Prefix-Free Regular Languages: Closure Properties, Difference, and Left Quotient

2012 ◽  
pp. 114-122 ◽  
Author(s):  
Monika Krausová
Keyword(s):  
Regular Languages ◽  
Closure Properties ◽  
Left Quotient

RESTARTING TILING AUTOMATA

2013 ◽  
Vol 24 (06) ◽  
pp. 863-878 ◽  
Author(s):  
DANIEL PRŮŠA ◽  
FRANTIŠEK MRÁZ
Keyword(s):  
Regular Languages ◽  
Two Dimensional ◽  
Scanning Strategy ◽  
Closure Properties ◽  
Computing Device ◽  
New Model ◽  
Picture Languages

We present a new model of a two-dimensional computing device called restarting tiling automaton. The automaton defines a set of tile-rewriting, weight-reducing rules and a scanning strategy by which a tile to rewrite is being searched. We investigate properties of the induced families of picture languages. Special attention is paid to picture languages that can be accepted independently of the scanning strategy. We show that this family strictly includes REC and exhibits similar closure properties. Moreover, we prove that its intersection with the set of one-row languages coincides with the regular languages.

Further Remarks on the Operational Nonterminal Complexity

2021 ◽  
pp. 1-15
Author(s):  
Jürgen Dassow
Keyword(s):  
Regular Language ◽  
Regular Languages ◽  
Partial Result ◽  
Natural Numbers ◽  
Left Quotient

For a regular language [Formula: see text], let [Formula: see text] be the minimal number of nonterminals necessary to generate [Formula: see text] by right linear grammars. Moreover, for natural numbers [Formula: see text] and an [Formula: see text]-ary regularity preserving operation [Formula: see text], let the range [Formula: see text] be the set of all numbers [Formula: see text] such that there are regular languages [Formula: see text] with [Formula: see text] for [Formula: see text] and [Formula: see text]. We show that, for the circular shift operation [Formula: see text], [Formula: see text] is infinite for all [Formula: see text], and we completely determine the set [Formula: see text]. Moreover, we give a precise range for the left right quotient and a partial result for the left quotient. Furthermore, we add some values to the range for the operation intersection which improves the result of [2].

UNWEIGHTED AND WEIGHTED HYPER-MINIMIZATION

2012 ◽  
Vol 23 (06) ◽  
pp. 1207-1225 ◽  
Author(s):  
ANDREAS MALETTI ◽  
DANIEL QUERNHEIM
Keyword(s):  
Finite Automata ◽  
Reduction Technique ◽  
Regular Languages ◽  
Minimization Algorithm ◽  
Compression Method ◽  
Closure Properties ◽  
State Reduction ◽  
Deterministic Finite Automata ◽  
Input Strings ◽  
Weighted Finite Automata

Hyper-minimization of deterministic finite automata (DFA) is a recently introduced state reduction technique that allows a finite change in the recognized language. A generalization of this lossy compression method to the weighted setting over semifields is presented, which allows the recognized weighted language to differ for finitely many input strings. First, the structure of hyper-minimal deterministic weighted finite automata is characterized in a similar way as in classical weighted minimization and unweighted hyper-minimization. Second, an efficient hyper-minimization algorithm, which runs in time [Formula: see text], is derived from this characterization. Third, the closure properties of canonical regular languages, which are languages recognized by hyper-minimal DFA, are investigated. Finally, some recent results in the area of hyper-minimization are recalled.

Two-Sided Strictly Locally Testable Languages

2021 ◽  
Vol 180 (1-2) ◽  
pp. 29-51
Author(s):  
Markus Holzer ◽  
Martin Kutrib ◽  
Friedrich Otto
Keyword(s):  
Binary Relation ◽  
Regular Languages ◽  
Decision Problems ◽  
Closure Properties ◽  
Positive Data ◽  
Proper Subclass ◽  
Testable Language ◽  
Even Linear Languages

A two-sided extension of strictly locally testable languages is presented. In order to determine membership within a two-sided strictly locally testable language, the input must be scanned from both ends simultaneously, whereby it is synchronously checked that the factors read are correlated with respect to a given binary relation. The class of two-sided strictly locally testable languages is shown to be a proper subclass of the even linear languages that is incomparable to the regular languages with respect to inclusion. Furthermore, closure properties of the class of two-sided strictly locally testable languages and decision problems are studied. Finally, it is shown that two-sided strictly k-testable languages are learnable in the limit from positive data.

SHUFFLE DECOMPOSITIONS OF REGULAR LANGUAGES

2002 ◽  
Vol 13 (06) ◽  
pp. 799-816 ◽  
Author(s):  
C. CÂMPEANU ◽  
K. SALOMAA ◽  
S. VÁGVÖLGYI
Keyword(s):  
Regular Language ◽  
Regular Languages ◽  
Equivalence Relations ◽  
Closure Properties ◽  
Context Free

We study the shuffle quotient operation and introduce equivalence relations it defines with respect to a (regular) language. Corresponding to an arbitrary shuffle decomposition we construct a normalized decomposition that is defined in terms of maximal languages. Using closure properties of the normalized decompositions we show that for certain subclasses of regular languages we can effectively decide whether or not the language has a non-trivial shuffle decomposition. We show that shuffle decomposition is undecidable for context-free languages.

Union-Freeness Revisited — Between Deterministic and Nondeterministic Union-Free Languages

2021 ◽  
pp. 1-23
Author(s):  
Benedek Nagy
Keyword(s):  
Normal Form ◽  
Regular Language ◽  
Regular Expression ◽  
Finite Automata ◽  
Finite Union ◽  
Regular Languages ◽  
Regular Expressions ◽  
Closure Properties ◽  
Language Class ◽  
Union Operation

Union-free expressions are regular expressions without using the union operation. Consequently, (nondeterministic) union-free languages are described by regular expressions using only concatenation and Kleene star. The language class is also characterised by a special class of finite automata: 1CFPAs have exactly one cycle-free accepting path from each of their states. Obviously such an automaton has exactly one accepting state. The deterministic counterpart of such class of automata defines the deterministic union-free (d-union-free, for short) languages. In this paper [Formula: see text]-free nondeterministic variants of 1CFPAs are used to define n-union-free languages. The defined language class is shown to be properly between the classes of (nondeterministic) union-free and d-union-free languages (in case of at least binary alphabet). In case of unary alphabet the class of n-union-free languages coincides with the class of union-free languages. Some properties of the new subregular class of languages are discussed, e.g., closure properties. On the other hand, a regular expression is in union normal form if it is a finite union of union-free expressions. It is well known that every regular expression can be written in union normal form, i.e., all regular languages can be described as finite unions of (nondeterministic) union-free languages. It is also known that the same fact does not hold for deterministic union-free languages, that is, there are regular languages that cannot be written as finite unions of d-union-free languages. As an important result here we show that every regular language can be defined by a finite union of n-union-free languages. This fact also allows to define n-union-complexity of regular languages.

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