Silent Transitions in Automata with Storage

Zetzsche, Georg

doi:10.1007/978-3-642-39212-2_39

Cited by 15 publications

(23 citation statements)

References 21 publications

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“…The case that all vertices are looped was shown by Lohrey and Steinberg [14] (see also the discussion of Theorem 3.4). Another case appeared in [19]. We prove Theorem 3.1 in Section 4.…”

Section: Resultsmentioning

confidence: 92%

“…Since R Γ is finite, this implies that the set of all w ∈ X * Γ with w ≡ Γ ε is recursively enumerable. (In fact, whether w ≡ Γ ε can be decided in polynomial time [19,23].) In particular, one can recursively enumerate runs of valence automata over VA(MΓ) and hence VA(MΓ) ⊆ RE.…”

Section: Undecidabilitymentioning

confidence: 99%

“…We address this question for a class of monoids that was introduced in [19] and accommodates a number of storage mechanisms that have been studied in automata theory. Examples include pushdown stacks, partially blind counters (which behave like Petri net places), and blind counters (which may attain negative values; these are in most situations interchangeable with reversal-bounded counters), and combinations thereof.…”

Section: Introductionmentioning

confidence: 99%

“…This version provides proofs of the results of [21] and the enhanced decidability result. Moreover, it contains proofs of some results that first appeared in [19,20], but have not yet undergone journal peer review.…”

Section: Introductionmentioning

confidence: 99%

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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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“…The case that all vertices are looped was shown by Lohrey and Steinberg [14] (see also the discussion of Theorem 3.4). Another case appeared in [19]. We prove Theorem 3.1 in Section 4.…”

Section: Resultsmentioning

confidence: 92%

Section: Undecidabilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The emptiness problem for valence automata over graph monoids

Zetzsche

2021

Information and Computation

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“…Our aim is to show that F 2 -automata working in linear time can recognize all context-free languages. It is stated in [21] that K X -automata which consume at least one input symbol at each step are as powerful as K X -automata without any time bound. However, it is not straightforward to see whether the same is true for F 2 -automata.…”

Section: Group Automata Under Linear Time Boundsmentioning

confidence: 99%

Language classes associated with automata over matrix groups

Salehi

D'Alessandro

Say

2018

RAIRO-Theor. Inf. Appl.

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We investigate the language classes recognized by group automata over matrix groups. For the case of 2 × 2 matrices, we prove that the corresponding group automata for rational matrix groups are more powerful than the corresponding group automata for integer matrix groups. Finite automata over some special matrix groups, such as the discrete Heisenberg group and the Baumslag-Solitar group are also examined. We also introduce the notion of time complexity for group automata and demonstrate some separations among related classes. The case of linear-time bounds is examined in detail throughout our repertory of matrix group automata.

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Recent Advances on Reachability Problems for Valence Systems (Invited Talk)

Zetzsche

2021

Lecture Notes in Computer Science

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Valence systems are an abstract model of computation that consists of a finite-state control and some storage mechanism. In contrast to traditional models, the storage mechanism is not fixed, but given as a parameter. This allows us to precisely state questions like: For which storage mechanisms is the reachability problem decidable?This survey reports on recent results that aim to understand the impact of the storage mechanism on decidability and complexity of several variants of the reachability problem. The considered problems are configuration reachability, model-checking first-order logic with reachability, and reachability under bounded context switching and scope-boundedness.

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Silent Transitions in Automata with Storage

Cited by 15 publications

References 21 publications

The emptiness problem for valence automata over graph monoids

The emptiness problem for valence automata over graph monoids

Language classes associated with automata over matrix groups

Recent Advances on Reachability Problems for Valence Systems (Invited Talk)

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