Formal Languages for Quasicrystals

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.

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Generation and recognition of formal languages by modifiable grammars

ACM SIGPLAN Notices ◽

10.1145/122193.122196 ◽

1990 ◽

Vol 25 (12) ◽

pp. 45-53 ◽

Cited By ~ 10

Author(s):

Boris Burshteyn

Keyword(s):

Formal Languages

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

Fundamenta Informaticae ◽

10.3233/fi-1981-4305 ◽

1981 ◽

Vol 4 (3) ◽

pp. 531-549 ◽

Cited By ~ 1

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.

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