Tree-Size Bounded Alternation

@article{Ruzzo1980TreeSizeBA,
  title={Tree-Size Bounded Alternation},
  author={W. L. Ruzzo},
  journal={J. Comput. Syst. Sci.},
  year={1980},
  volume={21},
  pages={218-235}
}
  • W. L. Ruzzo
  • Published 1980
  • Computer Science, Mathematics
  • J. Comput. Syst. Sci.
The size of an accepting computation tree of an alternating Turing machine (ATM) is introduced as a complexity measure. We present a number of applications of tree-size to the study of more traditional complexity classes. Tree-size on ATMs is shown to closely correspond to time on nondeterministic TMs and on nondeterministic auxiliary pushdown automata. One application of the later is a useful new characterization of the class of languages log-space-reducible to context-free languages… Expand
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  • Computer Science
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References

SHOWING 1-10 OF 27 REFERENCES
Alternating pushdown automata
TLDR
It is shown that alternating pushdown automata are strictly more powerful than nondeterministic pushdown Automata and the number of alternations allowed during computations. Expand
Path systems and language recognition
  • S. Cook
  • Computer Science, Mathematics
  • STOC
  • 1970
TLDR
The main result, theorem 2, gives a bound on the storage required for a Turing machine to simulate certain time-bounded pushdown machines and the Theorem of Savitch stating that a non-deterministic L(n) - storage bounded Turing machine can be simulated by a deterministic (L(n))2 - storage bound Turing machine. Expand
Relationships Between Nondeterministic and Deterministic Tape Complexities
  • W. Savitch
  • Computer Science, Mathematics
  • J. Comput. Syst. Sci.
  • 1970
TLDR
The amount of storage needed to simulate a nondeterministic tape bounded Turingmachine on a deterministic Turing machine is investigated and a specific set is produced, namely the set of all codings of threadable mazes, such that, if there is any set which distinguishes nondeter microscopic complexity classes from deterministic tape complexity classes, then this is one such set. Expand
Time and Tape Bounded Auxiliary Pushdown Automata
TLDR
This work considers language families defined by nondeterministic and deterministic log(n)-tape bounded auxiliary pushdown automata within polynomial time and relates questions concerning these classes to other complexity classes and to questions concerning the tape complexity of context-free languages. Expand
On the Tape Complexity of Deterministic Context-Free Languages
TLDR
A tape hardest deterministic context-free language is described and the best upper bound known on the tape complexity of (deterministic) context- free languages is (log(n) 2). Expand
Space-Bounded Reducibility among Combinatorial Problems
  • N. Jones
  • Computer Science, Mathematics
  • J. Comput. Syst. Sci.
  • 1975
TLDR
Two versions of the polynomial time-reducibility of Cook and Karp are defined, by means of Turing machines and by bounded-quantifier formulas, and they are shown to be complete for nondeterministic (deterministic) log n space. Expand
On parallelism in turing machines
  • D. Kozen
  • Mathematics, Computer Science
  • 17th Annual Symposium on Foundations of Computer Science (sfcs 1976)
  • 1976
TLDR
A natural characterization of the polynomial time hierarchy of Stockmeyer and Meyer in terms of parallel machines is given, and a generalization of Saviten's result NONDET-L(n)-SPACE ⊆ L(n)2-SPACE is given. Expand
On uniform circuit complexity
  • W. L. Ruzzo
  • Mathematics, Computer Science
  • 20th Annual Symposium on Foundations of Computer Science (sfcs 1979)
  • 1979
TLDR
It is shown that simultaneous size/depth of uniform circuits is the same as space/time of alternating Turing machines, with depth and time within a constant factor and likewise log(size) and space. Expand
A Simulation Result for the Auxiliary Pushdown Automata
  • T. Harju
  • Mathematics, Computer Science
  • J. Comput. Syst. Sci.
  • 1979
TLDR
S(n)-tape bounded nondeterministic Turing machines can be simulated by S(n) bounded deterministic automata which have an auxiliary pushdown storage of length S2(n). Expand
A Note on Tape-Bounded Complexity Classes and Linear Context-Free languages
TLDR
The equivalence of the following statements, for 0 g ~ < 1, m shown by describing a log(n)-complete hnear language, is shown. Expand
...
1
2
3
...