# New problems complete for nondeterministic log space

@article{Jones2005NewPC,
title={New problems complete for nondeterministic log space},
author={Neil D. Jones and Y. Edmund Lien and William T. Laaser},
journal={Mathematical systems theory},
year={2005},
volume={10},
pages={1-17}
}
• Published 1 December 1976
• Computer Science
• Mathematical systems theory
It is shown that a variety of problems have computational complexity equivalent to that of finding a path through a directed graph. These results, which parallel those of Karp at a lower complexity level, concern satisfiability of propositional formulas with two literals per clause, generation of elements by an associative binary operation, solution of linear equations with two variables per equation, equivalence of generalized sequential machines with final states, and deciding theLL(k) andLR…
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## References

SHOWING 1-10 OF 13 REFERENCES
The complexity of theorem-proving procedures
• S. Cook
• Mathematics, Computer Science
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 a
On the complexity of LR(k) testing
• Computer Science
CACM
• 1975
It is shown that the problem of determining whether an arbitrary context-free grammar is a member of some easily parsed subclass of grammars such as the LR(k) Grammars is NP-complete when k is expressed in unary.
The unsolvability of the Equivalence Problem for Λ-Free nondeterministic generalized machines
It is shown that the equivalence problem for A-free nondeterministic generalized machines is unsolvable, and it is observed that this result implies the unsolvability of the equality problem for
Reducibility Among Combinatorial Problems
• R. Karp
• Computer Science
50 Years of Integer Programming
• 1972
Throughout the 1960s I worked on combinatorial optimization problems including logic circuit design with Paul Roth and assembly line balancing and the traveling salesman problem with Mike Held, which made me aware of the importance of distinction between polynomial-time and superpolynomial-time solvability.
Symbolic logic and mechanical theorem proving
• Mathematics
Computer science classics
• 1973
The Theory of Parsing, Translation, and Compiling
• Computer Science
• 1972
It is the hope that the algorithms and concepts presented in this book will survive the next generation of computers and programming languages, and that at least some of them will be applicable to fields other than compiler writing.
On the Structure of Feasible Computation
• Computer Science
GI Jahrestagung
• 1974
During the last four years research on the lower level computational complexity has yielded a rich set of interesting results which have revealed deep and unexpected connections between various
Space-Bounded Reducibility among Combinatorial Problems
• N. Jones
• Computer Science, Mathematics
J. Comput. Syst. Sci.
• 1975