On Transition Minimality of Bideterministic Automata
- Cite this paper as:
- Tamm H. (2007) On Transition Minimality of Bideterministic Automata. In: Harju T., Karhumäki J., Lepistö A. (eds) Developments in Language Theory. DLT 2007. Lecture Notes in Computer Science, vol 4588. Springer, Berlin, Heidelberg
Bideterministic automata are deterministic automata with the property of their reversal automata also being deterministic. Bideterministic automata have previously been shown to be unique (up to an isomorphism) minimal NFAs with respect to the number of states. In this paper, we show that in addition to state minimality, bideterministic automata are also transition-minimal NFAs. However, as this transition minimality is not necessarily unique, we also present the necessary and sufficient conditions for a bideterministic automaton to be uniquely transition-minimal among NFAs. Furthermore, we show that bideterministic automata are transition-minimal ε-NFAs.
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