scholarly journals Deterministic automata for extended regular expressions

2017 ◽  
Vol 7 (1) ◽  
pp. 24-28
Author(s):  
Mirzakhmet Syzdykov
Keyword(s):  
Finite Automaton ◽  
Regular Languages ◽  
Regular Expressions ◽  
Deterministic Finite Automaton ◽  
Past Work ◽  
The Past ◽  
Deterministic Automata ◽  
Extended Regular Expressions

Abstract In this work we present the algorithms to produce deterministic finite automaton (DFA) for extended operators in regular expressions like intersection, subtraction and complement. The method like “overriding” of the source NFA(NFA not defined) with subset construction rules is used. The past work described only the algorithm for AND-operator (or intersection of regular languages); in this paper the construction for the MINUS-operator (and complement) is shown.

scholarly journals ON A SUPERCLASS OF A-GRAMMARS

2017 ◽  
Vol 20 (10) ◽  
pp. 102-108
Author(s):  
V.P. Tsvetov
Keyword(s):  
Finite Automaton ◽  
Formal Languages ◽  
Regular Languages ◽  
Finite Alphabet ◽  
Graph Structure ◽  
Graph Grammars ◽  
Deterministic Finite Automaton

In this paper we consider a superclass of automaton grammars that can be represented in terms of paths on graphs. With this approach, we assume that vertices of graph are labeled by symbols of finite alphabet A . We will call such grammars graph-generated grammars or G-grammars. In contrast to the graph grammars that are used to describe graph structure transformations, G-grammars using a graphs as a means of representing formal languages. We will give an algorithm for constructing G-grammar which generate the language recognized by deterministic finite automaton. Moreover, we will show that the class of languages generated by G-grammars is a proper superset of regular languages.

scholarly journals IN SEARCH OF MOST COMPLEX REGULAR LANGUAGES

2013 ◽  
Vol 24 (06) ◽  
pp. 691-708 ◽  
Author(s):  
JANUSZ BRZOZOWSKI
Keyword(s):  
Positive Integer ◽  
Finite Automaton ◽  
Cyclic Permutation ◽  
The State ◽  
Regular Languages ◽  
Final States ◽  
Deterministic Finite Automaton ◽  
Small Positive Integer ◽  
Initial State ◽  
State Complexity

Sequences (Ln| n ≥ k), called streams, of regular languages Lnare considered, where k is some small positive integer, n is the state complexity of Ln, and the languages in a stream differ only in the parameter n, but otherwise, have the same properties. The following measures of complexity are proposed for any stream: (1) the state complexity n of Ln, that is, the number of left quotients of Ln(used as a reference); (2) the state complexities of the left quotients of Ln; (3) the number of atoms of Ln; (4) the state complexities of the atoms of Ln; (5) the size of the syntactic semigroup of Ln; and the state complexities of the following operations: (6) the reverse of Ln; (7) the star of Ln; (8) union, intersection, difference and symmetric difference of Lmand Ln; and (9) the concatenation of Lmand Ln. A stream that has the highest possible complexity with respect to these measures is then viewed as a most complex stream. The language stream (Un(a, b, c) | n ≥ 3) is defined by the deterministic finite automaton with state set {0, 1, … , n−1}, initial state 0, set {n−1} of final states, and input alphabet {a, b, c}, where a performs a cyclic permutation of the n states, b transposes states 0 and 1, and c maps state n − 1 to state 0. This stream achieves the highest possible complexities with the exception of boolean operations where m = n. In the latter case, one can use Un(a, b, c) and Un(b, a, c), where the roles of a and b are interchanged in the second language. In this sense, Un(a, b, c) is a universal witness. This witness and its extensions also apply to a large number of combined regular operations.

Cardinality estimates for some classes of regular languages

2015 ◽  
Vol 25 (6) ◽  
Author(s):  
Dmitriy E. Alexandrov
Keyword(s):  
Finite Automaton ◽  
Regular Languages ◽  
Regular Expressions

AbstractWe consider a method that modifies regular expressions in order to solve the “exponential explosion” problem on the number of states of the finite automaton that recognizes a set of regular languages defined by the union of regular expressions of the form .∗ R

scholarly journals COMPRESSED MEMBERSHIP PROBLEMS FOR REGULAR EXPRESSIONS AND HIERARCHICAL AUTOMATA

2010 ◽  
Vol 21 (05) ◽  
pp. 817-841 ◽  
Author(s):  
MARKUS LOHREY
Keyword(s):  
Open Problem ◽  
Regular Languages ◽  
Regular Expressions ◽  
Membership Problem ◽  
Complexity Bounds ◽  
Straight Line ◽  
Membership Problems ◽  
Context Free ◽  
Straight Line Programs ◽  
Extended Regular Expressions

Membership problems for compressed strings in regular languages are investigated. Strings are represented by straight-line programs, i.e., context-free grammars that generate exactly one string. For the representation of regular languages, various formalisms with different degrees of succinctness (e.g., suitably extended regular expressions, hierarchical automata) are considered. Precise complexity bounds are derived. Among other results, it is shown that the compressed membership problem for regular expressions with intersection is PSPACE-complete. This solves an open problem of Plandowski and Rytter.

