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Laura Mančinska, Māris Ozols, Renāte Praude, Agnese Zalcmane

This article discusses limitations of Unary Nondeterministic Finite Automata, focusing on subset automatons, unreachable subsets, and the number of states. Results show insights on the reachability of states in UNFAs. Presented by Laura Mančinska, Māris Ozols, Renāte Praude, Agnese Zalcmane from the Department of Computer Science at the University of Latvia.

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Laura Mančinska, Māris Ozols, Renāte Praude, Agnese Zalcmane

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  1. Limitations ofUnary Finite Automata Laura Mančinska, Māris Ozols, Renāte Praude, Agnese Zalcmane Department of Computer Science,University of Latvia

  2. q2 {q1,q2} {q1,q3,q4,q5} {q1,q2,q3,q4} q1 q3 q4 q5 Unary Nondeterministic Finite Automata • UNFA is a quadruple (Q, f, Qa, Q0) where • Q – finite set of statesf: Q  2Q – transition functionQa Q – set of accepting statesQ0 Q – set of initial states Automaton accepts word of length L IFF there exists a path of length L from some initial state to some accepting state. “Subset automaton” for given UNFA:

  3. Result #1 An easy argument why approximately 1/4 of all subsets of state set are unreachable. Result #2 For every fixed kÎ{2, ..., number of states - 2} at least one subset of size k is unreachable.

  4. Thank you for attention!

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