Homomorphisms and inverse homomorphisms on graph-walking automata

被引:0
|
作者
Martynova, Olga [1 ]
Okhotin, Alexander [1 ]
机构
[1] St Petersburg State Univ, Dept Math & Comp Sci, 7 9 Universitetskaya Nab, St Petersburg 199034, Russia
关键词
Graph-walking automata; Tree-walking automata; Tree automata; Homomorphisms; State complexity; STATE COMPLEXITY; FINITE; OPERATIONS;
D O I
10.1016/j.tcs.2023.114197
中图分类号
TP301 [理论、方法];
学科分类号
081202 ;
摘要
Graph-walking automata analyze an input graph by moving between its nodes, following the edges. This paper investigates the effect of node-replacement graph homomorphisms and inverse homomorphisms on recognizability by these automata. For deterministic graph-walking automata, it is shown that the family of graph languages they recognize is closed under inverse homomorphisms: for an n-state automaton, the inverse homomorphic images of the graphs it accepts can be recognized by an automaton with at most kn + 1 states, where k is the number of labels of edge end-points in the pre-image graphs. At the same time, it is proved that in the worst case these inverse homomorphic images require a deterministic graph-walking automaton with at least kn states. The upper bound kn + 1 also holds for nondeterministic graph-walking automata. The second result is that already for tree-walking automata, both deterministic and nondeterministic, the families they recognize are not closed under injective homomorphisms. Here the proof is based on a new homomorphic characterization of regular tree languages: every regular tree language is representable as h(-1)(g(all trees)), for some injective node-replacement homomorphisms g and h.(c) 2023 Elsevier B.V. All rights reserved.
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页数:15
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