scholarly journals THE MAGIC NUMBER PROBLEM FOR SUBREGULAR LANGUAGE FAMILIES

2012 ◽  
Vol 23 (01) ◽  
pp. 115-131 ◽  
Author(s):  
MARKUS HOLZER ◽  
SEBASTIAN JAKOBI ◽  
MARTIN KUTRIB
Keyword(s):  
Finite Automaton ◽  
Magic Number ◽  
Regular Languages ◽  
Magic Numbers ◽  
Deterministic Finite Automaton ◽  
Number Problem ◽  
Nondeterministic Finite Automaton

We investigate the magic number problem, that is, the question whether there exists a minimal n-state nondeterministic finite automaton (NFA) whose equivalent minimal deterministic finite automaton (DFA) has α states, for all n and α satisfying n ≤ α ≤ 2n. A number α not satisfying this condition is called a magic number (for n). It was shown that no magic numbers exist for general regular languages, whereas trivial and non-trivial magic numbers for unary regular languages were identified. We obtain similar results for automata accepting subregular languages like, for example, star-free languages, prefix-, suffix-, and infix-closed languages, and prefix-, suffix-, and infix-free languages, showing that there are only trivial magic numbers, when they exist. For finite languages we obtain some partial results showing that certain numbers are non-magic.

scholarly journals P(L)AYING FOR SYNCHRONIZATION

2013 ◽  
Vol 24 (06) ◽  
pp. 765-780 ◽  
Author(s):  
F. M. FOMINYKH ◽  
P. V. MARTYUGIN ◽  
M. V. VOLKOV
Keyword(s):  
Finite Automaton ◽  
Deterministic Finite Automaton ◽  
Deterministic Automata ◽  
The Given

Two topics are presented: synchronization games and synchronization costs. In a synchronization game on a deterministic finite automaton, there are two players, Alice and Bob, whose moves alternate. Alice wants to synchronize the given automaton, while Bob aims to make her task as hard as possible. We answer a few natural questions related to such games. Speaking about synchronization costs, we consider deterministic automata in which each transition has a certain price. The problem is whether or not a given automaton can be synchronized within a given budget. We determine the complexity of this problem.

scholarly journals Accepting networks of evolutionary processors with resources restricted and structure limited filters

2021 ◽  
Vol 55 ◽  
pp. 8
Author(s):  
Jürgen Dassow ◽  
Bianca Truthe
Keyword(s):  
Finite Automaton ◽  
Regular Languages ◽  
Deterministic Finite Automaton ◽  
Production Rules ◽  
The Family

In this paper, we continue the research on accepting networks of evolutionary processors where the filters belong to several special families of regular languages. We consider families of codes or ideals and subregular families which are defined by restricting the resources needed for generating or accepting them (the number of states of the minimal deterministic finite automaton accepting a language of the family as well as the number of non-terminal symbols or the number of production rules of a right-linear grammar generating such a language). We insert the newly defined language families into the hierachy of language families obtained by using as filters languages of other subregular families (such as ordered, non-counting, power-separating, circular, suffix-closed regular, union-free, definite, combinational, finite, monoidal, nilpotent, or commutative languages).

PROVABLY SHORTER REGULAR EXPRESSIONS FROM FINITE AUTOMATA

2013 ◽  
Vol 24 (08) ◽  
pp. 1255-1279 ◽  
Author(s):  
HERMANN GRUBER ◽  
MARKUS HOLZER
Keyword(s):  
Graph Theory ◽  
Finite Automaton ◽  
Regular Expression ◽  
Finite Automata ◽  
Upper Bounds ◽  
Extremal Graph ◽  
Extremal Graph Theory ◽  
Regular Expressions ◽  
Deterministic Finite Automaton

Based on recent results from extremal graph theory, we prove that every n-state binary deterministic finite automaton can be converted into an equivalent regular expression of size O(1.742n) using state elimination. Furthermore, we give improved upper bounds on the language operations intersection and interleaving on regular expressions.

Model reformulation for conflict-free routing problems using Petri Net and Deterministic Finite Automaton

2015 ◽  
Vol 20 (3) ◽  
pp. 262-269 ◽  
Author(s):  
Ryosuke Nakamura ◽  
Kenji Sawada ◽  
Seiichi Shin ◽  
Kenji Kumagai ◽  
Hisato Yoneda
Keyword(s):  
Petri Net ◽  
Finite Automaton ◽  
Deterministic Finite Automaton ◽  
Routing Problems ◽  
Model Reformulation

ON "PLASTIC" WAVES IN SOLIDS

1959 ◽  
Vol 37 (9) ◽  
pp. 1017-1035 ◽  
Author(s):  
John M. Bowsher
Keyword(s):  
Theoretical Study ◽  
Short Review ◽  
Future Research ◽  
Past Work ◽  
The Past ◽  
Engineering Significance ◽  
The Subject

The study of the propagation of "plastic" waves in solids has reached a stage where it is necessary to consider which direction future research should take. In the past 90 or so years many experiments, mostly designed to elucidate certain points of engineering significance, and a few attempts at a theoretical study have cast some light on the subject and revealed it as one of formidable difficulty.Nearly all the experiments have of necessity relied on rather dubious theories for their interpretation, and part of the present paper will be devoted to a description of an apparatus which gives results capable of being interpreted with a very minimum of theory. The remainder of the paper is devoted to a short review of past work with particular emphasis on basic phenomena and to a brief discussion on the most pressing problems still remaining. The experiments described in the present paper bring to light a factor in the propagation of "plastic" waves that seems to have been overlooked in previous work.

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