Valence Grammars With Target Sets

Fernau, Henning; Stiebe, Ralf

doi:10.1142/9789812810908_0010

Cited by 6 publications

(10 citation statements)

References 7 publications

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“…Combining Theorems 4.2 with the result of Fernau and Stiebe [4] mentioned above (Theorem 2.1) gives us the following immediate corollary.…”

Section: Adjoining a Zerosupporting

confidence: 52%

Rational subsets of polycyclic monoids and valence automata

Render¹,

Kambites²

2009

Information and Computation

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We study the classes of languages defined by valence automata with rational target sets (or equivalently, regular valence grammars with rational target sets), where the valence monoid is drawn from the important class of polycyclic monoids. We show that for polycyclic monoids of rank 2 or more, such automata accept exactly the context-free languages. For the polycyclic monoid of rank 1 (that is, the bicyclic monoid), they accept a class of languages strictly including the partially blind one-counter languages. Key to the proof is a description of the rational subsets of polycyclic and bicyclic monoids, other consequences of which include the decidability of the rational subset membership problem, and the closure of the class of rational subsets under intersection and complement.

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“…Combining Theorems 4.2 with the result of Fernau and Stiebe [4] mentioned above (Theorem 2.1) gives us the following immediate corollary.…”

Section: Adjoining a Zerosupporting

confidence: 52%

Rational subsets of polycyclic monoids and valence automata

Render¹,

Kambites²

2009

Information and Computation

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“…Shortly thereafter, the same authors in [45] extended the concept of valence grammar by the notion like a valid derivation value is acceptable to be a part of a given target set. In that paper, they also have studied the closure properties of those grammars together with their generative power with target sets over the groups ℤ m , monoids ℕ m , and finite monoid.…”

Section: Theorem 6 [53]mentioning

confidence: 99%

“…In that paper, they also have studied the closure properties of those grammars together with their generative power with target sets over the groups ℤ m , monoids ℕ m , and finite monoid. Furthermore, they proved that grammars with permutations of regular languages as a controller can characterize the unordered vector languages and at the same time, demonstrated that valence grammars with finite monoids as target sets can be constructed into an equivalent matrix language [45]. Interestingly, in the same year, Stiebe alone in [47] came out with a notion such by assessing the productions of grammar with integer vectors, we can generate an equivalent matrix grammar as well as Parikh languages.…”

Section: Theorem 6 [53]mentioning

confidence: 99%

“…Despite their diversity, all of the introduced regulated grammars can be classified into several types depending on their common characteristics like (1) control by prescribed sequences such as matrix grammars [12][13][14][15][16][17], regularly controlled grammars [18], vector grammars [19], different variants of Petri net controlled grammars [20][21][22][23][24][25][26] and Parikh vector controlled grammars [27], (2) control by context conditions such as conditional grammars and ordered grammars [28], random context grammars [29], tree controlled grammars [30][31][32][33][34][35][36][37], semi-conditional grammars [38] and string-regulated graph grammars [39], (3) control by computed sequences such as programmed grammars [40] and valence grammars [41][42][43][44][45][46][47], (4) control by memory such as indexed grammars [48], (5) control by partial parallelism such as scattered context grammars [49], Russian parallel grammars [50], Indian parallel grammars [51] and global indexed grammars [52] and many other regulated grammars ...…”

Section: Introductionmentioning

confidence: 99%

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Structurally and Arithmetically Controlled Grammars

Ashaari¹,

Turaev²,

Okhunov³

2016

IJPCC

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Over the quarter century, it is gratifying to note that the significance of regulated or controlledgrammars (i.e. grammars with regulated rewriting) has been recognized by many parties where it has beenused widely in a great variety of scientific disciplines ranging from Linguistics through DNA Computing upto the Informatics and recently come to Big Data Analytics. Therefore, literally we can find hundreds ofstudies of well-known of various types of controlled grammars and their investigation have amount to athrilling trend within formal language theory. Given the extensive literature on issues related to controlledgrammars, this research focused on arithmetically controlled grammars and tree controlled grammars,which are practically important. Thereby, in this paper, we briefly recapitulate the background of formallanguage theory and highlight the key results of multiset grammars, valence grammars and tree controlledgrammars. In this paper, a new controlled grammar that can be generated using both control mechanismstogether is proposed for future research.

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“…If the targets of the automaton are rational subsets of the monoid, the corresponding model is called rational monoid automaton. The idea of allowing more general accepting configurations has been also applied to valence grammars, leading to the concept of valence grammars with target sets [5].…”

Section: Introductionmentioning

confidence: 99%

Generalized Results on Monoids as Memory

Salehi

D'Alessandro

Say

2017

Electron. Proc. Theor. Comput. Sci.

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We show that some results from the theory of group automata and monoid automata still hold for more general classes of monoids and models. Extending previous work for finite automata over commutative groups, we prove that the context-free language L 1 * = {a n b n : n ≥ 1} * can not be recognized by any rational monoid automaton over a finitely generated permutable monoid. We show that the class of languages recognized by rational monoid automata over finitely generated completely simple or completely 0-simple permutable monoids is a semi-linear full trio. Furthermore, we investigate valence pushdown automata, and prove that they are only as powerful as (finite) valence automata. We observe that certain results proven for monoid automata can be easily lifted to the case of context-free valence grammars.

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Valence Grammars With Target Sets

Cited by 6 publications

References 7 publications

Rational subsets of polycyclic monoids and valence automata

Rational subsets of polycyclic monoids and valence automata

Structurally and Arithmetically Controlled Grammars

Generalized Results on Monoids as Memory

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