Visits, Crosses, and Reversals for Nondeterministic Off-Line Machines

The different concepts involved in “reversal complexity”counting reversals (sweeps), visits to a square, or crossing sequences—are discussed for non-deterministic off-line Turing machines with one working tape and for preset Turing machines, a generalization of two-way checking automata. Restriction to finite reversals or visits or crosses yields the same family, NSPACE(log2n), for off-line one working tape Turing machines or for two-way checking automata. For each k, a k-reversal bounded machine has the power of a nondeterministic k-head finite automaton. Finite visit preset Turing machines with working tapes selected from context-free languages yield %plane1D;4AB;. For an arbitrary bounding function T(n), a T(n) reversal or visit bound on a nondeterministic off-line Turing machine corresponds to a T(n) log2 n space bound within a linear factor. However, there is no general linear speedup theorem for reversal bounds on a nondeterministic off-line Turing machine.

[1]  Patrick C. Fischer The Reduction of Tape Reversals for Off-Line One-Tape Turing Machines , 1968, J. Comput. Syst. Sci..

[2]  Roland Vollmar,et al.  Note on Tape Reversal Complexity of Languages , 1970, Inf. Control..

[3]  Sheila A. Greibach,et al.  One Way Finite Visit Automata , 1978, Theor. Comput. Sci..

[4]  Brenda S. Baker,et al.  Reversal-Bounded Multipushdown Machines , 1974, J. Comput. Syst. Sci..

[5]  Richard Edwin Stearns,et al.  Hierarchies of memory limited computations , 1965, SWCT.

[6]  J. Hopcroft,et al.  An Approach to a Unified Theory of Automata , 1967, SWAT.

[7]  Seymour Ginsburg,et al.  Principal AFL , 1970, J. Comput. Syst. Sci..

[8]  Alfred V. Aho,et al.  A Characterization of Two-Way Deterministic Classes of Languages , 1970, J. Comput. Syst. Sci..

[9]  Sheila A. Greibach,et al.  Checking Automata and One-Way Stack Languages , 1969, J. Comput. Syst. Sci..

[10]  Sheila A. Greibach,et al.  Time- and Tape-Bounded Turing Acceptors and AFLs , 1970, J. Comput. Syst. Sci..

[11]  Alfred V. Aho,et al.  A Characterization of Two-Way Deterministic Classes of Languages , 1969, J. Comput. Syst. Sci..

[12]  Oscar H. Ibarra,et al.  On Two-way Multihead Automata , 1973, J. Comput. Syst. Sci..

[13]  Seymour Ginsburg,et al.  Abstract Families of Languages , 1967, SWAT.

[14]  Juris Hartmanis Tape-Reversal Bounded Turing Machine Computations , 1968, J. Comput. Syst. Sci..

[15]  Sheila A. Greibach A Note on the Recognition of One Counter Languages , 1975, RAIRO Theor. Informatics Appl..

[16]  J. Hartmanis,et al.  On the Computational Complexity of Algorithms , 1965 .

[17]  Manuel Blum,et al.  Tape Reversal Complexity Hierarchies , 1968, SWAT.

[18]  Oscar H. Ibarra,et al.  Characterizations of Some Tape and Time Complexity Classes of Turing Machines in Terms of Multihead and Auxiliary Stack Automata , 1971, J. Comput. Syst. Sci..

[19]  Stephen A. Cook,et al.  Characterizations of Pushdown Machines in Terms of Time-Bounded Computers , 1971, J. ACM.

[20]  Seymour Ginsburg,et al.  Stack automata and compiling , 1967, JACM.

[21]  Michael J. Fischer Two Characterizations of the Context-Sensitive Languages , 1969, SWAT.

[22]  A. R. Meyer,et al.  Refinements of the Nondeterministic Time and Space Hierarchies , 1973, SWAT.

[23]  Jeffrey D. Ullman,et al.  Relations Between Time and Tape Complexities , 1968, JACM.

[24]  Sheila A. Greibach Remarks on the Complexity of Nondeterministic Counter Languages , 1976, Theor. Comput. Sci..