论文信息 - Positional Simulation of Two-Way Automata: Proof of a Conjecture of R. Kannan and Generalizations

Positional Simulation of Two-Way Automata: Proof of a Conjecture of R. Kannan and Generalizations

Abstract R. Kannan conjectured that every non-deterministic two-way finite automaton can be positionally simulated by a deterministic two-way finite automaton. The conjecture is proved here by reduction to a similar problem about finite monoids. The method and the result are then generalized to alternating two-way finite automata, certain alternating one-tape linear-time Turing machines, and one-pebble automata.

Jean-Camille Birget

[1] Jean-Pierre Pécuchet. Automates Boustrophedon, Semi-Groupe de Birget et Monoide Inversif Libre , 1985, RAIRO Theor. Informatics Appl..

[2] Harry B. Hunt,et al. On the time and tape complexity of languages I , 1973, STOC.

[3] Jeffrey D. Ullman,et al. Introduction to Automata Theory, Languages and Computation , 1979 .

[4] Richard J. Lipton,et al. Alternating Pushdown Automata (Preliminary Report) , 1978, FOCS.

[5] Ravi Kannan,et al. Alternation and the power of nondeterminism , 1983, STOC.

[6] Ernst L. Leiss,et al. On Equations for Regular Languages, Finite Automata, and Sequential Networks , 1980, Theor. Comput. Sci..

[7] F. C. Hennie,et al. One-Tape, Off-Line Turing Machine Computations , 1965, Inf. Control..

[8] Jean-Camille Birget. Proof of a conjecture of R. Kannan , 1989, STOC '89.

[9] Dexter Kozen,et al. On parallelism in turing machines , 1976, 17th Annual Symposium on Foundations of Computer Science (sfcs 1976).

[10] Jean-Camille Birget. Concatenation of Inputs in a Two-Way Automaton , 1989, Theor. Comput. Sci..

[11] Jean-Camille Birget,et al. Arbitrary vs. regular semigroups , 1984 .

[12] Richard J. Lipton,et al. Alternating Pushdown and Stack Automata , 1984, SIAM J. Comput..

[13] John C. Shepherdson,et al. The Reduction of Two-Way Automata to One-Way Automata , 1959, IBM J. Res. Dev..