A Note on Two-Dimensional Probabilistic Finite Automata.
ABSTRACT This note introduces two-dimensional probabilistic finite automata (2-pfa's), and investigates several properties of them. We first show that the class of sets recognized by 2-pfa's with bounded error probability, 2-PFA, is incomparable with the class of sets accepted by two-dimensional alternating finite automata. We then show that 2-PFA 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).
- SourceAvailable from: psu.edu
Conference Proceeding: A Lower Bound For Probabilistic Algorithms For Finite State MachinesFoundations of Computer Science, 1984. 25th Annual Symposium on; 11/1984
Conference Proceeding: Two-Dimensional Alternating Turing Machines[show abstract] [hide abstract]
ABSTRACT: This paper introduces a two-dimensional alternating Turing machine (2-ATM) which can be considered as a natural extension of a one-dimensional alternating Turing machine to two dimensions. This paper also introduces a three-way two-dimensional alternating Turing machine (TR2-ATM) which is an alternating version of a three-way two-dimensional Turing machine. We first investigate a relationship between the accepting powers of space bounded 2-ATM's (or TR2-ATM's) and ordinary space bounded two-dimensional Turing machines (or three-way two-dimensional Turing machines). We then introduce a simple, natural new complexity measure for 2-ATM's (or TR2-ATM's), called ‘leaf-size’, and provide a spectrum of complexity classes based on leaf-size bounded computations. We finally investigate recognizability of connected patterns by 2-ATM's (or TR2-ATM's).Proceedings of the 14th Annual ACM Symposium on Theory of Computing, May 5-7, 1982, San Francisco, California, USA; 01/1982
- [show abstract] [hide abstract]
ABSTRACT: An investigation of interactive proof systems (IPSs) where the verifier is a 2-way probabilistic finite state automaton (2pfa) is initiated. In this model, it is shown:(1) IPSs in which the verifier uses private randomization are strictly more powerful than IPSs in which the random choices of the verifier are made public to the prover.(2) IPSs in which the verifier uses public randomization are strictly more powerful than 2pfa's alone, that is, without a prover.(3) Every language which can be accepted by some deterministic Turing machine in exponential time can be accepted by some IPS.Additional results concern two other classes of verifiers: 2pfa's that halt in polynomial expected time, and 2-way probabilistic pushdown automata that halt in polynomial time. In particular, IPSs with verifiers in the latter class are as powerful as IPSs where verifiers are polynomial-time probabilistic Turing machines. In a companion paper , zero knowledge IPSs with 2pfa verifiers are investigated.J. ACM. 01/1992; 39:800-828.