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Laura Mančinska, Māris Ozols, Renāte Praude, Agnese Zalcmane

Limitations of Unary Finite Automata. Laura Mančinska, Māris Ozols, Renāte Praude, Agnese Zalcmane. Department of Computer Science, University of Latvia. q 2. {q 1 ,q 2 }. {q 1 ,q 3 ,q 4 ,q 5 }. {q 1 ,q 2 ,q 3 ,q 4 }. q 1. q 3. q 4. q 5. Unary Nondeterminist i c Finite Automata.

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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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