Nondeterministic Biautomata and Their Descriptional Complexity
نویسندگان
چکیده
Biautomata were recently introduced in [4] as a generalization of ordinary deterministic finite automata. A biautomaton consists of a deterministic finite control, a read-only input tape, and two reading heads, one reading the input from left to right, and the other head reading the input from right to left. An input word is accepted by a biautomaton, if there is an accepting computation starting with the heads on the two ends of the word and meeting somewhere in an accepting state. Although the choice of reading a symbol by either head is nondeterministic, the determinism of the biautomaton is enforced by two properties, which will be described later. Descriptional complexity issues for deterministic biautomata were addressed in [3]. We focus on the descriptional complexity of nondeterministic biautomata, which are defined as follows: a nondeterministic biautomaton is a sixtuple A = (Q,Σ, ·, ◦, I, F ), where Q is a finite set of states, Σ is an alphabet, · : Q×Σ → 2 is the forward transition function, ◦ : Q × Σ → 2 is the backward transition function, I ⊆ Q is the set of initial states, and F ⊆ Q is the set of final states. The transition functions · and ◦ are extended to words in the following way, for every word v ∈ Σ∗ and letter a ∈ Σ:
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