Concurrently controlled grammars

Mavlankulov, Gairatzhan; Othman, Mohamed; Turaev, Sherzod; Selamat, Mohd Hasan; Zhumabayeva, Laula; Zhukabayeva, Tamara

doi:10.14736/kyb-2018-4-0748

Cited by 3 publications

(3 citation statements)

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“…• scattered context grammars [29]-in which only a fixed number of symbols can be replaced in a step but the symbols can be different; • concurrently controlled grammars [30]-the control over a parallel application of the productions is realized by a Petri net with different parallel firing strategies.…”

Section: Regulated Parallel and Relational Grammarsmentioning

confidence: 99%

Binary Context-Free Grammars

et al. 2020

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A binary grammar is a relational grammar with two nonterminal alphabets, two terminal alphabets, a set of pairs of productions and the pair of the initial nonterminals that generates the binary relation, i.e., the set of pairs of strings over the terminal alphabets. This paper investigates the binary context-free grammars as mutually controlled grammars: two context-free grammars generate strings imposing restrictions on selecting production rules to be applied in derivations. The paper shows that binary context-free grammars can generate matrix languages whereas binary regular and linear grammars have the same power as Chomskyan regular and linear grammars.

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Section: Regulated Parallel and Relational Grammarsmentioning

confidence: 99%

Binary Context-Free Grammars

et al. 2020

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“…In Petri nets with a stack, the reachability problem may be reduced to the coverability problem and both are at least not elementary while their decidability status is still unknown [15]. The analysis of subclasses of Petri nets with a stack is an active field of research [1,19,5,24]. However for none of the above extensions, the coverability and termination problems belong to EXPSPACE.…”

Section: Introductionmentioning

confidence: 99%

“…For BVASS, the reachability problem is also TOWER-hard [12] and its decidability is still an open problem while the coverability and the boundedness problems are 2-EXPTIME-complete [13]. The analysis of subclasses of Petri nets with a stack is an active field of research [14,15,16,17]. However, for none of the above extensions, the coverability and termination problems belong to EXPSPACE.…”

Section: Introductionmentioning

confidence: 99%

Coverability and Termination in Recursive Petri Nets

Finkel

Haddad

Khmelnitsky

2019

Application and Theory of Petri Nets and Concurrency

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In the early two-thousands, Recursive Petri nets have been introduced in order to model distributed planning of multi-agent systems for which counters and recursivity were necessary. Although Recursive Petri nets strictly extend Petri nets and stack automata, most of the usual property problems are solvable but using non primitive recursive algorithms, even for coverability and termination. For almost all other extended Petri nets models containing a stack the complexity of coverability and termination are unknown or strictly larger than EXPSPACE. In contrast, we establish here that for Recursive Petri nets, the coverability and termination problems are EXPSPACE-complete as for Petri nets. From an expressiveness point of view, we show that coverability languages of Recursive Petri nets strictly include the union of coverability languages of Petri nets and context-free languages. Thus we get for free a more powerful model than Petri net.

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Coverability, Termination, and Finiteness in Recursive Petri Nets

Finkel

Haddad

Khmelnitsky

2022

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In the early two-thousands, Recursive Petri nets have been introduced in order to model distributed planning of multi-agent systems for which counters and recursivity were necessary. Although Recursive Petri nets strictly extend Petri nets and context-free grammars, most of the usual problems (reachability, coverability, finiteness, boundedness and termination) were known to be solvable by using non-primitive recursive algorithms. For almost all other extended Petri nets models containing a stack, the complexity of coverability and termination are unknown or strictly larger than EXPSPACE. In contrast, we establish here that for Recursive Petri nets, the coverability, termination, boundedness and finiteness problems are EXPSPACE-complete as for Petri nets. From an expressiveness point of view, we show that coverability languages of Recursive Petri nets strictly include the union of coverability languages of Petri nets and context-free languages. Thus we get a more powerful model than Petri net for free.

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Concurrently controlled grammars

Cited by 3 publications

References 0 publications

Binary Context-Free Grammars

Binary Context-Free Grammars

Coverability and Termination in Recursive Petri Nets

Coverability, Termination, and Finiteness in Recursive Petri Nets

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