Kaneps, J. Stochasticity of the languages recognizable by 2-way finite probabilistic automata Diskretnaya Matematika, 1989, vol. 1, no 4, pp. 63-77 (Russian). 17 Home/Search Document Not in Database Summary Related Articles Check |
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Space-Efficient Deterministic Simulation of Probabilistic Automata - Macarie (1993) (14 citations) (Correct)
.... weaker O(n) space deterministic simulation for 2 PFA s using the Markov chain tree theorem of Leighton and Rivest [LR 1986] In spite of the fact that the classes of languages recognized by PFA s and 2U PFA s are the same (if their transition probabilities are either all rationals or all reals) [Ka 1989], the class of languages recognized by 2 PFA s is larger than the class of languages recognized by PFA s with isolated cutpoint. Jung [Jung 1984] obtained an O(log n) deterministic space simulation for 2 PFA s. The main drawback of finite probabilistic automata is the fact that they do not seem ....
....do not fit in the Chomsky s hierarchy. The next step is to compare them with space bounded deterministic complexity classes. This problem is investigated in Section 3. We mention now a result relating complexity classes defined by one way and two way probabilistic finite automata. Theorem 2 [Ka 1989] S rat =2U PFA rat . In other words, every 2U PFA with rational transition probabilities can be simulated by a PFA with rational transition probabilities. 3 Space efficient deterministic simulation of stochastic languages In this section we compare the stochastic complexity classes we have ....
Kaneps, J. Stochasticity of the languages recognizable by 2-way finite probabilistic automata Diskretnaya Matematika, Vol. 1, no 4, 1989, pp. 63-77 (Russian).
On the Structure of Log-Space Probabilistic Complexity Classes - Macarie (1994) (Correct)
....even by languages over one letter alphabet. ffl The results of Theorem 9 are somewhat surprising. In general, when we reduce two way bounded error probabilistic automata to equivalent one way probabilistic automata the computation error does not remain bounded away from 1 2 . For example, see [Ka89]. ffl The result of Theorem 10 is stronger than the well known result PL = PL poly [Ju85] ffl From Theorem 11 it follows: P ae DSPACE(log k n) AM(2pfa(2) ae DSPACE(log k n) UAM(1pfa(2) ae DSPACE(log k n) UAM(1pcm(1) ae DSPACE(log k n) This can eventually help to ....
Kaneps, J. Stochasticity of the languages recognizable by 2-way finite probabilistic automata Diskretnaya Matematika, 1989, vol. 1, no 4, pp. 63-77 (Russian).
Connections Among Space-Bounded and Multihead Probabilistic.. - Macarie (1994) (Correct)
....we can decide X Y ,X = Y or X Y in O(log p n ) deterministic space. Observation 3 Combining the results of Theorems 1 and 4, we obtain PrSpace(log n) Dspace(log 2 n) Ju81] BCP83] 4 Open Problems Is the equality kPFA = kPFA stop true, for every k 2 N For k = 1, the equality holds [Ka89] [KaVe87] Are the classes kPFA , k 2 N , closed under complementation For k = 1 the answer is affirmative [Tur69] The same questions can be asked for bounded error and one sided error probabilistic finite automata. 5 Acknowledgments I am grateful to Joel Seiferas for reading an earlier version ....
Kaneps, J. Stochasticity of the languages recognizable by 2-way finite probabilistic automata Diskretnaya Matematika, 1989, vol. 1, no 4, pp. 63-77 (Russian).
Properties of Multihead Two-Way Probabilistic Finite Automata - Macarie (1994) (Correct)
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Kaneps, J. Stochasticity of the languages recognizable by 2-way finite probabilistic automata Diskretnaya Matematika, 1989, vol. 1, no 4, pp. 63-77 (Russian). 17
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