Article
A Note on TwoDimensional Probabilistic Finite Automata.
Information Sciences (Impact Factor: 4.04). 10/1998; 110:303314. DOI: 10.1016/S00200255(98)000085
Source: DBLP
ABSTRACT
This note introduces twodimensional probabilistic finite automata (2pfa's), and investigates several properties of them. We first show that the class of sets recognized by 2pfa's with bounded error probability, 2PFA, is incomparable with the class of sets accepted by twodimensional alternating finite automata. We then show that 2PFA is not closed under row catenation, column catenation, row +, and column + operations in Siromoney et al. (G. Siromoney, R. Siromoney, K. Krithivasan, Inform. and Control 22 (1973) 447).
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ABSTRACT: This paper investigates closure properties of the classes of sets recognized by spacebounded twodimensional probabilistic Turing machines with error probability less than 12. Let 2PTM(L(m,n)) be the class of sets recognized by L(m,n) spacebounded twodimensional probabilistic Turing machines with error probability less than 12, where L(m, n): N2 → N (N denotes the set of all the positive integers) be a function with two variables m (= the number of rows of input tapes) and n (= the number of columns of input tapes). We first show that (i) for any function ƒ(m) = o(logm) (resp., ƒ(m) = o(log m/log log m)) and any monotonic nondecreasing function g(n) which can be constructed by some onedimensional deterministic Turing machine, 2PTM(L(m, n)) is not closed under row catenation, row closure, and projection, where L(m, n) = ƒ(m)+ g(n) (resp., L(m,n) = ƒ(m) × g(n)), and (ii) for any function g(n) = o(log n) (resp., g(n) = o(logn/loglogn)) and any monotonic nondecreasing function ƒ(m) which can be constructed by some onedimensional deterministic Turing machine, 2PTM(L(m, n)) is not closed under column catenation, column closure, and projection, where L(m,n) = ƒ(m)+g(n)(resp., L(m, n) = ƒ(m) × g(n)). We then show that 2PTMT(L(m, n)) is closed under union, intersection, and complementation for any L(m, n), where 2PTMT(L(m, n)) denotes the class of sets recognized by L(m, n) spacebounded twodimensional probabilistic Turing machines with error probability less than 12 which always halt in the accepting or rejecting state for all the input tapes.Information Sciences 04/1999; 115(14):6181. DOI:10.1016/S00200255(98)100841 · 4.04 Impact Factor  International Journal of Pattern Recognition and Artificial Intelligence 06/2000; 14:477500. DOI:10.1142/S0218001400000313 · 0.67 Impact Factor

Conference Paper: A Space Lower Bound of TwoDimensional Probabilistic Turing Machines.
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ABSTRACT: This paper shows a sublogarithmic space lower bound for twodimensional probabilistic Turing machines (2ptm’s) over square tapes with bounded error, and shows, using this space lower bound theorem, that a specific set is not recognized by any o(log n) spacebounded 2 ptm. Furthermore, the paper investigates a relationship between 2ptm's and twodimensional Turing machines with both nondeterministic and probabilistic states, which we call “twodimensional stochastic Turing machines (2stm’s)”, and shows that for any loglog n ≤ L(n) = o(log n), L(n) spacebounded 2ptm’s with bounded error are less powerful than L(n) spacebounded 2stm’s with bounded error which start in nondeterministic mode, and make only one alternation between nondeterministic and probabilistic modes.Developments in Language Theory, 6th International Conference, DLT 2002, Kyoto, Japan, September 1821, 2002, Revised Papers; 01/2002
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