# 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} }

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…

## 61 Citations

Gradually intractable problems and nondeterministic log-space lower bounds

- Computer ScienceMathematical systems theory
- 2005

The paper places five different problems (thek-pebble game problem, two problems aboutk finite automata, the reachability problem for Petri nets withk tokens, and the teachability problem for graphs…

Nodes Connected by Path Languages

- Mathematics, Computer ScienceDevelopments in Language Theory
- 2011

This work gives an appealing characterization of the computational complexity of the labeled graph reachability problem in terms of two-way nondeterministic storage automata with auxiliary worktape that is logarithmic-space bounded.

The complexity of intersecting finite automata having few final states

- Mathematics, Computer Sciencecomputational complexity
- 2014

This work raises the issue of limiting the number of final states in the automata intersection problem, and considers idempotent commutative automata and group automata with one, two, or three final states over a singleton or larger alphabet, elucidating the complexity of the intersection nonemptiness and related problems in each case.

1 Motivational Discussion and Quick Overview 1 . 1 Space Complexity of Parameterized 2 SAT

- Computer Science
- 2019

We aim at investigating the solvability/insolvability of nondeterministic logarithmicspace (NL) decision, search, and optimization problems parameterized by size parameters using simultaneously…

The 2CNF Boolean Formula Satisfiability Problem and the Linear Space Hypothesis

- Computer ScienceMFCS
- 2017

It turns out that, parameterized with the number of variables, $\overline{\mathrm{2SAT}_3}$ is complete for a syntactically restricted version of NL, called Syntactic NL$_{\omega}$, under such short reductions.

On the Space Complexity of Parameterized Problems

- MathematicsIPEC
- 2012

It is shown that the undirected and the directed feedback vertex set problems have different parameterized space complexities, unless L = NL; which explains why the two problem variants seem to necessitate different algorithmic approaches even though their parameterized time complexity is the same.

The Complexity of Finding Paths in Graphs with Bounded Independence Number

- MathematicsSIAM J. Comput.
- 2005

It is shown not only that the authors can construct paths in logarithmic space, but that there even exists a logspace approximation scheme for this problem and that even telling whether the shortest path has a certain length is NL-complete and thus is as difficult as for arbitrary directed graphs.

The Complexity of Problems on Implicitly Represented Inputs

- Mathematics, Computer ScienceSOFSEM
- 2006

It is shown that P-complete problems have no symbolic algorithms using a polylogarithmic number of functional operations, unless P=NC, and complement PSPACE-hardness results for problems on OBDD-represented inputs by fixed-parameter intractability results, where the OBDd width serves as the fixed parameter.

Computing rank of finite algebraic structures with limited nondeterminism

- Computer Science, Mathematics
- 2014

It is proved that the problem of deciding whether the rank of a finite quasigroup, given as a Cayley table, is smaller than a specified number is decidable by a circuit of depth augmented with nondeterministic bits.

## References

SHOWING 1-10 OF 13 REFERENCES

The complexity of theorem-proving procedures

- Mathematics, Computer ScienceSTOC
- 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…

Relationships Between Nondeterministic and Deterministic Tape Complexities

- Computer ScienceJ. Comput. Syst. Sci.
- 1970

On the complexity of LR(k) testing

- Computer ScienceCACM
- 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

- MathematicsJACM
- 1968

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

- Computer Science50 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.

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 ScienceGI 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

- Computer Science, MathematicsJ. Comput. Syst. Sci.
- 1975