Word problems requiring exponential time(Preliminary Report)

@article{Stockmeyer1973WordPR,
  title={Word problems requiring exponential time(Preliminary Report)},
  author={L. Stockmeyer and A. Meyer},
  journal={Proceedings of the fifth annual ACM symposium on Theory of computing},
  year={1973}
}
  • L. Stockmeyer, A. Meyer
  • Published 1973
  • Computer Science
  • Proceedings of the fifth annual ACM symposium on Theory of computing
The equivalence problem for Kleene's regular expressions has several effective solutions, all of which are computationally inefficient. In [1], we showed that this inefficiency is an inherent property of the problem by showing that the problem of membership in any arbitrary context-sensitive language was easily reducible to the equivalence problem for regular expressions. We also showed that with a squaring abbreviation ( writing (E)2 for E×E) the equivalence problem for expressions required… Expand
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  • Mathematics, Computer Science
  • 22nd Annual Symposium on Foundations of Computer Science (sfcs 1981)
  • 1981
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References

SHOWING 1-10 OF 21 REFERENCES
Formal languages and their relation to automata
  • J. Hopcroft, J. Ullman
  • Computer Science
  • Addison-Wesley series in computer science and information processing
  • 1969
TLDR
The theory of formal languages as a coherent theory is presented and its relationship to automata theory is made explicit, including the Turing machine and certain advanced topics in language theory. Expand
The complexity of theorem-proving procedures
  • S. Cook
  • Computer Science, Mathematics
  • STOC
  • 1971
It is shown that any recognition problem solved by a polynomial time-bounded nondeterministic Turing machine can be “reduced” to the problem of determining whether a given propositional formula is aExpand
Derivatives of Regular Expressions
TLDR
In this paper the notion of a derivative of a regular expression is introduced atld the properties of derivatives are discussed and this leads, in a very natural way, to the construction of a state diagram from a regularexpression containing any number of logical operators. Expand
A Note Concerning Nondeterministic Tape Complexities
A set of sufficient condit ions on tape funct ions Ll(n) and L2(n) is presented t h a t guarantees the existence of a set accepted by an Ll (n) tape bounded nondeterminis t ic Turing machine, bu tExpand
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
Elementary bounds for presburger arithmetic
  • D. Oppen
  • Mathematics, Computer Science
  • STOC
  • 1973
TLDR
It is proved here that there exists a decision procedure for this theory of integers under addition, involving quantifier elimination, for which there is a superexponential upper bound on the size of formula produced when all variables have been eliminated. Expand
A hierarchy for nondeterministic time complexity
  • S. Cook
  • Mathematics, Computer Science
  • STOC
  • 1972
TLDR
For any real numbers r1, r2, 1 ≤ r1 < r2 , there is a set A of strings which has nondeterministic time complexity nr2 but not nondeterdependencies nr1, and the computing devices are non-deterministic multitape Turing machines. Expand
A Procedure for Checking Equality of Regular Expressions
TLDR
A simple “mechanical” procedure is described for checking equality of regular expressions, based on the work of A. Salomaa, which uses derivatives ofregular expressions and transition graphs to generate a finite set of left-linear equations. Expand
A note on disjunctive form tautologies
Cook [1] and Karp [2] have shown that a large class of combinatorial decision problems can be solved in time bounded by a polynomial in the size of the problem iff there is a polynomial timeExpand
On Effective Procedures for Speeding Up Algorithms
  • M. Blum
  • Mathematics, Computer Science
  • JACM
  • 1971
TLDR
If one has an algorithm for a given function f, and if there is an algorithm which is faster on all but a finite number of inputs, then even though one cannot get this faster algorithm effectively, one can still obtain a pseudo- speedup: this is a very fast algorithm which computes a variant of the function, one which differs from the original function on a finiteNumber of inputs. Expand
...
1
2
3
...