Decision Problems for Three Subclasses of Regular Languages

2020 ◽  
pp. 186-192
Author(s):  
Hui Xu ◽  
Jing Tian ◽  
Jia Liu
Keyword(s):  
Regular Languages ◽  
Decision Problems

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.

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.

scholarly journals AUTOMATIC AND POLYNOMIAL-TIME ALGEBRAIC STRUCTURES

2019 ◽  
Vol 84 (4) ◽  
pp. 1630-1669 ◽  
Author(s):  
NIKOLAY BAZHENOV ◽  
MATTHEW HARRISON-TRAINOR ◽  
ISKANDER KALIMULLIN ◽  
ALEXANDER MELNIKOV ◽  
KENG MENG NG
Keyword(s):  
Polynomial Time ◽  
Regular Languages ◽  
Decision Problems ◽  
Turing Machines ◽  
Algebraic Structures ◽  
Automatic Structure ◽  
Image Position

AbstractA structure is automatic if its domain, functions, and relations are all regular languages. Using the fact that every automatic structure is decidable, in the literature many decision problems have been solved by giving an automatic presentation of a particular structure. Khoussainov and Nerode asked whether there is some way to tell whether a structure has, or does not have, an automatic presentation. We answer this question by showing that the set of Turing machines that represent automata-presentable structures is ${\rm{\Sigma }}_1^1 $-complete. We also use similar methods to show that there is no reasonable characterisation of the structures with a polynomial-time presentation in the sense of Nerode and Remmel.

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.

Bipolar Abstract Argumentation with Dual Attacks and Supports

2020 ◽  
Author(s):  
Nico Potyka
Keyword(s):  
Computational Complexity ◽  
Decision Problems ◽  
Abstract Argumentation ◽  
Stable Semantics ◽  
Support Relations ◽  
Support Relationships ◽  
Computational Properties ◽  
Inherent Tendency

Bipolar abstract argumentation frameworks allow modeling decision problems by defining pro and contra arguments and their relationships. In some popular bipolar frameworks, there is an inherent tendency to favor either attack or support relationships. However, for some applications, it seems sensible to treat attack and support equally. Roughly speaking, turning an attack edge into a support edge, should just invert its meaning. We look at a recently introduced bipolar argumentation semantics and two novel alternatives and discuss their semantical and computational properties. Interestingly, the two novel semantics correspond to stable semantics if no support relations are present and maintain the computational complexity of stable semantics in general bipolar frameworks.

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