R. Freivalds. On the growth of the number of states in result of determinization of probabilistic finite automata. Automatic Control and Computer Sciences 13(3), 1982, pp. 39--42.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....probability of correctness. Another open problem involves the blow up in size while simulating a 1 way probabilistic finite automata (PFA) by a 1 way QFA. The only known way for doing this is by simulating the PFA by a 1 way DFA and then simulating the DFA by a QFA. Both simulating a PFA by a DFA [1, 8, 12] and simulating a DFA by a QFA (this paper) can involve exponential or nearly exponential increase in size. This means that the straightforward simulation of a probabilistic automaton by a QFA (described above) could result in a doubly exponential increase in the size. However, we do not know of ....

R. Freivalds. On the growth of the number of states in result of determinization of probabilistic finite automata. Automatic Control and Computer Sciences 13(3), 1982, pp. 39--42.

....Murtazina[GM79] However, even after these improvements the estimate remained exponential, only the base of the exponent became smaller. Construction of concrete languages for which deterministic automata are more complex than probabilistic ones appeared to be quite a complicated problem. Freivalds[Fr82] constructed probabilistic nite automata with n states for which the smallest equivalent deterministic automaton contains (2 p n ) states. The problem of constructing probabilistic automata with n states such that any equivalent deterministic automaton contains a n states still remains ....

....with isolated cutpoint which accepts Lm and has O(m log 2 m log log m ) states. Proof. We shall construct an automaton accepting Lm with the probability 3=4. For other accepting probabilities the construction is similar. In our construction we shall use automata constructed by Freivalds[Fr82] as subroutines. Freivalds[Fr82] considered automata in a one letter alphabet and proved the following result: Lemma 3 [Fr82] There exists a probabilistic nite automaton with an isolated cutpoint that recognizes whether the word consists of exactly n words and has O( log 2 n log log n ) ....

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R. Freivalds, On the growth of the number of states in result of determinization of probabilistic nite automata, Avtomatika i Vicislitelnaja Tehnika, 1982, N.3, 39-42 (in Russian)

....probability of correctness. Another open problem involves the blow up in size while simulating a 1 way probabilistic finite automata (PFA) by a 1 way QFA. The only known way for doing this is by simulating the PFA by a 1 way DFA and then simulating the DFA by a QFA. Both simulating a PFA by a DFA [1, 8, 12] and simulating a DFA by a QFA (this paper) can involve exponential or nearly exponential increase in size. This means that the straightforward simulation of a probabilistic automaton by a QFA (described above) could result in a doubly exponential increase in the size. However, we do not know of ....

R. Freivalds. On the growth of the number of states in result of determinization of probabilistic finite automata. Automatic Control and Computer Sciences 13(3), 1982, pp. 39--42.

....probability of correctness. Another open problem involves the blow up in size while simulating a 1 way probabilistic finite automata (PFA) by a 1 way QFA. The only known way for doing this is by simulating the PFA by a 1 way DFA and then simulating the DFA by a QFA. Both simulating a PFA by a DFA [1, 6, 10] and simulating a DFA by a QFA (this paper) can involve exponential or nearly exponential increase in size. This means that the straightforward simulation of a probabilistic automaton by a QFA (described above) could result in a doubly exponential increase in the size. However, we do not know of ....

R. Freivalds, On the growth of the number of states in result of determinization of probabilistic finite automata. Automatic Control and Computer Sciences, 1982, no. 3, 39-42.

....probability function) is mapping X x Q x Q into interval [0, 1] such that 7r(a, qi, qj) qj Q Construction of concrete languages for which the size of deterministic automata exceeds the size of all equivalent probabilistic automata has appeared to be quite a complicated problem. Freivalds[Fre82] constructed probabilistic finite automata with n states for which the smallest equivalent deterministic automa ton contains 7(2 v) states. The problem of constructing probabilistic automata with n states such that any equivalent deterministic automaton contains a states still remains open. ....

....1 e. Theorem 22 Any deterministic 1 way finite automaton recognizing Lp has at least p states. Generally, 1 way probabilistic finite automata can recognize some languages with the number of states being close to the logarithm of the number of states needed by a deterministic automaton[Amb96,Fre82]. However, this is not the case with Lp. Theorem 23 [AF98] Any 1 way probabilistic finite automaton recognizing Lp with probability 1 2 e, for a fixed e O, has at least p states. Corollary 21 [AF98] There is a language Lp such that the number of states needed by a probabilistic automaton is ....

Rfisi Freivalds. On the growth of the number of states in result of determinization of probabilistic finite automata. Avtomatika i Vychislitel'naya Tehnika, No. 3, 39-42, 1982. (in Russian).

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