Decision Problems for Restricted Variants of Two-Dimensional Automata
A two-dimensional finite automaton has a read-only input head that moves in four directions on a finite array of cells labelled by symbols of the input alphabet. A three-way two-dimensional automaton is prohibited from making upward moves, while a two-way two-dimensional automaton can only move downward and rightward.
We show that the language emptiness problem for unary three-way nondeterministic two-dimensional automata is Open image in new window -complete, and is in Open image in new window for general-alphabet two-way nondeterministic two-dimensional automata. We show that the language equivalence problem for two-way deterministic two-dimensional automata is decidable. This is the first known positive decidability result for the equivalence problem on two-dimensional automata over a general alphabet. We show that there exists a unary three-way deterministic two-dimensional automaton with a nonregular column projection, and we show that the row projection of a unary three-way nondeterministic two-dimensional automaton is always regular.
KeywordsDecision problem Language emptiness Language equivalence Three-way automata Two-dimensional automata Two-way automata
- 2.Blum, M., Hewitt, C.: Automata on a 2-dimensional tape. In: Miller, R.E. (ed.) SWAT 1967, pp. 155–160 (1967). https://doi.org/10.1109/FOCS.1967.6
- 3.Dong, J., Jin, W.: Comparison of two-way two-dimensional finite automata and three-way two-dimensional finite automata. In: Yang, X. (ed.) CSSS 2012, pp. 1904–1906 (2012). https://doi.org/10.1109/CSSS.2012.474
- 6.Hunt III, H.B.: On the time and tape complexity of languages I. In: Aho, A.V. (ed.) STOC 1973, pp. 10–19 (1973). https://doi.org/10.1145/800125.804030
- 16.Smith, T.J.: Two-dimensional automata. Technical report 2019–637, Queen’s University, Kingston (2019)Google Scholar
- 17.Taniguchi, K., Kasami, T.: Some decision problems for two-dimensional nonwriting automata. Trans. Inst. Electron. Comm. Engrs. Jpn. 54–C(7), 578–585 (1971)Google Scholar