On stateless multihead automata: Hierarchies and the emptiness problem

We look at stateless multihead finite automata in their two-way and one-way, deterministic and nondeterministic variations. The transition of a k -head automaton depends solely on the symbols currently scanned by its k heads, and every such transition moves each head one cell left or right, or instr...

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Published inTheoretical computer science Vol. 411; no. 3; pp. 581 - 593
Main Authors Ibarra, Oscar H., Karhumäki, Juhani, Okhotin, Alexander
Format Journal Article
LanguageEnglish
Published Oxford Elsevier B.V 06.01.2010
Elsevier
Subjects
Applied sciences
Computer science; control theory; systems
Exact sciences and technology
Language theory and syntactical analysis
Logic and foundations
Mathematical logic, foundations, set theory
Mathematics
Miscellaneous
Multihead automata
Recursion theory
Sciences and techniques of general use
Stateless automata
Theoretical computing
Stateless automata
Multihead automata
Finite automaton
Computer theory
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Summary:We look at stateless multihead finite automata in their two-way and one-way, deterministic and nondeterministic variations. The transition of a k -head automaton depends solely on the symbols currently scanned by its k heads, and every such transition moves each head one cell left or right, or instructs it to stay. We show that stateless ( k + 4 ) -head two-way automata are more powerful than stateless k -head two-way automata. In the one-way case, we prove a tighter result: stateless ( k + 1 ) -head one-way automata are more powerful than stateless k -head one-way automata. Finally, we show that the emptiness problem for stateless 2-head two-way automata is undecidable.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2009.09.001