Minimal NFA and biRFSA Languages

Michel Latteux, Yves Roos, Alain Terlutte
2008 RAIRO - Theoretical Informatics and Applications  
In this paper, we define the notion of biRFSA which is a residual finate state automaton (RFSA) whose the reverse is also an RFSA. The languages recognized by such automata are called biRFSA languages. We prove that the canonical RFSA of a biRFSA language is a minimal NFA for this language and that each minimal NFA for this language is a sub-automaton of the canonical RFSA. This leads to a characterization of the family of biRFSA languages. In the second part of this paper, we define the family
more » ... of biseparable automata. We prove that every biseparable NFA is uniquely minimal among all NFAs recognizing a same language, improving the result of H. Tamm and E. Ukkonen for bideterministic automata. Mathematics Subject Classification. 68Q45. The structure of deterministic finite automata (DFA) recognizing a given recognizable set L is simple since these DFAs have a common model, the unique minimal
doi:10.1051/ita:2008022 fatcat:jiddeu562jctva3ngtnyf67e6y