On transition minimality of bideterministic automata

Authors:
Hellis Tamm
Affiliations:
Institute of Cybernetics, Estonia
Venue:
DLT'07 Proceedings of the 11th international conference on Developments in language theory
Year:
2007

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Abstract

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 ∈-NFAs.