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).

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.

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.

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

MAGIC NUMBERS FOR SYMMETRIC DIFFERENCE NFAS

2005 ◽  
Vol 16 (05) ◽  
pp. 1027-1038 ◽  
Author(s):  
LYNETTE VAN ZIJL
Keyword(s):  
Finite Automaton ◽  
Finite Automata ◽  
Symmetric Difference ◽  
Magic Numbers ◽  
Deterministic Finite Automaton ◽  
Nondeterministic Finite Automata ◽  
Binary Case ◽  
Nondeterministic Finite Automaton

Iwama et al. showed that there exists an n-state binary nondeterministic finite automaton such that its equivalent minimal deterministic finite automaton has exactly 2n - α states, for all n ≥ 7 and 5 ≤ α ≤ 2n-2, subject to certain coprimality conditions. We investigate the same question for both unary and binary symmetric difference nondeterministic finite automata. In the binary case, we show that for any n ≥ 4, there is an n-state symmetric difference nondeterministic finite automaton for which the equivalent minimal deterministic finite automaton has 2n - 1 + 2k - 1 - 1 states, for 2 < k ≤ n - 1. In the unary case, we consider a large practical subclass of unary symmetric difference nondeterministic finite automata: for all n ≥ 2, we argue that there are many values of α such that there is no n-state unary symmetric difference nondeterministic finite automaton with an equivalent minimal deterministic finite automaton with 2n - α states, where 0 < α < 2n - 1. For each n ≥ 2, we quantify such values of α precisely.

scholarly journals State Complexity of Suffix Distance

2019 ◽  
Vol 30 (06n07) ◽  
pp. 1197-1216
Author(s):  
Timothy Ng ◽  
David Rappaport ◽  
Kai Salomaa
Keyword(s):  
Lower Bound ◽  
Finite Automaton ◽  
Regular Language ◽  
Upper Bounds ◽  
The State ◽  
Deterministic Finite Automaton ◽  
Tight Bound ◽  
State Complexity

The neighbourhood of a regular language with respect to the prefix, suffix and subword distance is always regular and a tight bound for the state complexity of prefix distance neighbourhoods is known. We give upper bounds for the state complexity of the neighbourhood of radius [Formula: see text] of an [Formula: see text]-state deterministic finite automaton language with respect to the suffix distance and the subword distance, respectively. For restricted values of [Formula: see text] and [Formula: see text] we give a matching lower bound for the state complexity of suffix distance neighbourhoods.

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