# Note on the Succinctness of Deterministic, Nondeterministic, Probabilistic and Quantum Finite Automata

Carlo Mereghetti; Beatrice Palano; Giovanni Pighizzini

RAIRO - Theoretical Informatics and Applications (2010)

- Volume: 35, Issue: 5, page 477-490
- ISSN: 0988-3754

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topMereghetti, Carlo, Palano, Beatrice, and Pighizzini, Giovanni. "Note on the Succinctness of Deterministic, Nondeterministic, Probabilistic and Quantum Finite Automata." RAIRO - Theoretical Informatics and Applications 35.5 (2010): 477-490. <http://eudml.org/doc/222058>.

@article{Mereghetti2010,

abstract = {
We investigate the succinctness of several kinds of unary automata by studying
their state complexity in accepting the family \{Lm\} of cyclic
languages, where Lm = akm | k ∈ N. In particular, we show that,
for any m, the number of states necessary and sufficient for accepting
the unary language Lm with isolated cut point on one-way probabilistic
finite automata is $p_1^\{\alpha_1\}+ p_2^\{\alpha_2\} +\cdots +p_s^\{\alpha_s\}$,
with $p_1^\{\alpha_1\}p_2^\{\alpha_2\} \cdots p_s^\{\alpha_s\}$ being the
factorization of m. To prove this result, we give a general state
lower bound for accepting unary languages with isolated cut point on the
one-way probabilistic model. Moreover, we exhibit one-way quantum finite
automata that, for any m, accept Lm with isolated cut point and only
two states. These results are settled within a survey on unary automata
aiming to compare the descriptional power of deterministic, nondeterministic,
probabilistic and quantum paradigms.
},

author = {Mereghetti, Carlo, Palano, Beatrice, Pighizzini, Giovanni},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Deterministic; nondeterministic; probabilistic; quantum unary
finite automata.; unary automata; cyclic languages},

language = {eng},

month = {3},

number = {5},

pages = {477-490},

publisher = {EDP Sciences},

title = {Note on the Succinctness of Deterministic, Nondeterministic, Probabilistic and Quantum Finite Automata},

url = {http://eudml.org/doc/222058},

volume = {35},

year = {2010},

}

TY - JOUR

AU - Mereghetti, Carlo

AU - Palano, Beatrice

AU - Pighizzini, Giovanni

TI - Note on the Succinctness of Deterministic, Nondeterministic, Probabilistic and Quantum Finite Automata

JO - RAIRO - Theoretical Informatics and Applications

DA - 2010/3//

PB - EDP Sciences

VL - 35

IS - 5

SP - 477

EP - 490

AB -
We investigate the succinctness of several kinds of unary automata by studying
their state complexity in accepting the family {Lm} of cyclic
languages, where Lm = akm | k ∈ N. In particular, we show that,
for any m, the number of states necessary and sufficient for accepting
the unary language Lm with isolated cut point on one-way probabilistic
finite automata is $p_1^{\alpha_1}+ p_2^{\alpha_2} +\cdots +p_s^{\alpha_s}$,
with $p_1^{\alpha_1}p_2^{\alpha_2} \cdots p_s^{\alpha_s}$ being the
factorization of m. To prove this result, we give a general state
lower bound for accepting unary languages with isolated cut point on the
one-way probabilistic model. Moreover, we exhibit one-way quantum finite
automata that, for any m, accept Lm with isolated cut point and only
two states. These results are settled within a survey on unary automata
aiming to compare the descriptional power of deterministic, nondeterministic,
probabilistic and quantum paradigms.

LA - eng

KW - Deterministic; nondeterministic; probabilistic; quantum unary
finite automata.; unary automata; cyclic languages

UR - http://eudml.org/doc/222058

ER -

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## Citations in EuDML Documents

top- Maria Paola Bianchi, Giovanni Pighizzini, Normal forms for unary probabilistic automata
- Maria Paola Bianchi, Giovanni Pighizzini, Normal forms for unary probabilistic automata
- Maria Paola Bianchi, Giovanni Pighizzini, Normal forms for unary probabilistic automata
- Shenggen Zheng, Jozef Gruska, Daowen Qiu, On the state complexity of semi-quantum finite automata
- Carlo Mereghetti, Beatrice Palano, Quantum finite automata with control language

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