Finite automata and unary languages
Theoretical Computer Science
Relating the type of ambiguity of finite automata to the succinctness of their representation
SIAM Journal on Computing
Separating Exponentially Ambiguous Finite Automata from Polynomially Ambiguous Finite Automata
SIAM Journal on Computing
Introduction to the Theory of Computation
Introduction to the Theory of Computation
Errata to: "finite automata and unary languages"
Theoretical Computer Science
Economy of description by automata, grammars, and formal systems
SWAT '71 Proceedings of the 12th Annual Symposium on Switching and Automata Theory (swat 1971)
Unambiguous finite automata over a unary alphabet
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Pseudonoise sequences based on algebraic feedback shift registers
IEEE Transactions on Information Theory
Minimal DFA for symmetric difference NFA
DCFS'12 Proceedings of the 14th international conference on Descriptional Complexity of Formal Systems
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Okhotin [9] showed an exponential trade-off in the conversion from nondeterministic unary finite automata to unambiguous nondeterministic unary finite automata. In this paper, we consider the trade-off in the case of unary symmetric difference finite automata to finitely ambiguous unary symmetric difference finite automata. Surprisingly, the trade-off is linear in the number of states of the finite automaton. In particular, for every n-state unary nondeterministic symmetric difference finite automaton, there is an equivalent finitely ambiguous n-state unary symmetric difference nondeterministic finite automaton. We also note other relevant ambiguity issues in the unary case, such as the ambiguity of k-deterministic finite automata.