Reversibility of computations in graph-walking automata

Kunc, Michal; Okhotin, Alexander

doi:10.1016/j.ic.2020.104631

Cited by 11 publications

(19 citation statements)

References 33 publications

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“…It begins with a generalization of an alphabet to the case of graphs: a signature. Definition 1 (Kunc and Okhotin [13]). A signature S is a quintuple S = (D, −, Σ, Σ 0 , (D a ) a∈Σ ), where:…”

Section: Graph-walking Automatamentioning

confidence: 99%

“…On the other hand, Disser et al [5] recently proved that if such an automaton is additionally equipped with O(log log n) memory and O(log log n) pebbles, then it can traverse every graph with n nodes, and this amount of resources is optimal. For graph-walking automata, there are results on the construction of halting and reversible automata by Kunc and Okhotin [13], as well as recent lower bounds on the complexity of these transformations established by the authors [15].…”

Section: Introductionmentioning

confidence: 99%

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Homomorphisms on graph-walking automata

Martynova¹,

Okhotin²

2021

Preprint

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Graph-walking automata (GWA) are a model for graph traversal using finitestate control: these automata move between the nodes of an input graph, following its edges. This paper investigates the effect of node-replacement graph homomorphisms on recognizability by these automata. It is not difficult to see that the family of graph languages recognized by GWA is closed under inverse homomorphisms. The main result of this paper is that, for n-state automata operating on graphs with k labels of edge end-points, the inverse homomorphic images require GWA with kn + O(1) states in the worst case. The second result is that already for tree-walking automata, the family they recognize is not closed under injective homomorphisms. Here the proof is based on an easy homomorphic characterization of regular tree languages.

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Section: Graph-walking Automatamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Homomorphisms on graph-walking automata

Martynova¹,

Okhotin²

2021

Preprint

Self Cite

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“…Definition 1 (Kunc and Okhotin [9]). A signature S consists of • A finite set D of directions, that is, labels attached to edge end-points;…”

Section: Graph-walking Automata and Their Subclassesmentioning

confidence: 99%

“…For the general case of GWA, constructions of halting, returning and reversible automata were given by Kunc and Okhotin [9], who showed that an n-state GWA operating on graphs with k edge labels can be transformed to a returning GWA with 3nk states and to a reversible GWA with 6nk + 1 states, which is always halting. Applied to special cases of GWA, such as TWA or multi-head automata, these generic constructions produce fewer states than the earlier specialized constructions.…”

Section: Introductionmentioning

confidence: 99%

“…The goal of this paper is to obtain lower bounds on the complexity of these transformations. To begin with, the constructions by Kunc and Okhotin [9] are revisited in Section 3, and it turns out that the elements they are built of can be recombined more efficiently, resulting in improved upper bounds based on the existing methods. This way, the transformation to a returning GWA is improved to use 2nk + n states, the transformation to halting can use 2nk + 1 states, and constructing a reversible GWA (which is both returning and halting) requires at most 4nk + 1 states.…”

Section: Introductionmentioning

confidence: 99%

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State complexity of halting, returning and reversible graph-walking automata

Martynova,

Okhotin

2020

Preprint

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Graph-walking automata (GWA) traverse graphs by moving between the nodes following the edges, using a finite-state control to decide where to go next. It is known that every GWA can be transformed to a GWA that halts on every input, to a GWA returning to the initial node in order to accept, and to a reversible GWA. This paper establishes lower bounds on the state blow-up of these transformations, as well as closely matching upper bounds. It is shown that making an n-state GWA traversing k-ary graphs halt on every input requires at most 2nk + 1 states and at least 2(n − 1)(k − 3) states in the worst case; making a GWA return to the initial node before acceptance takes at most 2nk + n and at least 2(n − 1)(k − 3) states in the worst case; Automata satisfying both properties at once have at most 4nk + 1 and at least 4(n − 1)(k − 3) states in the worst case. Reversible automata have at most 4nk + 1 and at least 4(n − 1)(k − 3) − 1 states in the worst case.

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State Complexity of Union and Intersection on Graph-Walking Automata

Мартынова

Okhotin

2021

Descriptional Complexity of Formal Systems

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Reversibility of computations in graph-walking automata

Cited by 11 publications

References 33 publications

Homomorphisms on graph-walking automata

Homomorphisms on graph-walking automata

State complexity of halting, returning and reversible graph-walking automata

State Complexity of Union and Intersection on Graph-Walking Automata

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