# On the Tape Complexity of Deterministic Context-Free Languages

@article{Sudborough1978OnTT, title={On the Tape Complexity of Deterministic Context-Free Languages}, author={Ivan Hal Sudborough}, journal={J. ACM}, year={1978}, volume={25}, pages={405-414} }

Let DSPACE(L(n)) denote the family of languages recognized by deterministic L(n)-tape bounded Turmg machines The pnnopal result described m this paper is the equivalence of the following statements (l) The determtmsttc context-free language L~ 2) (described m the paper) is m DSPACE(Iog(n)) (2) The simple LL(I) languages are m DSPACE(tog(n)) (3) The simple precedence languages are in DSPACE(Iog(n)). (4) DSPACE(Iog(n)) is identical to the famdy of languages recogmzed by deterministic two-way…

## 225 Citations

On deterministic context-free languages, multihead automata, and the power of an auxiliary pushdown store

- Computer ScienceSTOC '76
- 1976

It is shown that an auxiliary pushdown store does, in fact, add some power to some restricted families of log(n)-tape bounded Turing machines with restricted tape alphabets, and it is indicated that every 2k-head nondeterministic finite automation language can be recognized in 0(n3k) steps.

The complexity of the membership problem for some extensions of context-free languagest†

- Computer Science, Linguistics
- 1977

It is shown that the following families of languages can be recognized by deterministic multitape Turing machines either in polynomial time or within (log n)2 tape: the context independent developmental (EOL) languages; the simple matrix languages; and the languages generated by derivation restricted state grammars.

Tree-size bounded alternation(Extended Abstract)

- Computer ScienceSTOC
- 1979

The size of an accepting computation tree of an alternating Turing machine (ATM) is introduced as a complexity measure. Tree-size on ATM's is shown to closely correspond to time on nondeterministic…

Parallel Time O(log n) Acceptance of . . .

- Computer Science

This work shows that, if a context-free language is in fact deterministic, then O(log n) time recognition is indeed possible on a PRAM, and describes a well-known parallel algorithm for simulating a deterministic space-bounded Turing machine.

Time and Tape Bounded Auxiliary Pushdown Automata

- Computer ScienceMFCS
- 1977

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.

On the power of polynomial time bit-reductions

- Mathematics[1993] Proceedings of the Eigth Annual Structure in Complexity Theory Conference
- 1993

The question of how complex a leaf language must be in order to characterize some given class C is investigated, which leads to the examination of the closure of different language classes under bit-reducibility.

Parameterizations of Logarithmic-Space Reductions, Stack-State Complexity of Nonuniform Families of Pushdown Automata, and a Road to the LOGCFL⊆LOGDCFL/poly Question

- Computer ScienceArXiv
- 2021

This work introduces reasonable “parameterizations” ofLOGCFL and LOGDCFL and applies them as a technical tool to establish a close connection between the LOGCFL/poly question and the polynomial stack-state complexity of nonuniform families of two-way pushdown automata.

Counting and empty alternating pushdown automata ∗

- Computer Science
- 1992

It is shown that AC, SAC and P can be characterized as the logarithmic closure of certain types of languages, which are either those given by linear alternating grammars or they are languages which are recognized by alternating pushdown automata with the restriction that their storage has to be empty if they make an alternating transition.

On The Space Complexity Of Turn Bounded Pushdown Automata

- Computer ScienceInt. J. Comput. Math.
- 2003

It follows that finite-turn pushdown automata are logarithmic space bounded and the class of metalinear context-free languages is complete for NL, from which two corollaries follow.

## References

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On deterministic context-free languages, multihead automata, and the power of an auxiliary pushdown store

- Computer ScienceSTOC '76
- 1976

It is shown that an auxiliary pushdown store does, in fact, add some power to some restricted families of log(n)-tape bounded Turing machines with restricted tape alphabets, and it is indicated that every 2k-head nondeterministic finite automation language can be recognized in 0(n3k) steps.

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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.

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The time complexity of recognition of L_0, a context-free language, is the least upper bound for time complexity in terms of deterministic polynomial time acceptable languages.

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The s-languages are those languages recognized by a particular restricted form of deterministic pushdown automaton, called an s-machine, and it is shown that they have the prefix property, and that they include the regular sets with end-markers.

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The operator precedence languages are shown to be a proper subset of the backwards-deterministic Wirth-Weber precedence languages which in turn are a proper subclass of the deterministic context-free languages.