Intersection and union of regular languages and state complexity
Information Processing Letters
A lower bound technique for the size of nondeterministic finite automata
Information Processing Letters
Residual Finite State Automata
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
Bideterministic automata and minimal representations of regular languages
Theoretical Computer Science - Implementation and application of automata
Identification of biRFSA languages
Theoretical Computer Science - In honour of Professor Christian Choffrut on the occasion of his 60th birthday
Nondeterministic State Complexity of Basic Operations for Prefix-Free Regular Languages
Fundamenta Informaticae
CIAA'04 Proceedings of the 9th international conference on Implementation and Application of Automata
Finding lower bounds for nondeterministic state complexity is hard
DLT'06 Proceedings of the 10th international conference on Developments in Language Theory
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Residual finite state automata (RFSA) are a subclass of nondeterministic finite automata (NFA) with the property that every state of an RFSA defines a residual language of the language accepted by the RFSA. Recently, a notion of a biresidual automaton (biRFSA) – an RFSA such that its reversal automaton is also an RFSA – was introduced by Latteux, Roos, and Terlutte, who also showed that a subclass of biRFSAs called biseparable automata consists of unique state-minimal NFAs for their languages. In this paper, we present some new minimality results concerning biRFSAs and biseparable automata. We consider two lower bound methods for the number of states of NFAs – the fooling set and the extended fooling set technique – and present two results related to these methods. First, we show that the lower bound provided by the fooling set technique is tight for and only for biseparable automata. And second, we prove that the lower bound provided by the extended fooling set technique is tight for any language accepted by a biRFSA. Also, as a third result of this paper, we show that any reversible canonical biRFSA is a transition-minimal ε-NFA. To prove this result, the theory of transition-minimal ε-NFAs by S. John is extended.