  
Abuzer Yakaryılmaz
Keyword(s):  
Lower Bounds ◽  
Finite Automaton ◽  
Finite Automata ◽  
Upper And Lower Bounds ◽  
Minimum Amount ◽  
Deterministic Finite Automaton ◽  
Open Problems

It is one of the most famous open problems to determine the minimum amount of states required by a deterministic finite automaton to distinguish a pair of strings, which was stated by Christian Choffrut more than thirty years ago. We investigate the same question for different automata models and we obtain new upper and lower bounds for some of them including alternating, ultrametric, quantum, and affine finite automata.

Study on Automatic Test Paper Generation Algorithm Based on the Maximum Flow of the Upper and Lower Bounds

2013 ◽  
Vol 756-759 ◽  
pp. 3065-3069
Author(s):  
Ying Zhang ◽  
Shi Hang Huang ◽  
Ying Liu ◽  
Zhen Fang ◽  
De Peng Dang
Keyword(s):  
Lower Bounds ◽  
Management System ◽  
Maximum Flow ◽  
Upper And Lower Bounds ◽  
Generation Model ◽  
Test Paper ◽  
Generation Algorithm ◽  
The Core ◽  
Flow Algorithm ◽  
Complex Constraints

The core of exam management system is how to generate test paper automatically. The existing algorithmic is difficult to simultaneously achieve the requirements with efficient, random, flexible and expansive performance. In this paper, we introduce the maximum flow algorithm of the upper and lower bounds in the graph theory, create a test paper generation model based on constraint conditions, and implement the test paper generation under complex constraints. In addition, to illustrate the success rate and efficiency, the system generated automatically test papers on proposition needs. In turn, it verifies the correctness and rationality of the model. The algorithm proposed in this paper will provide theoretical and technical support for other systems, and it further promotes the development of the exam management system.

DESCRIPTIONAL COMPLEXITY OF SPLICING SYSTEMS

2008 ◽  
Vol 19 (04) ◽  
pp. 813-826 ◽  
Author(s):  
REMCO LOOS ◽  
ANDREAS MALCHER ◽  
DETLEF WOTSCHKE
Keyword(s):  
Lower Bounds ◽  
Finite Automata ◽  
Regular Languages ◽  
Upper And Lower Bounds ◽  
Descriptional Complexity ◽  
Nondeterministic Finite Automata ◽  
Total Length ◽  
Splicing Systems

In this paper, the descriptional complexity of extended finite splicing systems is studied. These systems are known to generate exactly the class of regular languages. Upper and lower bounds are shown relating the size of these splicing systems, defined as the total length of the rules and the initial language of the system, to the size of their equivalent minimal nondeterministic finite automata (NFA). In addition, an accepting model of extended finite splicing systems is studied. Using this variant one can obtain systems which are more than polynomially more succinct than the equivalent NFA or generating extended finite splicing system.

scholarly journals Cayley Automatic Representations of Wreath Products

2016 ◽  
Vol 27 (02) ◽  
pp. 147-159 ◽  
Author(s):  
Dmitry Berdinsky ◽  
Bakhadyr Khoussainov
Keyword(s):  
Wreath Product ◽  
Lower Bounds ◽  
Finite Automata ◽  
Cayley Graphs ◽  
Wreath Products ◽  
Upper And Lower Bounds ◽  
Automatic Groups ◽  
Pushdown Automata

We construct the representations of Cayley graphs of wreath products using finite automata, pushdown automata and nested stack automata. These representations are in accordance with the notion of Cayley automatic groups introduced by Kharlampovich, Khoussainov and Miasnikov and its extensions introduced by Elder and Taback. We obtain the upper and lower bounds for a length of an element of a wreath product in terms of the representations constructed.

scholarly journals Finite automata with undirected state graphs

2021 ◽  
Author(s):  
Martin Kutrib ◽  
Andreas Malcher ◽  
Christian Schneider
Keyword(s):  
Lower Bounds ◽  
Finite Automata ◽  
Upper And Lower Bounds ◽  
Deterministic Case ◽  
Boolean Operations ◽  
State Complexity ◽  
Descriptional Complexity ◽  
Language Classes ◽  
Different Types ◽  
State Graphs

AbstractWe investigate finite automata whose state graphs are undirected. This means that for any transition from state p to q consuming some letter a from the input there exists a symmetric transition from state q to p consuming a letter a as well. So, the corresponding language families are subregular, and in particular in the deterministic case, subreversible. In detail, we study the operational descriptional complexity of deterministic and nondeterministic undirected finite automata. To this end, the different types of automata on alphabets with few letters are characterized. Then, the operational state complexity of the Boolean operations as well as the operations concatenation and iteration is investigated, where tight upper and lower bounds are derived for unary as well as arbitrary alphabets under the condition that the corresponding language classes are closed under the operation considered.

scholarly journals An Assessment of Algorithms for Deriving Failure Deterministic Finite Automata

2017 ◽  
Vol 29 (1) ◽  
Author(s):  
Madoda Nxumalo ◽  
Derrick G Kourie ◽  
Loek Cleophas ◽  
Bruce W Watson
Keyword(s):  
Lower Bounds ◽  
Test Data ◽  
Finite Length ◽  
Spanning Tree ◽  
Finite Automata ◽  
Regular Languages ◽  
Deterministic Finite Automata ◽  
Abstract Algorithm ◽  
Generating Algorithms

Failure deterministic finite automata (FDFAs) represent regular languages more compactly than deterministic finite automata (DFAs). Four algorithms that convert arbitrary DFAs to language-equivalent FDFAs are empirically investigated. Three are concrete variants of a previously published abstract algorithm, the DFA-Homomorphic Algorithm (DHA). The fourth builds a maximal spanning tree from the DFA to derive what it calls a delayed input DFA. A first suite of test data consists of DFAs that recognise randomised sets of finite length keywords. Since the classical Aho-Corasick algorithm builds an optimal FDFA from such a set (and only from such a set), it provides benchmark FDFAs against which the performance of the general algorithms can be compared. A second suite of test data consists of random DFAs generated by a specially designed algorithm that also builds language-equivalent FDFAs, some of which may have non-divergent cycles. These random FDFAs provide (not necessarily tight) lower bounds for assessing the effectiveness of the four general FDFA generating algorithms.

scholarly journals On the Generalized Distance Energy of Graphs

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 17 ◽  
Author(s):  
Abdollah Alhevaz ◽  
Maryam Baghipur ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Connected Graph ◽  
Distance Matrix ◽  
Wiener Index ◽  
Diagonal Matrix ◽  
Upper And Lower Bounds ◽  
Star Graph ◽  
Extremal Graphs ◽  
Generalized Distance

The generalized distance matrix D α ( G ) of a connected graph G is defined as D α ( G ) = α T r ( G ) + ( 1 − α ) D ( G ) , where 0 ≤ α ≤ 1 , D ( G ) is the distance matrix and T r ( G ) is the diagonal matrix of the node transmissions. In this paper, we extend the concept of energy to the generalized distance matrix and define the generalized distance energy E D α ( G ) . Some new upper and lower bounds for the generalized distance energy E D α ( G ) of G are established based on parameters including the Wiener index W ( G ) and the transmission degrees. Extremal graphs attaining these bounds are identified. It is found that the complete graph has the minimum generalized distance energy among all connected graphs, while the minimum is attained by the star graph among trees of order n.

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