Sequential grammars and automata with valences

Fernau, Henning; Stiebe, Ralf

doi:10.1016/s0304-3975(01)00282-1

Cited by 28 publications

(40 citation statements)

References 6 publications

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“…Valence languages have been introduced in a grammar setting in [29]. They are equivalent to so-called regular unordered vector languages [11] and can be characterized by blind multicounter automata, see [19,21,24].…”

Section: Discussionmentioning

confidence: 99%

Parallel communicating grammar systems with terminal transmission

Fernau

2001

Acta Informatica

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We introduce a new variant of PC grammar systems, called PC grammar systems with terminal transmission, PCGSTT for short. We show that right-linear centralized PCGSTT have nice formal language theoretic properties: they are closed under gsm mappings (in particular, under intersection with regular sets and under homomorphisms) and union; a slight variant is, in addition, closed under concatenation and star; their power lies between that of n-parallel grammars introduced by Wood and that of matrix languages of index n, and their relation to equal matrix grammars of degree n is discussed. We show that membership for these language classes is complete for NL. In a second part of the paper, we discuss questions concerning grammatical inference of these systems. More precisely, we show that PCGSTT whose component grammars are terminal distinguishable right-linear, a notion introduced by Radhakrishnan and Nagaraja in [33,34], are identifiable in the limit if certain data communication information is supplied in addition.

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Section: Discussionmentioning

confidence: 99%

Parallel communicating grammar systems with terminal transmission

Fernau

2001

Acta Informatica

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“…Here, "effectively" means again that given a representation of a language L from C and a description of T , one can effectively compute a representation of T L. For a language L, we denote by T (L) the smallest full trio containing L. Note that if L = ∅, the class T (L) contains precisely the languages T L for rational transductions T . For example, it is well-known that for every monoid M , the class VA(M ) is a full trio [6]. A full AFL is a full trio that is also closed under Kleene iteration, i.e.…”

Section: Undecidabilitymentioning

confidence: 99%

The emptiness problem for valence automata over graph monoids

Zetzsche

2021

Information and Computation

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This work studies which storage mechanisms in automata permit decidability of the emptiness problem. The question is formalized using valence automata, an abstract model of automata in which the storage mechanism is given by a monoid. For each of a variety of storage mechanisms, one can choose a (typically infinite) monoid M such that valence automata over M are equivalent to (one-way) automata with this type of storage. In fact, many important storage mechanisms can be realized by monoids defined by finite graphs, called graph monoids. Examples include pushdown stacks, partially blind counters (which behave like Petri net places), blind counters (which may attain negative values), and combinations thereof.Hence, we study for which graph monoids the emptiness problem for valence automata is decidable. A particular model realized by graph monoids is that of Petri nets with a pushdown stack. For these, decidability is a long-standing open question and we do not answer it here.However, if one excludes subgraphs corresponding to this model, a characterization can be achieved. Moreover, we provide a description of those storage mechanisms for which decidability remains open. This leads to a model that naturally generalizes both pushdown Petri nets and the priority multicounter machines introduced by Reinhardt.The cases that are proven decidable constitute a natural and apparently new extension of Petri nets with decidable reachability. It is finally shown that this model can be combined with another such extension by Atig and Ganty: We present a further decidability result that subsumes both of these Petri net extensions.

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“…Subsequently, the notion of group automaton has been extended in at least two meaningful ways. The first one is that of monoid automaton, also known as valence automaton, by assuming that the register associated with the model is a monoid [6,12,13]. The second one is that of valence pushdown automaton introduced in [6], where the underlying model of computation is a pushdown automaton.…”

Section: Introductionmentioning

confidence: 99%

“…In the case of context-free grammars, a thorough study of several remarkable structural properties of the languages generated by the corresponding valence grammars has been done in [6], over arbitrary monoids and in particular over commutative groups.…”

Section: Introductionmentioning

confidence: 99%

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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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Sequential grammars and automata with valences

Cited by 28 publications

References 6 publications

Parallel communicating grammar systems with terminal transmission

Parallel communicating grammar systems with terminal transmission

The emptiness problem for valence automata over graph monoids

Generalized Results on Monoids as Memory

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