Formal languages of labelled graphs

Computing ◽  
1976 ◽  
Vol 16 (1-2) ◽  
pp. 113-137 ◽  
Author(s):  
M. Nagl
Keyword(s):  
Formal Languages ◽  
Labelled Graphs

Languages Accepted by Weighted Restarting Automata*

2021 ◽  
Vol 180 (1-2) ◽  
pp. 151-177
Author(s):  
Qichao Wang
Keyword(s):  
General Class ◽  
Formal Languages ◽  
Input Word ◽  
Additional Requirement ◽  
Tropical Semiring

Weighted restarting automata have been introduced to study quantitative aspects of computations of restarting automata. In earlier works we studied the classes of functions and relations that are computed by weighted restarting automata. Here we use them to define classes of formal languages by restricting the weight associated to a given input word through an additional requirement. In this way, weighted restarting automata can be used as language acceptors. First, we show that by using the notion of acceptance relative to the tropical semiring, we can avoid the use of auxiliary symbols. Furthermore, a certain type of word-weighted restarting automata turns out to be equivalent to non-forgetting restarting automata, and another class of languages accepted by word-weighted restarting automata is shown to be closed under the operation of intersection. This is the first result that shows that a class of languages defined in terms of a quite general class of restarting automata is closed under intersection. Finally, we prove that the restarting automata that are allowed to use auxiliary symbols in a rewrite step, and to keep on reading after performing a rewrite step can be simulated by regular-weighted restarting automata that cannot do this.

scholarly journals MET: a Java package for fast molecule equivalence testing

2020 ◽  
Vol 12 (1) ◽  
Author(s):  
Jördis-Ann Schüler ◽  
Steffen Rechner ◽  
Matthias Müller-Hannemann
Keyword(s):  
Chemical Properties ◽  
Graph Isomorphism ◽  
Isomorphism Problem ◽  
Equivalence Classes ◽  
Equivalence Testing ◽  
Equivalence Test ◽  
Graph Isomorphism Problem ◽  
2D Structure ◽  
Node Labels ◽  
Labelled Graphs

AbstractAn important task in cheminformatics is to test whether two molecules are equivalent with respect to their 2D structure. Mathematically, this amounts to solving the graph isomorphism problem for labelled graphs. In this paper, we present an approach which exploits chemical properties and the local neighbourhood of atoms to define highly distinctive node labels. These characteristic labels are the key for clever partitioning molecules into molecule equivalence classes and an effective equivalence test. Based on extensive computational experiments, we show that our algorithm is significantly faster than existing implementations within , and . We provide our Java implementation as an easy-to-use, open-source package (via GitHub) which is compatible with . It fully supports the distinction of different isotopes and molecules with radicals.

A Classification and Closure Properties of Languages for Describing Concurrent System Behaviours

1981 ◽  
Vol 4 (3) ◽  
pp. 531-549 ◽  
Author(s):  
Miklós Szijártó
Keyword(s):  
Formal Languages ◽  
Parallel Program ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Concurrent System ◽  
Closure Properties ◽  
Sequential Program ◽  
Necessary And Sufficient ◽  
Special Case ◽  
Independence Relations

The correspondence between sequential program schemes and formal languages is well known (Blikle and Mazurkiewicz (1972), Engelfriet (1974)). The situation is more complicated in the case of parallel program schemes, and trace languages (Mazurkiewicz (1977)) have been introduced to describe them. We introduce the concept of the closure of a language on a so called independence relation on the alphabet of the language, and formulate several theorems about them and the trace languages. We investigate the closedness properties of Chomsky classes under closure on independence relations, and as a special case we derive a new necessary and sufficient condition for the regularity of the commutative closure of a language.

Application of formal languages in polynomial transformations of instances between NP-complete problems

2013 ◽  
Vol 14 (8) ◽  
pp. 623-633
Author(s):  
Jorge A. Ruiz-Vanoye ◽  
Joaquín Pérez-Ortega ◽  
Rodolfo A. Pazos Rangel ◽  
Ocotlán Díaz-Parra ◽  
Héctor J. Fraire-Huacuja ◽  
...  
Keyword(s):  
Formal Languages ◽  
Complete Problems ◽  
Polynomial Transformations ◽  
Np Complete
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