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.

SOME REMARKS ON THE HAIRPIN COMPLETION

2010 ◽  
Vol 21 (05) ◽  
pp. 859-872 ◽  
Author(s):  
FLORIN MANEA ◽  
VICTOR MITRANA ◽  
TAKASHI YOKOMORI
Keyword(s):  
Regular Language ◽  
Regular Languages ◽  
Decision Problems ◽  
Strict Sense ◽  
Closure Properties ◽  
New Words ◽  
The Family

We consider several problems regarding the iterated or non-iterated hairpin completion of some subclasses of regular languages. Thus we obtain a characterization of the class of regular languages as the weak-code images of the k-hairpin completion of center-disjoint k-locally testable languages in the strict sense. This result completes two results from [3] and [11]. Then we investigate some decision problems and closure properties of the family of the iterated hairpin completion of singleton languages. Finally, we discuss some algorithms regarding the possibility of computing the values of k such that the non-iterated or iterated k-hairpin completion of a given regular language does not produce new words.

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.

Closure properties and decision problems of dag automata

2005 ◽  
Vol 94 (5) ◽  
pp. 231-240 ◽  
Author(s):  
Siva Anantharaman ◽  
Paliath Narendran ◽  
Michael Rusinowitch
Keyword(s):  
Decision Problems ◽  
Closure Properties

The complexity of weakly recognizing morphisms

2018 ◽  
Vol 53 (1-2) ◽  
pp. 1-17
Author(s):  
Lukas Fleischer ◽  
Manfred Kufleitner
Keyword(s):  
Computational Complexity ◽  
Regular Languages ◽  
Decision Problems ◽  
Membership Problem ◽  
Surjective Morphism ◽  
Infinite Words ◽  
Descriptional Complexity ◽  
Emptiness Problem ◽  
Free Semigroups ◽  
Büchi Automaton

Weakly recognizing morphisms from free semigroups onto finite semigroups are a classical way for defining the class of ω-regular languages, i.e., a set of infinite words is weakly recognizable by such a morphism if and only if it is accepted by some Büchi automaton. We study the descriptional complexity of various constructions and the computational complexity of various decision problems for weakly recognizing morphisms. The constructions we consider are the conversion from and to Büchi automata, the conversion into strongly recognizing morphisms, as well as complementation. We also show that the fixed membership problem is NC1-complete, the general membership problem is in L and that the inclusion, equivalence and universality problems are NL-complete. The emptiness problem is shown to be NL-complete if the input is given as a non-surjective morphism.

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.

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